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Overman, Tom, Garrett Blum, and Diego Klabjan. "A Primal-Dual Algorithm for Hybrid Federated Learning." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 13 (March 24, 2024): 14482–89. http://dx.doi.org/10.1609/aaai.v38i13.29363.
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Very few methods for hybrid federated learning, where clients only hold subsets of both features and samples, exist. Yet, this scenario is very important in practical settings. We provide a fast, robust algorithm for hybrid federated learning that hinges on Fenchel Duality. We prove the convergence of the algorithm to the same solution as if the model was trained centrally in a variety of practical regimes. Furthermore, we provide experimental results that demonstrate the performance improvements of the algorithm over a commonly used method in federated learning, FedAvg, and an existing hybrid FL algorithm, HyFEM. We also provide privacy considerations and necessary steps to protect client data.
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Yang, Peng, and Ping Li. "Distributed Primal-Dual Optimization for Online Multi-Task Learning." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 6631–38. http://dx.doi.org/10.1609/aaai.v34i04.6139.
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Conventional online multi-task learning algorithms suffer from two critical limitations: 1) Heavy communication caused by delivering high velocity of sequential data to a central machine; 2) Expensive runtime complexity for building task relatedness. To address these issues, in this paper we consider a setting where multiple tasks are geographically located in different places, where one task can synchronize data with others to leverage knowledge of related tasks. Specifically, we propose an adaptive primal-dual algorithm, which not only captures task-specific noise in adversarial learning but also carries out a projection-free update with runtime efficiency. Moreover, our model is well-suited to decentralized periodic-connected tasks as it allows the energy-starved or bandwidth-constraint tasks to postpone the update. Theoretical results demonstrate the convergence guarantee of our distributed algorithm with an optimal regret. Empirical results confirm that the proposed model is highly effective on various real-world datasets.
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Wang, Shuai, Yanqing Xu, Zhiguo Wang, Tsung-Hui Chang, Tony Q. S. Quek, and Defeng Sun. "Beyond ADMM: A Unified Client-Variance-Reduced Adaptive Federated Learning Framework." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 8 (June 26, 2023): 10175–83. http://dx.doi.org/10.1609/aaai.v37i8.26212.
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As a novel distributed learning paradigm, federated learning (FL) faces serious challenges in dealing with massive clients with heterogeneous data distribution and computation and communication resources. Various client-variance-reduction schemes and client sampling strategies have been respectively introduced to improve the robustness of FL. Among others, primal-dual algorithms such as the alternating direction of method multipliers (ADMM) have been found being resilient to data distribution and outperform most of the primal-only FL algorithms. However, the reason behind remains a mystery still. In this paper, we firstly reveal the fact that the federated ADMM is essentially a client-variance-reduced algorithm. While this explains the inherent robustness of federated ADMM, the vanilla version of it lacks the ability to be adaptive to the degree of client heterogeneity. Besides, the global model at the server under client sampling is biased which slows down the practical convergence. To go beyond ADMM, we propose a novel primal-dual FL algorithm, termed FedVRA, that allows one to adaptively control the variance-reduction level and biasness of the global model. In addition, FedVRA unifies several representative FL algorithms in the sense that they are either special instances of FedVRA or are close to it. Extensions of FedVRA to semi/un-supervised learning are also presented. Experiments based on (semi-)supervised image classification tasks demonstrate superiority of FedVRA over the existing schemes in learning scenarios with massive heterogeneous clients and client sampling.
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Lai, Hanjiang, Yan Pan, Cong Liu, Liang Lin, and Jie Wu. "Sparse Learning-to-Rank via an Efficient Primal-Dual Algorithm." IEEE Transactions on Computers 62, no. 6 (June 2013): 1221–33. http://dx.doi.org/10.1109/tc.2012.62.
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Tao, Wei, Wei Li, Zhisong Pan, and Qing Tao. "Gradient Descent Averaging and Primal-dual Averaging for Strongly Convex Optimization." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 11 (May 18, 2021): 9843–50. http://dx.doi.org/10.1609/aaai.v35i11.17183.
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Averaging scheme has attracted extensive attention in deep learning as well as traditional machine learning. It achieves theoretically optimal convergence and also improves the empirical model performance. However, there is still a lack of sufficient convergence analysis for strongly convex optimization. Typically, the convergence about the last iterate of gradient descent methods, which is referred to as individual convergence, fails to attain its optimality due to the existence of logarithmic factor. In order to remove this factor, we first develop gradient descent averaging (GDA), which is a general projection-based dual averaging algorithm in the strongly convex setting. We further present primal-dual averaging for strongly convex cases (SC-PDA), where primal and dual averaging schemes are simultaneously utilized. We prove that GDA yields the optimal convergence rate in terms of output averaging, while SC-PDA derives the optimal individual convergence. Several experiments on SVMs and deep learning models validate the correctness of theoretical analysis and effectiveness of algorithms.
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Ding, Yuhao, and Javad Lavaei. "Provably Efficient Primal-Dual Reinforcement Learning for CMDPs with Non-stationary Objectives and Constraints." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (June 26, 2023): 7396–404. http://dx.doi.org/10.1609/aaai.v37i6.25900.
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We consider primal-dual-based reinforcement learning (RL) in episodic constrained Markov decision processes (CMDPs) with non-stationary objectives and constraints, which plays a central role in ensuring the safety of RL in time-varying environments. In this problem, the reward/utility functions and the state transition functions are both allowed to vary arbitrarily over time as long as their cumulative variations do not exceed certain known variation budgets. Designing safe RL algorithms in time-varying environments is particularly challenging because of the need to integrate the constraint violation reduction, safe exploration, and adaptation to the non-stationarity. To this end, we identify two alternative conditions on the time-varying constraints under which we can guarantee the safety in the long run. We also propose the Periodically Restarted Optimistic Primal-Dual Proximal Policy Optimization (PROPD-PPO) algorithm that can coordinate with both two conditions. Furthermore, a dynamic regret bound and a constraint violation bound are established for the proposed algorithm in both the linear kernel CMDP function approximation setting and the tabular CMDP setting under two alternative conditions. This paper provides the first provably efficient algorithm for non-stationary CMDPs with safe exploration.
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Bai, Qinbo, Amrit Singh Bedi, Mridul Agarwal, Alec Koppel, and Vaneet Aggarwal. "Achieving Zero Constraint Violation for Constrained Reinforcement Learning via Primal-Dual Approach." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 4 (June 28, 2022): 3682–89. http://dx.doi.org/10.1609/aaai.v36i4.20281.
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Reinforcement learning is widely used in applications where one needs to perform sequential decisions while interacting with the environment. The problem becomes more challenging when the decision requirement includes satisfying some safety constraints. The problem is mathematically formulated as constrained Markov decision process (CMDP). In the literature, various algorithms are available to solve CMDP problems in a model-free manner to achieve epsilon-optimal cumulative reward with epsilon feasible policies. An epsilon-feasible policy implies that it suffers from constraint violation. An important question here is whether we can achieve epsilon-optimal cumulative reward with zero constraint violations or not. To achieve that, we advocate the use of a randomized primal-dual approach to solve the CMDP problems and propose a conservative stochastic primal-dual algorithm (CSPDA) which is shown to exhibit O(1/epsilon^2) sample complexity to achieve epsilon-optimal cumulative reward with zero constraint violations. In the prior works, the best available sample complexity for the epsilon-optimal policy with zero constraint violation is O(1/epsilon^5). Hence, the proposed algorithm provides a significant improvement compared to the state of the art.
