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Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a proximity operator comes with its structure at no additional cost, and…

Optimization and Control · Mathematics 2023-02-10 Gilles Bareilles , Franck Iutzeler , Jérôme Malick

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…

Optimization and Control · Mathematics 2018-05-29 Ching-pei Lee , Cong Han Lim , Stephen J. Wright

Policy gradient methods, which have been extensively studied in the last decade, offer an effective and efficient framework for reinforcement learning problems. However, their performances can often be unsatisfactory, suffering from…

Machine Learning · Computer Science 2026-01-27 Shihab Ahmed , El Houcine Bergou , Aritra Dutta , Yue Wang

Newton's method for finding an unconstrained minimizer for strictly convex functions, generally speaking, does not converge from any starting point. We introduce and study the damped regularized Newton's method (DRNM). It converges globally…

Optimization and Control · Mathematics 2017-06-27 Roman Polyak

This paper aims to establish an entropy-regularized value-based reinforcement learning method that can ensure the monotonic improvement of policies at each policy update. Unlike previously proposed lower-bounds on policy improvement in…

Machine Learning · Computer Science 2020-08-26 Lingwei Zhu , Takamitsu Matsubara

Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating…

Optimization and Control · Mathematics 2025-06-09 Philipp Plank , Yufei Zhang

We propose a method for designing policies for convex stochastic control problems characterized by random linear dynamics and convex stage cost. We consider policies that employ quadratic approximate value functions as a substitute for the…

Optimization and Control · Mathematics 2023-11-10 Alan Yang , Stephen Boyd

Stochastic gradient methods are among the most important algorithms in training machine learning problems. While classical assumptions such as strong convexity allow a simple analysis they are rarely satisfied in applications. In recent…

Machine Learning · Computer Science 2025-03-18 Simon Weissmann , Sara Klein , Waïss Azizian , Leif Döring

We consider a general-sum N-player linear-quadratic game with stochastic dynamics over a finite horizon and prove the global convergence of the natural policy gradient method to the Nash equilibrium. In order to prove the convergence of the…

Optimization and Control · Mathematics 2022-08-16 Ben Hambly , Renyuan Xu , Huining Yang

The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…

Optimization and Control · Mathematics 2019-01-09 Fatemeh Mansoori , Ermin Wei

The softmax policy gradient (PG) method, which performs gradient ascent under softmax policy parameterization, is arguably one of the de facto implementations of policy optimization in modern reinforcement learning. For $\gamma$-discounted…

Machine Learning · Computer Science 2022-12-19 Gen Li , Yuting Wei , Yuejie Chi , Yuxin Chen

In stochastic optimization, a common tool to deal sequentially with large sample is to consider the well-known stochastic gradient algorithm. Nevertheless, since the stepsequence is the same for each direction, this can lead to bad results…

Optimization and Control · Mathematics 2023-03-03 Antoine Godichon-Baggioni , Pierre Tarrago

This paper discusses algorithms for solving Markov decision processes (MDPs) that have monotone optimal policies. We propose a two-stage alternating convex optimization scheme that can accelerate the search for an optimal policy by…

Systems and Control · Computer Science 2017-04-04 Robert Mattila , Cristian R. Rojas , Vikram Krishnamurthy , Bo Wahlberg

Approaches to policy optimization have been motivated from diverse principles, based on how the parametric model is interpreted (e.g. value versus policy representation) or how the learning objective is formulated, yet they share a common…

Machine Learning · Computer Science 2022-06-20 Ramki Gummadi , Saurabh Kumar , Junfeng Wen , Dale Schuurmans

Neural Network based approximations of the Value function make up the core of leading Policy Based methods such as Trust Regional Policy Optimization (TRPO) and Proximal Policy Optimization (PPO). While this adds significant value when…

Machine Learning · Computer Science 2024-06-03 Hari Srikanth

In this work we present an adaptive Newton-type method to solve nonlinear constrained optimization problems in which the constraint is a system of partial differential equations discretized by the finite element method. The adaptive…

Optimization and Control · Mathematics 2017-06-05 Thomas Carraro , Simon Dörsam , Stefan Frei , Daniel Schwarz

We introduce a new second-order inertial optimization method for machine learning called INNA. It exploits the geometry of the loss function while only requiring stochastic approximations of the function values and the generalized…

Machine Learning · Computer Science 2021-08-17 Camille Castera , Jérôme Bolte , Cédric Févotte , Edouard Pauwels

This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…

Optimization and Control · Mathematics 2026-01-12 Dimitris Boskos , Jorge Cortés , Sonia Martínez

In this paper, we present a probability one convergence proof, under suitable conditions, of a certain class of actor-critic algorithms for finding approximate solutions to entropy-regularized MDPs using the machinery of stochastic…

Machine Learning · Computer Science 2019-10-23 Wesley Suttle , Zhuoran Yang , Kaiqing Zhang , Ji Liu

Trust-region methods have yielded state-of-the-art results in policy search. A common approach is to use KL-divergence to bound the region of trust resulting in a natural gradient policy update. We show that the natural gradient and trust…

Machine Learning · Computer Science 2019-02-11 Joni Pajarinen , Hong Linh Thai , Riad Akrour , Jan Peters , Gerhard Neumann