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In the paper, we propose a class of efficient adaptive bilevel methods based on mirror descent for nonconvex bilevel optimization, where its upper-level problem is nonconvex possibly with nonsmooth regularization, and its lower-level…

Optimization and Control · Mathematics 2023-11-21 Feihu Huang

Direct policy gradient methods for reinforcement learning and continuous control problems are a popular approach for a variety of reasons: 1) they are easy to implement without explicit knowledge of the underlying model 2) they are an…

Machine Learning · Computer Science 2019-03-26 Maryam Fazel , Rong Ge , Sham M. Kakade , Mehran Mesbahi

This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…

Optimization and Control · Mathematics 2025-06-04 Mohammad S. Alkousa , Belal A. Alashqar , Fedor S. Stonyakin , Tarek Nabhani , Seydamet S. Ablaev

We investigate different randomizations for mirror descent method. We try to propose such a randomization that allows us to use sparsity of the problem as much as it possible. In the paper one can also find a generalization of randomizaed…

Optimization and Control · Mathematics 2016-12-12 Anton Anikin , Alexander Gasnikov , Alexander Gornov

Policy gradient methods are among the most effective methods in challenging reinforcement learning problems with large state and/or action spaces. However, little is known about even their most basic theoretical convergence properties,…

Machine Learning · Computer Science 2020-10-16 Alekh Agarwal , Sham M. Kakade , Jason D. Lee , Gaurav Mahajan

In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the…

Optimization and Control · Mathematics 2013-09-10 Cong D. Dang , Guanghui Lan

We consider infinite-horizon discounted Markov decision processes and study the convergence rates of the natural policy gradient (NPG) and the Q-NPG methods with the log-linear policy class. Using the compatible function approximation…

Machine Learning · Computer Science 2023-02-22 Rui Yuan , Simon S. Du , Robert M. Gower , Alessandro Lazaric , Lin Xiao

Aligning a lens system relative to an imager is a critical challenge in camera manufacturing. While optimal alignment can be mathematically computed under ideal conditions, real-world deviations caused by manufacturing tolerances often…

Robotics · Computer Science 2025-10-06 Matthias Burkhardt , Tobias Schmähling , Pascal Stegmann , Michael Layh , Tobias Windisch

One of the key approaches to save samples in reinforcement learning (RL) is to use knowledge from an approximate model such as its simulator. However, how much does an approximate model help to learn a near-optimal policy of the true…

Machine Learning · Computer Science 2020-07-15 Fei Feng , Wotao Yin , Lin F. Yang

The Polyak-Lojasiewicz (PL) inequality is a sufficient condition for establishing linear convergence of gradient descent, even in non-convex settings. While several recent works use a PL-based analysis to establish linear convergence of…

Machine Learning · Computer Science 2021-10-07 Adityanarayanan Radhakrishnan , Mikhail Belkin , Caroline Uhler

Recent advancements in off-policy Reinforcement Learning (RL) have significantly improved sample efficiency, primarily due to the incorporation of various forms of regularization that enable more gradient update steps than traditional…

Machine Learning · Computer Science 2024-06-21 Michal Nauman , Michał Bortkiewicz , Piotr Miłoś , Tomasz Trzciński , Mateusz Ostaszewski , Marek Cygan

Policy gradient (PG) methods are popular and efficient for large-scale reinforcement learning due to their relative stability and incremental nature. In recent years, the empirical success of PG methods has led to the development of a…

Machine Learning · Computer Science 2022-05-24 Yuhao Ding , Junzi Zhang , Javad Lavaei

In earthwork and construction, excavators often encounter large rocks mixed with various soil conditions, requiring skilled operators. This paper presents a framework for achieving autonomous excavation using reinforcement learning (RL)…

Robotics · Computer Science 2026-01-29 Yuki Kadokawa , Hirotaka Tahara , Takamitsu Matsubara

We study three families of online convex optimization algorithms: follow-the-proximally-regularized-leader (FTRL-Proximal), regularized dual averaging (RDA), and composite-objective mirror descent. We first prove equivalence theorems that…

Machine Learning · Computer Science 2011-09-21 H. Brendan McMahan

Natural policy gradient (NPG) and its variants are widely-used policy search methods in reinforcement learning. Inspired by prior work, a new NPG variant coined NPG-HM is developed in this paper, which utilizes the Hessian-aided momentum…

Machine Learning · Computer Science 2024-01-23 Jie Feng , Ke Wei , Jinchi Chen

Diffusion policies have achieved superior performance in imitation learning and offline reinforcement learning (RL) due to their rich expressiveness. However, the conventional diffusion training procedure requires samples from target…

Machine Learning · Computer Science 2025-07-01 Haitong Ma , Tianyi Chen , Kai Wang , Na Li , Bo Dai

Low-complexity non-smooth convex regularizers are routinely used to impose some structure (such as sparsity or low-rank) on the coefficients for linear predictors in supervised learning. Model consistency consists then in selecting the…

Optimization and Control · Mathematics 2019-01-17 Jalal Fadili , Guillaume Garrigos , Jérome Malick , Gabriel Peyré

Modern deep reinforcement learning (RL) algorithms are motivated by either the generalised policy iteration (GPI) or trust-region learning (TRL) frameworks. However, algorithms that strictly respect these theoretical frameworks have proven…

Machine Learning · Computer Science 2024-11-21 Jakub Grudzien Kuba , Christian Schroeder de Witt , Jakob Foerster

We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal…

Machine Learning · Computer Science 2015-07-03 Alain Rakotomamonjy , Remi Flamary , Gilles Gasso

Reward maximization, safe exploration, and intrinsic motivation are often studied as separate objectives in reinforcement learning (RL). We present a unified geometric framework, that views these goals as instances of a single optimization…

Machine Learning · Computer Science 2025-09-03 Nikola Milosevic , Nico Scherf