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Bai, Qinbo, Amrit Singh Bedi, and Vaneet Aggarwal. "Achieving Zero Constraint Violation for Constrained Reinforcement Learning via Conservative Natural Policy Gradient Primal-Dual Algorithm." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (June 26, 2023): 6737–44. http://dx.doi.org/10.1609/aaai.v37i6.25826.
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We consider the problem of constrained Markov decision process (CMDP) in continuous state actions spaces where the goal is to maximize the expected cumulative reward subject to some constraints. We propose a novel Conservative Natural Policy Gradient Primal Dual Algorithm (CNPGPD) to achieve zero constraint violation while achieving state of the art convergence results for the objective value function. For general policy parametrization, we prove convergence of value function to global optimal upto an approximation error due to restricted policy class. We improve the sample complexity of existing constrained NPGPD algorithm. To the best of our knowledge, this is the first work to establish zero constraint violation with Natural policy gradient style algorithms for infinite horizon discounted CMDPs. We demonstrate the merits of proposed algorithm via experimental evaluations.
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Gupta, Ankita, Lakhwinder Kaur, and Gurmeet Kaur. "Drought stress detection technique for wheat crop using machine learning." PeerJ Computer Science 9 (May 19, 2023): e1268. http://dx.doi.org/10.7717/peerj-cs.1268.
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The workflow of this research is based on numerous hypotheses involving the usage of pre-processing methods, wheat canopy segmentation methods, and whether the existing models from the past research can be adapted to classify wheat crop water stress. Hence, to construct an automation model for water stress detection, it was found that pre-processing operations known as total variation with L1 data fidelity term (TV-L1) denoising with a Primal-Dual algorithm and min-max contrast stretching are most useful. For wheat canopy segmentation curve fit based K-means algorithm (Cfit-kmeans) was also validated for the most accurate segmentation using intersection over union metric. For automated water stress detection, rapid prototyping of machine learning models revealed that there is a need only to explore nine models. After extensive grid search-based hyper-parameter tuning of machine learning algorithms and 10 K fold cross validation it was found that out of nine different machine algorithms tested, the random forest algorithm has the highest global diagnostic accuracy of 91.164% and is the most suitable for constructing water stress detection models.
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Liu, Bo, Ian Gemp, Mohammad Ghavamzadeh, Ji Liu, Sridhar Mahadevan, and Marek Petrik. "Proximal Gradient Temporal Difference Learning: Stable Reinforcement Learning with Polynomial Sample Complexity." Journal of Artificial Intelligence Research 63 (November 15, 2018): 461–94. http://dx.doi.org/10.1613/jair.1.11251.
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In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD) reinforcement learning methods can be formally derived, not by starting from their original objective functions, as previously attempted, but rather from a primal-dual saddle-point objective function. We also conduct a saddle-point error analysis to obtain finite-sample bounds on their performance. Previous analyses of this class of algorithms use stochastic approximation techniques to prove asymptotic convergence, and do not provide any finite-sample analysis. We also propose an accelerated algorithm, called GTD2-MP, that uses proximal "mirror maps" to yield an improved convergence rate. The results of our theoretical analysis imply that the GTD family of algorithms are comparable and may indeed be preferred over existing least squares TD methods for off-policy learning, due to their linear complexity. We provide experimental results showing the improved performance of our accelerated gradient TD methods.
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Herguedas-Alonso, A. Estela, Víctor M. García-Suárez, and Juan L. Fernández-Martínez. "Compressed Sensing Techniques Applied to Medical Images Obtained with Magnetic Resonance." Mathematics 11, no. 16 (August 18, 2023): 3573. http://dx.doi.org/10.3390/math11163573.
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The fast and reliable processing of medical images is of paramount importance to adequately generate data to feed machine learning algorithms that can prevent and diagnose health issues. Here, different compressed sensing techniques applied to magnetic resonance imaging are benchmarked as a means to reduce the acquisition time spent in the collection of data and signals that form the image. It is shown that by using these techniques, it is possible to reduce the number of signals needed and, therefore, substantially decrease the time to acquire the measurements. To this end, different algorithms are considered and compared: the iterative re-weighted least squares, the iterative soft thresholding algorithm, the iterative hard thresholding algorithm, the primal dual algorithm and the log barrier algorithm. Such algorithms have been implemented in different analysis programs that have been used to perform the reconstruction of the images, and it was found that the iterative soft thresholding algorithm gives the optimal results. It is found that the images obtained with this algorithm have lower quality than the original ones, but in any case, the quality should be good enough to distinguish each body structure and detect any health problems under an expert evaluation and/or statistical analysis.
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Zhao, Xiao, Xuhui Xia, and Guodong Yu. "Primal-Dual Learning Based Risk-Averse Optimal Integrated Allocation of Hybrid Energy Generation Plants under Uncertainty." Energies 12, no. 12 (June 13, 2019): 2275. http://dx.doi.org/10.3390/en12122275.
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A groundswell of opinion in utilizing environmentally friendly energy technologies has been put forth worldwide. In this paper, we consider an energy generation plant distribution and allocation problem under uncertainty to get the utmost out of available developments, as well as to control costs and greenhouse emissions. Different clean and traditional energy technologies are considered in this paper. In particular, we present a risk-averse stochastic mixed-integer linear programming (MILP) model to minimize the total expected costs and control the risk of CO2 emissions exceeding a certain budget. We employ the conditional value-at-risk (CVaR) model to represent risk preference and risk constraint of emissions. We prove that our risk-averse model can be equivalent to the traditional risk-neutral model under certain conditions. Moreover, we suggest that the risk-averse model can provide solutions generating less CO2 than traditional models. To handle the computational difficulty in uncertain scenarios, we propose a Lagrange primal-dual learning algorithm to solve the model. We show that the algorithm allows the probability distribution of uncertainty to be unknown, and that desirable approximation can be achieved by utilizing historical data. Finally, an experiment is presented to demonstrate the performance of our method. The risk-averse model encourages the expansion of clean energy plants over traditional models for the reduction CO2 emissions.
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Ye, Yao, and Heng-you Lan. "Novel Accelerated Cyclic Iterative Approximation for Hierarchical Variational Inequalities Constrained by Multiple-Set Split Common Fixed-Point Problems." Mathematics 12, no. 18 (September 21, 2024): 2935. http://dx.doi.org/10.3390/math12182935.
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In this paper, we investigate a class of hierarchical variational inequalities (HVIPs, i.e., strongly monotone variational inequality problems defined on the solution set of multiple-set split common fixed-point problems) with quasi-pseudocontractive mappings in real Hilbert spaces, with special cases being able to be found in many important engineering practical applications, such as image recognizing, signal processing, and machine learning. In order to solve HVIPs of potential application value, inspired by the primal-dual algorithm, we propose a novel accelerated cyclic iterative algorithm that combines the inertial method with a correction term and a self-adaptive step-size technique. Our approach eliminates the need for prior knowledge of the bounded linear operator norm. Under appropriate assumptions, we establish strong convergence of the algorithm. Finally, we apply our novel iterative approximation to solve multiple-set split feasibility problems and verify the effectiveness of the proposed iterative algorithm through numerical results.
