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Sparse proximal Reinforcement Learning via Nested Optimization

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2020年第11期50卷 4020-4032页

作者： Song, Tianheng Li, Dazi Jin, Qibing Hirasawa, Kotaro Beijing Univ Chem Technol Inst Automat Beijing 100029 Peoples R China

We consider the tasks of feature selection and policy evaluation based on linear value function approximation in reinforcement learning problems. High-dimension feature vectors and limited number of samples can easily cause over-fitting and computation expensive. To prevent this problem, l(1)-regularized method obtains sparse solutions and thus improves generalization performance. We propose an efficient l(1)-regularized recursive least squares-based online algorithm with O(n(2)) complexity per time-step, termed l(1)-RC. With the help of nested optimization decomposition, l(1)-RC solves a series of standard optimization problems and avoids minimizing mean squares projected Bellman error with l(1)-regularization directly. In l(1)-RC, we propose RC with iterative refinement to minimize the operator error, and we propose an alternating direction method of multipliers with proximal operator to minimize the fixed-point error. The convergence of l(1)-RC is established based on ordinary differential equation method and some extensions are also given. In empirical computations, some state-of-the-art l(1)-regularized methods are chosen as the baselines, and l(1)-RC are tested in both policy evaluation and learning control benchmarks. The empirical results show the effectiveness and advantages ofl(1)-RC.

关键词： Alternating direction method of multipliers (ADMM) l(1)-regularization nested optimization proximal algorithm temporal difference (TD) value function approximation (VFA)

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Splitting proximal with penalization schemes for additive convex hierarchical minimization problems

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OPTIMIZATION METHODS & SOFTWARE 2020年第6期35卷 1098-1118页

作者： Nimana, Nimit Petrot, Narin Khon Kaen Univ Dept Math Fac Sci Khon Kaen Thailand Naresuan Univ Fac Sci Dept Math Phitsanulok Thailand Naresuan Univ Fac Sci Ctr Excellence Nonlinear Anal & Optimizat Phitsanulok Thailand

We consider a splitting proximal algorithm with penalization for minimizing a finite sum of proper, convex and lower semicontinuous functions subject to the set of minimizers of another proper, convex and lower semicontinuous function. We show convergences of the generated sequence of iterates to an optimal solution of the considered convex hierarchical minimization problem. Some numerical experiments on the regularized least squares problems are given to show the effectiveness of the obtained theoretical results.

关键词： Additive convex hierarchical minimization convex optimization penalization proximal algorithm regularized least squares problems

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Perspective maximum likelihood-type estimation via proximal decomposition

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ELECTRONIC JOURNAL OF STATISTICS 2020年第1期14卷 207-238页

作者： Combettes, Patrick L. Mueller, Christian L. North Carolina State Univ Dept Math Raleigh NC 27695 USA Flatiron Inst Ctr Computat Math New York NY USA Helmholtz Zentrum Inst Computat Biol Munich Germany Ludwig Maximilians Univ Munchen Dept Stat Munich Germany

We introduce a flexible optimization model for maximum likelihood-type estimation (M-estimation) that encompasses and generalizes a large class of existing statistical models, including Huber's concomitant M-estimator, Owen's Huber/Berhu concomitant estimator, the scaled lasso, support vector machine regression, and penalized estimation with structured sparsity. The model, termed perspective M-estimation, leverages the observation that convex M-estimators with concomitant scale as well as various regularizers are instances of perspective functions, a construction that extends a convex function to a jointly convex one in terms of an additional scale variable. These nonsmooth functions are shown to be amenable to proximal analysis, which leads to principled and provably convergent optimization algorithms via proximal splitting. We derive novel proximity operators for several perspective functions of interest via a geometrical approach based on duality. We then devise a new proximal splitting algorithm to solve the proposed M-estimation problem and establish the convergence of both the scale and regression iterates it produces to a solution. Numerical experiments on synthetic and real-world data illustrate the broad applicability of the proposed framework.

关键词： Convex optimization heteroscedastic model concomitant M-estimator perspective function proximal algorithm robust regression

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proximal statistic: Asymptotic normality

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STATISTICS & PROBABILITY LETTERS 2020年 167卷 108896-108896页

作者： Pacini, David Univ Bristol Bristol Avon England

This note introduces an asymptotically normal statistic for the value function of a convex stochastic minimization program, which may have more than one minimizer. The statistic uses a recursive estimator, based on th... 详细信息

关键词： Set identification proximal algorithm

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Sparse Distortionless Beamformer Based on Nonconvex Optimization 29

Sparse Distortionless Beamformer Based on Nonconvex Optimiza...