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Mahadevan, Sridhar, Stephen Giguere, and Nicholas Jacek. "Basis Adaptation for Sparse Nonlinear Reinforcement Learning." Proceedings of the AAAI Conference on Artificial Intelligence 27, no. 1 (June 30, 2013): 654–60. http://dx.doi.org/10.1609/aaai.v27i1.8665.
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This paper presents a new approach to representation discovery in reinforcement learning (RL) using basis adaptation. We introduce a general framework for basis adaptation as {\em nonlinear separable least-squares value function approximation} based on finding Frechet gradients of an error function using variable projection functionals. We then present a scalable proximal gradient-based approach for basis adaptation using the recently proposed mirror-descent framework for RL. Unlike traditional temporal-difference (TD) methods for RL, mirror descent based RL methods undertake proximal gradient updates of weights in a dual space, which is linked together with the primal space using a Legendre transform involving the gradient of a strongly convex function. Mirror descent RL can be viewed as a proximal TD algorithm using Bregman divergence as the distance generating function. We present a new class of regularized proximal-gradient based TD methods, which combine feature selection through sparse L1 regularization and basis adaptation. Experimental results are provided to illustrate and validate the approach.
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Huang, Shuangping, Lianwen Jin, and Yunyu Li. "Online Multikernel Learning Based on a Triple-Norm Regularizer for Semantic Image Classification." Mathematical Problems in Engineering 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/346496.
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Currently image classifiers based on multikernel learning (MKL) mostly use batch approach, which is slow and difficult to scale up for large datasets. In the meantime, standard MKL model neglects the correlations among examples associated with a specific kernel, which makes it infeasible to adjust the kernel combination coefficients. To address these issues, a new and efficient multikernel multiclass algorithm called TripleReg-MKL is proposed in this work. Taking the principle of strong convex optimization into consideration, we propose a new triple-norm regularizer (TripleReg) to constrain the empirical loss objective function, which exploits the correlations among examples to tune the kernel weights. It highlights the application of multivariate hinge loss and a conservative updating strategy to filter noisy samples, thereby reducing the model complexity. This novel MKL formulation is then solved in an online mode using a primal-dual framework. A theoretical analysis of the complexity and convergence of TripleReg-MKL is presented. It shows that the new algorithm has a complexity ofOCMTand achieves a fast convergence rate ofOlogT/T. Extensive experiments on four benchmark datasets demonstrate the effectiveness and robustness of this new approach.
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Chu, Dejun, Changshui Zhang, Shiliang Sun, and Qing Tao. "Structured BFGS Method for Optimal Doubly Stochastic Matrix Approximation." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (June 26, 2023): 7193–201. http://dx.doi.org/10.1609/aaai.v37i6.25877.
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Doubly stochastic matrix plays an essential role in several areas such as statistics and machine learning. In this paper we consider the optimal approximation of a square matrix in the set of doubly stochastic matrices. A structured BFGS method is proposed to solve the dual of the primal problem. The resulting algorithm builds curvature information into the diagonal components of the true Hessian, so that it takes only additional linear cost to obtain the descent direction based on the gradient information without having to explicitly store the inverse Hessian approximation. The cost is substantially fewer than quadratic complexity of the classical BFGS algorithm. Meanwhile, a Newton-based line search method is presented for finding a suitable step size, which in practice uses the existing knowledge and takes only one iteration. The global convergence of our algorithm is established. We verify the advantages of our approach on both synthetic data and real data sets. The experimental results demonstrate that our algorithm outperforms the state-of-the-art solvers and enjoys outstanding scalability.
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Navarro, Jorge, Eduardo Fernández, Efrain Solares, Abril Flores, and Raymundo Díaz. "Learning the Parameters of ELECTRE-Based Primal-Dual Sorting Methods that Use Either Characteristic or Limiting Profiles." Axioms 12, no. 3 (March 11, 2023): 294. http://dx.doi.org/10.3390/axioms12030294.
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Two multicriteria-sorting methods that generalize the relational paradigm have been recently presented in the literature. One uses objects representative of classes, the other uses objects in the limiting boundaries of classes; both can use either a reflexive or an asymmetric preference relation. However, defining the parameters of relation-based methods is not straightforward. The present work operationalizes those methods with a methodology that takes examples provided by the decision-maker and, using an accuracy measure that specifically fits the characteristics of the methods, exploits an evolutionary algorithm to determine the parameters that best reproduce such examples. The assessment of the proposal showed that (i) it can achieve considerably high levels of out-of-sample effectiveness with only a few decision examples; (ii) the inference process is more effective learning the parameters of the method based on representative objects; (iii) it tends to be more effective with a reflexive relation; (iv) the effectiveness decreases while increasing the number of classes, which is not always the case when increasing the number of criteria. Theoretical properties of the proposed methodology will be investigated in future works.
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Dey, Sumanta, Pallab Dasgupta, and Soumyajit Dey. "P2BPO: Permeable Penalty Barrier-Based Policy Optimization for Safe RL." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 19 (March 24, 2024): 21029–36. http://dx.doi.org/10.1609/aaai.v38i19.30094.
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Safe Reinforcement Learning (SRL) algorithms aim to learn a policy that maximizes the reward while satisfying the safety constraints. One of the challenges in SRL is that it is often difficult to balance the two objectives of reward maximization and safety constraint satisfaction. Existing algorithms utilize constraint optimization techniques like penalty-based, barrier penalty-based, and Lagrangian-based dual or primal policy optimizations methods. However, they suffer from training oscillations and approximation errors, which impact the overall learning objectives. This paper proposes the Permeable Penalty Barrier-based Policy Optimization (P2BPO) algorithm that addresses this issue by allowing a small fraction of penalty beyond the penalty barrier, and a parameter is used to control this permeability. In addition, an adaptive penalty parameter is used instead of a constant one, which is initialized with a low value and increased gradually as the agent violates the safety constraints. We have also provided a theoretical proof of the proposed method's performance guarantee bound, which ensures that P2BPO can learn a policy satisfying the safety constraints with high probability while achieving a higher expected reward. Furthermore, we compare P2BPO with other SRL algorithms on various SRL tasks and demonstrate that it achieves better rewards while adhering to the constraints.
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Guo, Hengquan, Hongchen Cao, Jingzhu He, Xin Liu, and Yuanming Shi. "POBO: Safe and Optimal Resource Management for Cloud Microservices." ACM SIGMETRICS Performance Evaluation Review 51, no. 4 (February 22, 2024): 20–21. http://dx.doi.org/10.1145/3649477.3649489.
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Resource management in microservices is challenging due to the uncertain latency-resource relationship, dynamic environment, and strict Service-Level Agreement (SLA) guarantees. This paper presents a Pessimistic and Optimistic Bayesian Optimization framework, named POBO, for safe and optimal resource configuration for microservice applications. POBO leverages Bayesian learning to estimate the uncertain latency-resource functions and combines primal-dual and penalty-based optimization to maximize resource efficiency while guaranteeing strict SLAs. We prove that POBO can achieve sublinear regret and SLA violation compared with the optimal resource configuration in hindsight. We have implemented a prototype of POBO and conducted extensive experiments on a real-world microservice application. Our results show that POBO can find the safe and optimal configuration efficiently, outperforming Kubernetes' built-in auto-scaling module and the state-of-the-art algorithm.
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Liao, Dongping, Xitong Gao, and Chengzhong Xu. "Impartial Adversarial Distillation: Addressing Biased Data-Free Knowledge Distillation via Adaptive Constrained Optimization." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 4 (March 24, 2024): 3342–50. http://dx.doi.org/10.1609/aaai.v38i4.28120.