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29th European Signal Processing Conference (EUSIPCO)

作者： Kawamura, Taiga Yatabe, Kohei Miyazaki, Ryoichi Natl Inst Technol Tokuyama Coll Yamaguchi Japan Waseda Univ Tokyo Japan

ISBN: (纸本)9789082797060

Minimum power distortionless response (MPDR) beamformer is a popular beamformer that minimizes its output power under the distortionless constraint. To improve the performance of the MPDR beamformer, a sparse distortionless beamformer has been proposed. It minimizes the l(1) norm of the output signal under the same constraint so that the output has sparse time-frequency representation. While the l(1)-norm-based formulation is theoretically advantageous owing to its convexity, its practical performance might not be excellent because of the bias of the l(1) norm. To reduce the bias and improve the performance, we propose a sparse distortionless beamformer based on a nonconvex sparsity-inducing objective function. The proposed beamformer is performed via a heuristic application of a primal-dual splitting algorithm. The experiments showed that the proposed beamformer can achieve higher performance and is more robust against mismatch of the target direction.

关键词： Microphone array speech enhancement sparse time-frequency representation proximal algorithm

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STRUCTURED SUPPORT EXPLORATION FOR MULTILAYER SPARSE MATRIX FACTORIZATION

STRUCTURED SUPPORT EXPLORATION FOR MULTILAYER SPARSE MATRIX ...

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Quoc-Tung Le Gribonval, Remi Univ Lyon ENS Lyon UCBL CNRSInriaLIP F-69342 Lyon 07 France

ISBN: (纸本)9781728176055

Matrix factorization with sparsity constraints plays an important role in many machine learning and signal processing problems such as dictionary learning, data visualization, dimension reduction. Among the most popular tools for sparse matrix factorization are proximal algorithms, a family of algorithms based on proximal operators. In this paper, we address two problems with the application of proximal algorithms to sparse matrix factorization. On the one hand, we analyze a weakness of proximal algorithms in sparse matrix factorization: the premature convergence of the support. A remedy is also proposed to address this problem. On the other hand, we describe a new tractable proximal operator called Generalized Hungarian Method, associated to so-called k-regular matrices, which are useful for the factorization of a class of matrices associated to fast linear transforms. We further illustrate the effectiveness of our proposals by numerical experiments on the Hadamard Transform and magnetoencephalography matrix factorization.

关键词： Matrix factorization Sparsity Support Exploration Hungarian Method proximal algorithm

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Energy Efficient Spectrum Allocation and Mode Selection for D2D Communications in Heterogeneous Networks

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IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS 2020年 6卷 382-393页

作者： Galanopoulos, Apostolos Foukalas, Fotis Khattab, Tamer Trinity Coll Dublin Dublin D02 PN40 Ireland Qatar Univ Coll Engn Elect Engn Doha 2713 Qatar

In this paper, we consider a heterogeneous network consisting of both macro Base Station (MBS) and pico Base Stations (PBSs) in order to provide a spectrum allocation and mode selection in device-to-device (D2D) communications. A number of Component Carriers (CC) are considered available for allocation to the MBS and PBSs that are being utilized through carrier aggregation (CA) while mode selection decisions are made by each BS in order to balance between power consumption minimization and UE data rate requirements. A power minimization (energy-efficient) problem is formulated in order to provide a joint spectrum allocation and mode selection solution. This problem is solved using a state of the art optimization method known as proximal algorithm. First, a non-cooperative (centralized) solution is provided and second, a cooperative (distributed) employing distributed proximal algorithm is devised reducing the induced complexity. The cooperative solution is achieved by implementing distributed alternating direction method of multipliers (D-ADMM). Simulation results are carried out for all cases that reveal the energy efficient spectrum allocation and mode selection according under certain channels' conditions that can balance between achieving high data rate requirements and power minimization. Finally, useful insights are presented such as complexity, convergence, delay and actual implementation of such a solution for the future wireless networks.

关键词： Device-to-device communication Resource management Interference Power demand Minimization Wireless sensor networks Receivers Device-to-device energy efficiency spectrum allocation mode selection heterogeneous networks proximal algorithm distributed alternating method of multipliers

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Point Process Estimation with Mirror Prox algorithms

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APPLIED MATHEMATICS AND OPTIMIZATION 2020年第3期82卷 919-947页

作者： He, Niao Harchaoui, Zaid Wang, Yichen Song, Le Univ Illinois Dept Ind Enterprise Syst Engn Urbana IL 61801 USA Univ Washington Dept Stat Seattle WA 98195 USA Georgia Inst Technol Dept Computat Sci & Engn Atlanta GA 30332 USA

Point process models have been extensively used in many areas of science and engineering, from quantitative sociology to medical imaging. Computing the maximum likelihood estimator of a point process model often leads to a convex optimization problem displaying a challenging feature, namely the lack of Lipschitz-continuity of the objective function. This feature can be a barrier to the application of common first order convex optimization methods. We present an approach where the estimation of a point process model is framed as a saddle point problem instead. This formulation allows us to develop Mirror Prox algorithms to efficiently solve the saddle point problem. We introduce a general Mirror Prox algorithm, as well as a variant appropriate for large-scale problems, and establish worst-case complexity guarantees for both algorithms. We illustrate the performance of the proposed algorithms for point process estimation on real datasets from medical imaging, social networks, and recommender systems.

关键词： Mirror Prox proximal algorithm Point process Saddle point problem

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Low-rank tensor learning with nonconvex overlapped nuclear norm regularization

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2022年第1期23卷 6083-6142页

作者： Quanming Yao Yaqing Wang Bo Han James T. Kwok Department of Electronic Engineering Tsinghua University Baidu Research Baidu Inc. Department of Computer Science Hong Kong Baptist University Department of Computer Science and Engineering Hong Kong University of Science and Technology

Nonconvex regularization has been popularly used in low-rank matrix learning. However, extending it for low-rank tensor learning is still computationally expensive. To address this problem, we develop an efficient solver for use with a nonconvex extension of the overlapped nuclear norm regularizer. Based on the proximal average algorithm, the proposed algorithm can avoid expensive tensor folding/unfolding operations. A special "sparse plus low-rank" structure is maintained throughout the iterations, and allows fast computation of the individual proximal steps. Empirical convergence is further improved with the use of adaptive momentum. We provide convergence guarantees to critical points on smooth losses and also on objectives satisfying the Kurdyka-Łojasiewicz condition. While the optimization problem is nonconvex and nonsmooth, we show that its critical points still have good statistical performance on the tensor completion problem. Experiments on various synthetic and real-world data sets show that the proposed algorithm is efficient in both time and space and more accurate than the existing state-of-the-art.

关键词： low-rank tensor proximal algorithm proximal average algorithm nonconvex regularization overlapped nuclear norm

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Spatial matrix completion for spatially misaligned and high-dimensional air pollution data

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ENVIRONMETRICS 2022年第4期33卷 e2713-e2713页

作者： Vu, Phuong T. Szpiro, Adam A. Simon, Noah Univ Washington Dept Biostat Seattle WA 98195 USA Seattle Childrens Res Inst 1920 Terry Ave Seattle WA 98101 USA

In health-pollution cohort studies, accurate predictions of pollutant concentrations at new locations are needed, since the locations of fixed monitoring sites and study participants are often spatially misaligned. For multi-pollution data, principal component analysis (PCA) is often incorporated to obtain low-rank (LR) structure of the data prior to spatial prediction. Recently developed predictive PCA modifies the traditional algorithm to improve the overall predictive performance by leveraging both LR and spatial structures within the data. However, predictive PCA requires complete data or an initial imputation step. Nonparametric imputation techniques without accounting for spatial information may distort the underlying structure of the data, and thus further reduce the predictive performance. We propose a convex optimization problem inspired by the LR matrix completion framework and develop a proximal algorithm to solve it. Missing data are imputed and handled concurrently within the algorithm, which eliminates the necessity of a separate imputation step. We review the connections among those existing methods developed for spatially misaligned multivariate data, and show that our algorithm has lower computational burden and leads to reliable predictive performance as the severity of missing data increases.

关键词： low-rank matrix completion principal component analysis proximal algorithm spatial prediction

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