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Data-Free Knowledge Distillation (DFKD) enables knowledge transfer from a pretrained teacher to a light-weighted student without original training data. Existing works are limited by a strong assumption that samples used to pretrain the teacher model are balanced, which is, however, unrealistic for many real-world tasks. In this work, we investigated a pragmatic yet under-explored problem: how to perform DFKD from a teacher model pretrained from imbalanced data. We observe a seemingly counter-intuitive phenomenon, i.e., adversarial DFKD algorithms favour minority classes, while causing a disastrous impact on majority classes. We theoretically prove that a biased teacher could cause severe disparity on different groups of synthetic data in adversarial distillation, which further exacerbates the mode collapse of a generator and consequently degenerates the overall accuracy of a distilled student model. To tackle this problem, we propose a class-adaptive regularization method, aiming to encourage impartial representation learning of a generator among different classes under a constrained learning formulation. We devise a primal-dual algorithm to solve the target optimization problem. Through extensive experiments, we show that our method mitigates the biased learning of majority classes in DFKD and improves the overall performance compared with baselines. Code will be available at https://github.com/ldpbuaa/ipad.
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Zhang, Dewei, Yin Liu, and Sam Davanloo Tajbakhsh. "A First-Order Optimization Algorithm for Statistical Learning with Hierarchical Sparsity Structure." INFORMS Journal on Computing 34, no. 2 (March 2022): 1126–40. http://dx.doi.org/10.1287/ijoc.2021.1069.
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In many statistical learning problems, it is desired that the optimal solution conform to an a priori known sparsity structure represented by a directed acyclic graph. Inducing such structures by means of convex regularizers requires nonsmooth penalty functions that exploit group overlapping. Our study focuses on evaluating the proximal operator of the latent overlapping group lasso developed by Jacob et al. in 2009 . We implemented an alternating direction method of multiplier with a sharing scheme to solve large-scale instances of the underlying optimization problem efficiently. In the absence of strong convexity, global linear convergence of the algorithm is established using the error bound theory. More specifically, the paper contributes to establishing primal and dual error bounds when the nonsmooth component in the objective function does not have a polyhedral epigraph. We also investigate the effect of the graph structure on the speed of convergence of the algorithm. Detailed numerical simulation studies over different graph structures supporting the proposed algorithm and two applications in learning are provided. Summary of Contribution: The paper proposes a computationally efficient optimization algorithm to evaluate the proximal operator of a nonsmooth hierarchical sparsity-inducing regularizer and establishes its convergence properties. The computationally intensive subproblem of the proposed algorithm can be fully parallelized, which allows solving large-scale instances of the underlying problem. Comprehensive numerical simulation studies benchmarking the proposed algorithm against five other methods on the speed of convergence to optimality are provided. Furthermore, performance of the algorithm is demonstrated on two statistical learning applications related to topic modeling and breast cancer classification. The code along with the simulation studies and benchmarks are available on the corresponding author’s GitHub website for evaluation and future use.
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Bebortta, Sujit, Subhranshu Sekhar Tripathy, Shakila Basheer, and Chiranji Lal Chowdhary. "FedEHR: A Federated Learning Approach towards the Prediction of Heart Diseases in IoT-Based Electronic Health Records." Diagnostics 13, no. 20 (October 10, 2023): 3166. http://dx.doi.org/10.3390/diagnostics13203166.
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In contemporary healthcare, the prediction and identification of cardiac diseases is crucial. By leveraging the capabilities of Internet of Things (IoT)-enabled devices and Electronic Health Records (EHRs), the healthcare sector can largely benefit to improve patient outcomes by increasing the accuracy of disease prediction. However, protecting data privacy is essential to promote participation and adhere to rules. The suggested methodology combines EHRs with IoT-generated health data to predict heart disease. For its capacity to manage high-dimensional data and choose pertinent features, a soft-margin L1-regularised Support Vector Machine (sSVM) classifier is used. The large-scale sSVM problem is successfully solved using the cluster primal–dual splitting algorithm, which improves computational complexity and scalability. The integration of federated learning provides a cooperative predictive analytics methodology that upholds data privacy. The use of a federated learning framework in this study, with a focus on peer-to-peer applications, is crucial for enabling collaborative predictive modeling while protecting the confidentiality of each participant’s private medical information.
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Ogumeyo, S. A., and E. A. Okogun. "Determination of periodic optimal recruitment and wastage schedule using dynamic programming approach." Dutse Journal of Pure and Applied Sciences 9, no. 2a (July 14, 2023): 14–23. http://dx.doi.org/10.4314/dujopas.v9i2a.2.
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In this paper we propose a dynamic programming (DP) model that can assist organizations in determining future manpower requirement in terms of number, level of skills, and competence as well as formulating plans to meet those requirements. The model which incorporates both wastage and recruitment costs in its formulation is derived with an algorithm for obtaining planned periodic wastages and recruitments which can result in maximum net accruable revenue. We applied data obtained from an institution of higher learning to illustrate our proposed DP model based on wastage and recruitment costs and the results reveals that there should be no staff wastage in periods 2, 5, 9 and 10, and no recruitment should take in periods 2, 5, 8, 9 and 12 if the total accruable revenue from human resources to the organization is to be maximized. We also observed that the dual objective function value and that of the primal are equal which is in agreement with the duality theorem for symmetric duals.
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Ma, Xin, Yubin Cai, Hong Yuan, and Yanqiao Deng. "Partially Linear Component Support Vector Machine for Primary Energy Consumption Forecasting of the Electric Power Sector in the United States." Sustainability 15, no. 9 (April 23, 2023): 7086. http://dx.doi.org/10.3390/su15097086.
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Energy forecasting based on univariate time series has long been a challenge in energy engineering and has become one of the most popular tasks in data analytics. In order to take advantage of the characteristics of observed data, a partially linear model is proposed based on principal component analysis and support vector machine methods. The principal linear components of the input with lower dimensions are used as the linear part, while the nonlinear part is expressed by the kernel function. The primal-dual method is used to construct the convex optimization problem for the proposed model, and the sequential minimization optimization algorithm is used to train the model with global convergence. The univariate forecasting scheme is designed to forecast the primary energy consumption of the electric power sector of the United States using real-world data sets ranging from January 1973 to January 2020, and the model is compared with eight commonly used machine learning models as well as the linear auto-regressive model. Comprehensive comparisons with multiple evaluation criteria (including 19 metrics) show that the proposed model outperforms all other models in all scenarios of mid-/long-term forecasting, indicating its high potential in primary energy consumption forecasting.
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Shalev-Shwartz, Shai, and Yoram Singer. "A primal-dual perspective of online learning algorithms." Machine Learning 69, no. 2-3 (July 11, 2007): 115–42. http://dx.doi.org/10.1007/s10994-007-5014-x.
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NIELSEN, FRANK, and RICHARD NOCK. "APPROXIMATING SMALLEST ENCLOSING BALLS WITH APPLICATIONS TO MACHINE LEARNING." International Journal of Computational Geometry & Applications 19, no. 05 (October 2009): 389–414. http://dx.doi.org/10.1142/s0218195909003039.
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In this paper, we first survey prior work for computing exactly or approximately the smallest enclosing balls of point or ball sets in Euclidean spaces. We classify previous work into three categories: (1) purely combinatorial, (2) purely numerical, and (3) recent mixed hybrid algorithms based on coresets. We then describe two novel tailored algorithms for computing arbitrary close approximations of the smallest enclosing Euclidean ball. These deterministic heuristics are based on solving relaxed decision problems using a primal-dual method. The primal-dual method is interpreted geometrically as solving for a minimum covering set, or dually as seeking for a minimum piercing set. Finally, we present some applications in machine learning of the exact and approximate smallest enclosing ball procedure, and discuss about its extension to non-Euclidean information-theoretic spaces.
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Dai, Juntao, Jiaming Ji, Long Yang, Qian Zheng, and Gang Pan. "Augmented Proximal Policy Optimization for Safe Reinforcement Learning." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (June 26, 2023): 7288–95. http://dx.doi.org/10.1609/aaai.v37i6.25888.
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Safe reinforcement learning considers practical scenarios that maximize the return while satisfying safety constraints. Current algorithms, which suffer from training oscillations or approximation errors, still struggle to update the policy efficiently with precise constraint satisfaction. In this article, we propose Augmented Proximal Policy Optimization (APPO), which augments the Lagrangian function of the primal constrained problem via attaching a quadratic deviation term. The constructed multiplier-penalty function dampens cost oscillation for stable convergence while being equivalent to the primal constrained problem to precisely control safety costs. APPO alternately updates the policy and the Lagrangian multiplier via solving the constructed augmented primal-dual problem, which can be easily implemented by any first-order optimizer. We apply our APPO methods in diverse safety-constrained tasks, setting a new state of the art compared with a comprehensive list of safe RL baselines. Extensive experiments verify the merits of our method in easy implementation, stable convergence, and precise cost control.
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Xiao, Ming, and Mikael Skoglund. "Coding for Large-Scale Distributed Machine Learning." Entropy 24, no. 9 (September 12, 2022): 1284. http://dx.doi.org/10.3390/e24091284.
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This article aims to give a comprehensive and rigorous review of the principles and recent development of coding for large-scale distributed machine learning (DML). With increasing data volumes and the pervasive deployment of sensors and computing machines, machine learning has become more distributed. Moreover, the involved computing nodes and data volumes for learning tasks have also increased significantly. For large-scale distributed learning systems, significant challenges have appeared in terms of delay, errors, efficiency, etc. To address the problems, various error-control or performance-boosting schemes have been proposed recently for different aspects, such as the duplication of computing nodes. More recently, error-control coding has been investigated for DML to improve reliability and efficiency. The benefits of coding for DML include high-efficiency, low complexity, etc. Despite the benefits and recent progress, however, there is still a lack of comprehensive survey on this topic, especially for large-scale learning. This paper seeks to introduce the theories and algorithms of coding for DML. For primal-based DML schemes, we first discuss the gradient coding with the optimal code distance. Then, we introduce random coding for gradient-based DML. For primal–dual-based DML, i.e., ADMM (alternating direction method of multipliers), we propose a separate coding method for two steps of distributed optimization. Then coding schemes for different steps are discussed. Finally, a few potential directions for future works are also given.
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Ding, Weiwei, Youlin Shang, Zhengfen Jin, and Yibao Fan. "Semi-Proximal ADMM for Primal and Dual Robust Low-Rank Matrix Restoration from Corrupted Observations." Symmetry 16, no. 3 (March 5, 2024): 303. http://dx.doi.org/10.3390/sym16030303.
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The matrix nuclear norm minimization problem has been extensively researched in recent years due to its widespread applications in control design, signal and image restoration, machine learning, big data problems, and more. One popular model is nuclear norm minimization with the l2-norm fidelity term, but it is only effective for those problems with Gaussian noise. A nuclear norm minimization problem with the l1-norm fidelity term has been studied in this paper, which can deal with the problems with not only non-Gaussian noise but also Gaussian noise or their mixture. Moreover, it also keeps the efficiency for the noiseless case. Given the nonsmooth proposed model, we transform it into a separated form by introducing an auxiliary variable and solve it by the semi-proximal alternating direction method of multipliers (sPADMM). Furthermore, we first attempt to solve its dual problem by sPADMM. Then, the convergence guarantees for the aforementioned algorithms are given. Finally, some numerical studies are dedicated to show the robustness of the proposed model and the effectiveness of the presented algorithms.
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Fernández-Fuentes, Xosé, David Mera, Andrés Gómez, and Ignacio Vidal-Franco. "Towards a Fast and Accurate EIT Inverse Problem Solver: A Machine Learning Approach." Electronics 7, no. 12 (December 11, 2018): 422. http://dx.doi.org/10.3390/electronics7120422.
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Different industrial and medical situations require the non-invasive extraction of information from the inside of bodies. This is usually done through tomographic methods that generate images based on internal body properties. However, the image reconstruction involves a mathematical inverse problem, for which accurate resolution demands large computation time and capacity. In this paper we explore the use of Machine Learning to develop an accurate solver for reconstructing Electrical Impedance Tomography images in real-time. We compare the results with the Iterative Gauss-Newton and the Primal Dual Interior Point Method, which are both largely used and well-validated solvers. The approaches were compared from the qualitative as well as the quantitative viewpoints. The former was focused on correctly detecting the internal body features. The latter was based on accurately predicting internal property distributions. Experiments revealed that our approach achieved better accuracy and Cohen’s kappa coefficient (97.57% and 94.60% respectively) from the qualitative viewpoint. Moreover, it also obtained better quantitative metrics with a Mean Absolute Percentage Error of 18.28%. Experiments confirmed that Neural Networks algorithms can reconstruct internal body properties with high accuracy, so they would be able to replace more complex and slower alternatives.
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Chege, Simon. "Deep Learning Aided Resource Allocation in Hybrid NOMA-Enabled Overloaded Systems." International Journal of Electrical and Electronic Engineering & Telecommunications 14, no. 1 (2025): 1–12. https://doi.org/10.18178/ijeetc.14.1.1-12.
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Beyond 5G (B5G) networks will deploy hybrid multi-radio access technologies for improved Spectrum Efficiency (SE) and Energy Efficiency (EE). For further capacity enhancement, code and power domain multiplexing are applied on hybrid Power Domain Sparse Code Nonorthogonal Multiple Access (PD-SCMA) schemes. In order to realize optimal performance, robust Resource Allocation (RA) policies are required with the best candidate for the complex overloaded B5G systems based on Artificial Intelligence (AI) techniques. This work develops a deep neural network (DNN) aided resource allocation scheme for an uplink PD-SCMA network with Near-User (NU) and Far- User (FU) groups, multiplexed in the power and code domain. The RA problem is formulated as a non-convex joint optimization problem then decomposed into three subproblems namely Codebook Assignment (CA), User Clustering (UC) and power allocation (PA). For the three sub-problems, a three-stage generic fully connected DNN is trained to approximate the PA, CA and UC resource allocation solution by the proposed modified Primal-Dual Interior Point Method (mPD-IPM). The proposed mPD-IPM generates the near-optimal RA solutions that form the DNN input labels. The DNN-mPD-IPM not only greatly enhances the computational efficiency but also achieves improved convergence rates and guarantees both the ergodic and nonergodic sum rates of the system compared to generic algorithms. Simulation results show that the DNN aided resource allocation closely learns the system capacity and computational performance of the proposed mPD-IPM and further outperforms generic RA algorithms. Compared to cross-layer codebooks, mPD-IPM and DNN-mPD-IPM achieves approximately 19% higher capacity. The proposed DNN-mPD-IPM that learns to approximate the proposed mPD-IPM has an execution time that is approximately 70% lower than mPD-IPM.
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Davey, Ashley, and Harry Zheng. "Deep Learning for Constrained Utility Maximisation." Methodology and Computing in Applied Probability, November 26, 2021. http://dx.doi.org/10.1007/s11009-021-09912-3.
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AbstractThis paper proposes two algorithms for solving stochastic control problems with deep learning, with a focus on the utility maximisation problem. The first algorithm solves Markovian problems via the Hamilton Jacobi Bellman (HJB) equation. We solve this highly nonlinear partial differential equation (PDE) with a second order backward stochastic differential equation (2BSDE) formulation. The convex structure of the problem allows us to describe a dual problem that can either verify the original primal approach or bypass some of the complexity. The second algorithm utilises the full power of the duality method to solve non-Markovian problems, which are often beyond the scope of stochastic control solvers in the existing literature. We solve an adjoint BSDE that satisfies the dual optimality conditions. We apply these algorithms to problems with power, log and non-HARA utilities in the Black-Scholes, the Heston stochastic volatility, and path dependent volatility models. Numerical experiments show highly accurate results with low computational cost, supporting our proposed algorithms.
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Xu, Hai-Ming, Hui Xue, Xiao-Hong Chen, and Yun-Yun Wang. "Solving Indefinite Kernel Support Vector Machine with Difference of Convex Functions Programming." Proceedings of the AAAI Conference on Artificial Intelligence 31, no. 1 (February 13, 2017). http://dx.doi.org/10.1609/aaai.v31i1.10889.
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Indefinite kernel support vector machine (IKSVM) has recently attracted increasing attentions in machine learning. Different from traditional SVMs, IKSVM essentially is a non-convex optimization problem. Some algorithms directly change the spectrum of the indefinite kernel matrix at the cost of losing some valuable information involved in the kernels so as to transform the non-convex problem into a convex one. Other algorithms aim to solve the dual form of IKSVM, but suffer from the dual gap between the primal and dual problems in the case of indefinite kernels. In this paper, we directly focus on the non-convex primal form of IKSVM and propose a novel algorithm termed as IKSVM-DC. According to the characteristics of the spectrum for the indefinite kernel matrix, IKSVM-DC decomposes the objective function into the subtraction of two convex functions and thus reformulates the primal problem as a difference of convex functions (DC) programming which can be optimized by the DC algorithm (DCA). In order to accelerate convergence rate, IKSVM-DC further combines the classical DCA with a line search step along the descent direction at each iteration. A theoretical analysis is then presented to validate that IKSVM-DC can converge to a local minimum. Systematical experiments on real-world datasets demonstrate the superiority of IKSVM-DC compared to state-of-the-art IKSVM related algorithms.
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Tang, Kejie, Weidong Liu, and Xiaojun Mao. "Multi-consensus decentralized primal-dual fixed point algorithm for distributed learning." Machine Learning, April 8, 2024. http://dx.doi.org/10.1007/s10994-024-06537-8.
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Fukami, Takumi, Tomoya Murata, Kenta Niwa, and Iifan Tyou. "DP-Norm: Differential Privacy Primal-Dual Algorithm for Decentralized Federated Learning." IEEE Transactions on Information Forensics and Security, 2024, 1. http://dx.doi.org/10.1109/tifs.2024.3390993.
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Chen, Ningyuan, and Guillermo Gallego. "A Primal–Dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint." Mathematics of Operations Research, February 10, 2022. http://dx.doi.org/10.1287/moor.2021.1220.
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We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving consumer can be observed, but the demand function associated with each type is initially unknown. The firm sets personalized prices dynamically for each type and attempts to maximize the revenue over the season. We provide a learning algorithm that is near optimal when the demand and capacity scale in proportion. The algorithm utilizes the primal–dual formulation of the problem and learns the dual optimal solution explicitly. It allows the algorithm to overcome the curse of dimensionality (the rate of regret is independent of the number of types) and sheds light on novel algorithmic designs for learning problems with resource constraints.
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Yang, Yichen, and Zhaohui Liu. "Heuristics for Finding Sparse Solutions of Linear Inequalities." Asia-Pacific Journal of Operational Research, December 15, 2021. http://dx.doi.org/10.1142/s021759592240005x.
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In this paper, we consider the problem of finding a sparse solution, with a minimal number of nonzero components, for a set of linear inequalities. This optimization problem is combinatorial and arises in various fields such as machine learning and compressed sensing. We present three new heuristics for the problem. The first two are greedy algorithms minimizing the sum of infeasibilities in the primal and dual spaces with different selection rules. The third heuristic is a combination of the greedy heuristic in the dual space and a local search algorithm. In numerical experiments, our proposed heuristics are compared with the weighted-[Formula: see text] algorithm and DCA programming with three different non-convex approximations of the zero norm. The computational results demonstrate the efficiency of our methods.
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Huang, Jinshu, Yiming Gao, and Chunlin Wu. "On dynamical system modeling of Learned Primal-Dual with a linear operator $\mathcal{K}$: Stability and convergence properties." Inverse Problems, May 10, 2024. http://dx.doi.org/10.1088/1361-6420/ad49ca.
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Abstract Learned Primal-Dual (LPD) is a deep learning based method for composite optimization problems that is based on unrolling/unfolding the primal-dual hybrid gradient algorithm. While achieving great successes in applications, the mathematical interpretation of LPD as a truncated iterative scheme is not necessarily sufficient to fully understand its properties. In this paper, we study the LPD with a general linear operator. We model the forward propagation of LPD as a system of difference equations and a system of differential equations in discrete- and continuous-time settings (for primal and dual variables/trajectories), which are named discrete-time LPD and continuous-time LPD, respectively. Forward analyses such as stabilities and the convergence of the state variables of the discrete-time LPD to the solution of continuous-time LPD are given. Moreover, we analyze the learning problems with/without regularization terms of both discrete-time and continuous-time LPD from the optimal control viewpoint. We prove convergence results of their optimal solutions with respect to the network state initialization and training data, showing in some sense the topological stability of the learning problems. We also establish convergence from the solution of the discrete-time LPD learning problem to that of the continuous-time LPD learning problem through a piecewise linear extension, under some appropriate assumptions on the space of learnable parameters. This study demonstrates theoretically the robustness of the LPD structure and the associated training process, and can induce some future research and applications.
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Santos Garcia, Carlos, Mathilde Larchevêque, Solal O'Sullivan, Martin Van Waerebeke, Robert R. Thomson, Audrey Repetti, and Jean-Christophe Pesquet. "A primal-dual data-driven method for computational optical imaging with a photonic lantern." PNAS Nexus, April 16, 2024. http://dx.doi.org/10.1093/pnasnexus/pgae164.
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Abstract Optical fibres aim to image in-vivo biological processes. In this context, high spatial resolution and stability to fibre movements are key to enable decision-making processes (e.g., for microendoscopy). Recently, a single-pixel imaging technique based on a multicore fibre photonic lantern has been designed, named computational optical imaging using a lantern (COIL). A proximal algorithm based on a sparsity prior, dubbed SARA-COIL, has been further proposed to solve the associated inverse problem, to enable image reconstructions for high resolution COIL microendoscopy. In this work, we develop a data-driven approach for COIL. We replace the sparsity prior in the proximal algorithm by a learned denoiser, leading to a plug-and-play (PnP) algorithm. The resulting PnP method, based on a proximal primal-dual algorithm, enables to solve the Morozov formulation of the inverse problem. We use recent results in learning theory to train a network with desirable Lipschitz properties, and we show that the resulting primal-dual PnP algorithm converges to a solution to a monotone inclusion problem. Our simulations highlight that the proposed data-driven approach improves the reconstruction quality over variational SARA-COIL method on both simulated and real data.
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Chen, Ningyuan, and Guillermo Gallego. "A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint." SSRN Electronic Journal, 2018. http://dx.doi.org/10.2139/ssrn.3301153.
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Dutta, Haimonti. "A Consensus Algorithm for Linear Support Vector Machines." Management Science, August 30, 2021. http://dx.doi.org/10.1287/mnsc.2021.4042.
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In the era of big data, an important weapon in a machine learning researcher’s arsenal is a scalable support vector machine (SVM) algorithm. Traditional algorithms for learning SVMs scale superlinearly with the training set size, which becomes infeasible quickly for large data sets. In recent years, scalable algorithms have been designed which study the primal or dual formulations of the problem. These often suggest a way to decompose the problem and facilitate development of distributed algorithms. In this paper, we present a distributed algorithm for learning linear SVMs in the primal form for binary classification called the gossip-based subgradient (GADGET) SVM. The algorithm is designed such that it can be executed locally on sites of a distributed system. Each site processes its local homogeneously partitioned data and learns a primal SVM model; it then gossips with random neighbors about the classifier learnt and uses this information to update the model. To learn the model, the SVM optimization problem is solved using several techniques, including a gradient estimation procedure, stochastic gradient descent method, and several variants including minibatches of varying sizes. Our theoretical results indicate that the rate at which the GADGET SVM algorithm converges to the global optimum at each site is dominated by an [Formula: see text] term, where λ measures the degree of convexity of the function at the site. Empirical results suggest that this anytime algorithm—where the quality of results improve gradually as computation time increases—has performance comparable to its centralized, pseudodistributed, and other state-of-the-art gossip-based SVM solvers. It is at least 1.5 times (often several orders of magnitude) faster than other gossip-based SVM solvers known in literature and has a message complexity of O(d) per iteration, where d represents the number of features of the data set. Finally, a large-scale case study is presented wherein the consensus-based SVM algorithm is used to predict failures of advanced mechanical components in a chocolate manufacturing process using more than one million data points. This paper was accepted by J. George Shanthikumar, big data analytics.
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Hu, Rui, Jianan Cui, Chenxu Li, Chengjin Yu, Yunmei Chen, and Huafeng Liu. "Dynamic low-count PET image reconstruction using spatio-temporal primal dual network." Physics in Medicine & Biology, June 13, 2023. http://dx.doi.org/10.1088/1361-6560/acde3e.
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Abstract Objective. Dynamic positron emission tomography (PET) imaging, which can provide information on dynamic changes in physiological metabolism, is now widely used in clinical diagnosis and cancer treatment. However, the reconstruction from dynamic data is extremely challenging due to the limited counts received in individual frame, especially in ultra short frames. Recently, the unrolled model-based deep learning methods have shown inspiring results for low-count PET image reconstruction with good interpretability. Nevertheless, the existing model-based deep learning methods mainly focus on the spatial correlations while ignore the temporal domain. 

Approach. In this paper, inspired by the Learned Primal Dual algorithm, we propose the spatio-temporal primal dual network for dynamic low-count PET image reconstruction. Both spatial and temporal correlations are encoded by 3D convolution operators. The physical projection of PET is embedded in the iterative learning process of the network, which provides the physical constraints and enhances interpretability. 

Main results. The experiments of both simulation data and real rat scan data have shown that the proposed method can achieve substantial noise reduction in both temporal and spatial domains and outperform the maximum likelihood expectation maximization (MLEM), spatio-temporal kernel method (KEM-ST), Learned Primal Dual (LPD) and FBPnet.

Significance. Experimental results show STPDnet better reconstruction performance in the low count situation, which makes the proposed method particularly suitable in whole-body dynamic imaging and parametric PET imaging that require extreme short frames and usually suffer from high level of noise.
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Henry-Labordere, Pierre. "Deep Primal-Dual Algorithm for BSDEs: Applications of Machine Learning to CVA and IM." SSRN Electronic Journal, 2017. http://dx.doi.org/10.2139/ssrn.3071506.
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Zhao, Yong-Ping, Yao-Bin Chen, Zhao Hao, Hao Wang, Zhe Yang, and Jian-Feng Tan. "Imbalanced Kernel Extreme Learning Machines for Fault Detection of Aircraft Engine." Journal of Dynamic Systems, Measurement, and Control 142, no. 10 (June 1, 2020). http://dx.doi.org/10.1115/1.4047117.
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Abstract To deal with class imbalance learning (CIL) problems, a novel algorithm is proposed based on kernel extreme learning machine (KELM), named KELM-CIL. To solve it, two algorithms are developed from the dual and primal spaces, respectively, thus yielding D-KELM-CIL and P-KELM-CIL. However, both D-KELM-CIL and P-KELM-CIL are not sparse algorithms. Hence, a sparse strategy based on Cholesky factorization is utilized to realize their sparseness, producing CD-KELM-CIL and CP-KELM-CIL. For large-size problems, a probabilistic trick is applied to accelerate them further, hence obtaining PCD-KELM-CIL and PCP-KELM-CIL. To test the effectiveness and efficacy of the proposed algorithms, experiments on benchmark datasets are carried out. When the proposed algorithms are applied to fault detection of aircraft engine, they show good generalization performance and real-time performance, especially for CP-KELM-CIL and PCP-KELM-CIL, which indicates that they can be developed as candidate techniques for fault detection of aircraft engine.
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Bekci, Recep Yusuf, Mehmet Gümüş, and Sentao Miao. "Inventory Control and Learning for One-Warehouse Multistore System with Censored Demand." Operations Research, August 2, 2023. http://dx.doi.org/10.1287/opre.2021.0694.
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Efficient Learning Algorithms for Dynamic Inventory Allocation in Multiwarehouse Multistore Systems with Censored Demand Motivated by collaboration with a prominent fast-fashion retailer in Europe, the researchers focus their attention on the one-warehouse multistore (OWMS) inventory control problem, specifically addressing scenarios in which the demand distribution is unknown a priori. The OWMS problem revolves around a central warehouse that receives initial replenishments and subsequently distributes inventory to multiple stores within a finite time horizon. The objective lies in minimizing the total expected cost. To overcome the hurdles posed by the unknown demand distribution, the researchers propose a primal-dual algorithm that continuously learns from demand observations and dynamically adjusts inventory control decisions in real time. Thorough theoretical analysis and empirical evaluations highlight the promising performance of this approach, offering valuable insights for efficient inventory allocation within the ever-evolving retail industry.
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Chen, Xi, Jiameng Lyu, Yining Wang, and Yuan Zhou. "EXPRESS: Network Revenue Management with Demand Learning and Fair Resource-Consumption Balancing." Production and Operations Management, February 5, 2024. http://dx.doi.org/10.1177/10591478231225176.
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In addition to maximizing the total revenue, decision-makers in lots of industries would like to guarantee balanced consumption across different resources. For instance, in the retailing industry, ensuring a balanced consumption of resources from different suppliers enhances fairness and helps maintain a healthy channel relationship; in the cloud computing industry, resource-consumption balance helps increase customer satisfaction and reduce operational costs. Motivated by these practical needs, this paper studies the price-based network revenue management (NRM) problem with both demand learning and fair resource-consumption balancing. We introduce the regularized revenue, that is, the total revenue with a balancing regularization, as our objective to incorporate fair resource-consumption balancing into the revenue maximization goal. We propose a primal-dual-type online policy with the upper-confidence-bound demand learning method to maximize the regularized revenue. We adopt several innovative techniques to make our algorithm a unified and computationally efficient framework for the continuous price set and a wide class of balancing regularizers. Our algorithm achieves a worst-case regret of [Formula: see text], where [Formula: see text] denotes the number of products and [Formula: see text] denotes the number of time periods. Numerical experiments in a few NRM examples demonstrate the effectiveness of our algorithm in simultaneously achieving revenue maximization and fair resource-consumption balancing.
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Zheng, Zemin, Jie Zhang, and Yang Li. "L0-Regularized Learning for High-Dimensional Additive Hazards Regression." INFORMS Journal on Computing, June 13, 2022. http://dx.doi.org/10.1287/ijoc.2022.1208.
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Sparse learning in high-dimensional survival analysis is of great practical importance, as exemplified by modern applications in credit risk analysis and high-throughput genomic data analysis. In this article, we consider the L0-regularized learning for simultaneous variable selection and estimation under the framework of additive hazards models and utilize the idea of primal dual active sets to develop an algorithm targeted at solving the traditionally nonpolynomial time optimization problem. Under interpretable conditions, comprehensive statistical properties, including model selection consistency, oracle inequalities under various estimation losses, and the oracle property, are established for the global optimizer of the proposed approach. Moreover, our theoretical analysis for the algorithmic solution reveals that the proposed L0-regularized learning can be more efficient than other regularization methods in that it requests a smaller sample size as well as a lower minimum signal strength to identify the significant features. The effectiveness of the proposed method is evidenced by simulation studies and real-data analysis. Summary of Contribution: Feature selection is a fundamental statistical learning technique under high dimensions and routinely encountered in various areas, including operations research and computing. This paper focuses on the L0-regularized learning for feature selection in high-dimensional additive hazards regression. The matching algorithm for solving the nonconvex L0-constrained problem is scalable and enjoys comprehensive theoretical properties.
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Prigent, Sylvain, Hoai-Nam Nguyen, Ludovic Leconte, Cesar Augusto Valades-Cruz, Bassam Hajj, Jean Salamero, and Charles Kervrann. "SPITFIR(e): a supermaneuverable algorithm for fast denoising and deconvolution of 3D fluorescence microscopy images and videos." Scientific Reports 13, no. 1 (January 27, 2023). http://dx.doi.org/10.1038/s41598-022-26178-y.
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AbstractModern fluorescent microscopy imaging is still limited by the optical aberrations and the photon budget available in the specimen. A direct consequence is the necessity to develop flexible and “off-road” algorithms in order to recover structural details and improve spatial resolution, which is critical when restraining the illumination to low levels in order to limit photo-damages. Here, we report SPITFIR(e) a flexible method designed to accurately and quickly restore 2D–3D fluorescence microscopy images and videos (4D images). We designed a generic sparse-promoting regularizer to subtract undesirable out-of-focus background and we developed a primal-dual algorithm for fast optimization. SPITFIR(e) is a ”swiss-knife” method for practitioners as it adapts to any microscopy techniques, to various sources of signal degradation (noise, blur), to variable image contents, as well as to low signal-to-noise ratios. Our method outperforms existing state-of-the-art algorithms, and is more flexible than supervised deep-learning methods requiring ground truth datasets. The performance, the flexibility, and the ability to push the spatiotemporal resolution limit of sub-diffracted fluorescence microscopy techniques are demonstrated on experimental datasets acquired with various microscopy techniques from 3D spinning-disk confocal up to lattice light sheet microscopy.
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Zhao, Chen, Feng Mi, Xintao Wu, Kai Jiang, Latifur Khan, and Feng Chen. "Dynamic Environment Responsive Online Meta-Learning with Fairness Awareness." ACM Transactions on Knowledge Discovery from Data, February 20, 2024. http://dx.doi.org/10.1145/3648684.
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The fairness-aware online learning framework has emerged as a potent tool within the context of continuous lifelong learning. In this scenario, the learner’s objective is to progressively acquire new tasks as they arrive over time, while also guaranteeing statistical parity among various protected sub-populations, such as race and gender, when it comes to the newly introduced tasks. A significant limitation of current approaches lies in their heavy reliance on the i.i.d (independent and identically distributed) assumption concerning data, leading to a static regret analysis of the framework. Nevertheless, it’s crucial to note that achieving low static regret does not necessarily translate to strong performance in dynamic environments characterized by tasks sampled from diverse distributions. In this paper, to tackle the fairness-aware online learning challenge in evolving settings, we introduce a unique regret measure, FairSAR, by incorporating long-term fairness constraints into a strongly adapted loss regret framework. Moreover, to determine an optimal model parameter at each time step, we introduce an innovative adaptive fairness-aware online meta-learning algorithm, referred to as FairSAOML. This algorithm possesses the ability to adjust to dynamic environments by effectively managing bias control and model accuracy. The problem is framed as a bi-level convex-concave optimization, considering both the model’s primal and dual parameters, which pertain to its accuracy and fairness attributes, respectively. Theoretical analysis yields sub-linear upper bounds for both loss regret and the cumulative violation of fairness constraints. Our experimental evaluation on various real-world datasets in dynamic environments demonstrates that our proposed FairSAOML algorithm consistently outperforms alternative approaches rooted in the most advanced prior online learning methods.
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Terris, Matthieu, Chao Tang, Adrian Jackson, and Yves Wiaux. "The AIRI plug-and-play algorithm for image reconstruction in radio-interferometry: variations and robustness." Monthly Notices of the Royal Astronomical Society, January 24, 2025. https://doi.org/10.1093/mnras/staf022.
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Abstract Plug-and-Play (PnP) algorithms are appealing alternatives to proximal algorithms when solving inverse imaging problems. By learning a Deep Neural Network (DNN) denoiser behaving as a proximal operator, one waives the computational complexity of optimisation algorithms induced by sophisticated image priors, and the sub-optimality of handcrafted priors compared to DNNs. Such features are highly desirable in radio-interferometric (RI) imaging, where precision and scalability of the image reconstruction process are key. In previous work, we introduced AIRI, PnP counterpart to the unconstrained variant of the SARA optimisation algorithm, relying on a forward-backward algorithmic backbone. Here, we introduce variations of AIRI towards a more general and robust PnP paradigm in RI imaging. Firstly, we show that the AIRI denoisers can be used without any alteration to instantiate a PnP counterpart to the constrained SARA optimisation algorithm itself, relying on a primal-dual forward-backward algorithmic backbone, thus extending the remit of the AIRI paradigm. Secondly, we show that AIRI algorithms are robust to strong variations in the nature of the training dataset, with denoisers trained on medical images yielding similar reconstruction quality to those trained on astronomical images. Thirdly, we develop a functionality to quantify the model uncertainty introduced by the randomness in the training process. We validate the image reconstruction and uncertainty quantification functionality of AIRI algorithms against the SARA family and CLEAN, both in simulation and on real data of the ESO 137-006 galaxy acquired with the MeerKAT telescope. AIRI code is available in the BASPLib code library† on GitHub.