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Reinforcement learning (RL) tackles sequential decision-making problems by creating agents that interacts with their environment. However, existing algorithms often view these problem as static, focusing on point estimates for model…

Machine Learning · Statistics 2024-03-21 Frank Shih , Faming Liang

Reinforcement learning (RL) is currently one of the most prominent methods for optimizing dynamical systems, with breakthrough results across various fields. The framework is based on the concept of a Markov decision process (MDP), leading…

Optimization and Control · Mathematics 2025-11-17 Rene Carmona , Mathieu Lauriere

Approximate dynamic programming has been used successfully in a large variety of domains, but it relies on a small set of provided approximation features to calculate solutions reliably. Large and rich sets of features can cause existing…

Artificial Intelligence · Computer Science 2015-03-17 Marek Petrik , Gavin Taylor , Ron Parr , Shlomo Zilberstein

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

Machine Learning · Computer Science 2010-10-19 Sham M. Kakade , Shai Shalev-Shwartz , Ambuj Tewari

Finite element discretizations of problems in computational physics often rely on adaptive mesh refinement (AMR) to preferentially resolve regions containing important features during simulation. However, these spatial refinement strategies…

Computational Engineering, Finance, and Science · Computer Science 2022-09-27 Corbin Foucart , Aaron Charous , Pierre F. J. Lermusiaux

Temporal-difference (TD) learning is widely regarded as one of the most popular algorithms in reinforcement learning (RL). Despite its widespread use, it has only been recently that researchers have begun to actively study its finite time…

Machine Learning · Computer Science 2025-04-16 Han-Dong Lim , Donghwan Lee

Learning and optimal control under robust Markov decision processes (MDPs) have received increasing attention, yet most existing theory, algorithms, and applications focus on finite-horizon or discounted models. Long-run average-reward…

Optimization and Control · Mathematics 2025-12-12 Shengbo Wang , Nian Si

Many robotic tasks are composed of a lot of temporally correlated sub-tasks in a highly complex environment. It is important to discover situational intentions and proper actions by deliberating on temporal abstractions to solve problems…

Machine Learning · Computer Science 2022-07-26 Se-Wook Yoo , Seung-Woo Seo

This paper establishes a rigorous connection between regularized discrete-time reinforcement learning (RL) and continuous-time stochastic optimal control. Specifically, classical RL algorithms are typically solving a regularized…

Optimization and Control · Mathematics 2026-04-24 Huyên Pham , Yuming Paul Zhang , Yuhua Zhu

Reinforcement learning systems require good representations to work well. For decades practical success in reinforcement learning was limited to small domains. Deep reinforcement learning systems, on the other hand, are scalable, not…

Machine Learning · Computer Science 2020-03-18 Sina Ghiassian , Banafsheh Rafiee , Yat Long Lo , Adam White

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

Optimization and Control · Mathematics 2021-06-08 Yong Sheng Soh , Venkat Chandrasekaran

We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…

Machine Learning · Computer Science 2022-05-18 Joao Monteiro , Mohamed Osama Ahmed , Hossein Hajimirsadeghi , Greg Mori

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

Numerical Analysis · Mathematics 2018-01-31 Martin Benning , Martin Burger

In this paper, we study the finite-sample statistical rates of distributional temporal difference (TD) learning with linear function approximation. The purpose of distributional TD learning is to estimate the return distribution of a…

Machine Learning · Statistics 2025-11-18 Kaicheng Jin , Yang Peng , Jiansheng Yang , Zhihua Zhang

In order for autonomous mobile robots to navigate in human spaces, they must abide by our social norms. Reinforcement learning (RL) has emerged as an effective method to train sequential decision-making policies that are able to respect…

Robotics · Computer Science 2024-03-01 Adam Sigal , Hsiu-Chin Lin , AJung Moon

Most conventional Reinforcement Learning (RL) algorithms aim to optimize decision-making rules in terms of the expected returns. However, especially for risk management purposes, other risk-sensitive criteria such as the value-at-risk or…

Machine Learning · Computer Science 2012-03-19 Tetsuro Morimura , Masashi Sugiyama , Hisashi Kashima , Hirotaka Hachiya , Toshiyuki Tanaka

Bootstrapping is behind much of the successes of Deep Reinforcement Learning. However, learning the value function via bootstrapping often leads to unstable training due to fast-changing target values. Target Networks are employed to…

Chaotic dynamical systems pose a fundamental challenge for Reinforcement Learning (RL): exponential sensitivity to initial conditions induces high-variance bootstrap targets and poorly conditioned gradient updates. Chaotic dynamics arise…

Machine Learning · Computer Science 2026-05-29 James Rudd-Jones , Mirco Musolesi , María Pérez-Ortiz

Modal regression, a widely used regression protocol, has been extensively investigated in statistical and machine learning communities due to its robustness to outliers and heavy-tailed noises. Understanding modal regression's theoretical…

Machine Learning · Statistics 2022-03-15 Tielang Gong , Yuxin Dong , Hong Chen , Bo Dong , Wei Feng , Chen Li

Many value-based deep reinforcement learning algorithms rely on target networks - lagged copies of the online network - to stabilize training. While effective, this mechanism introduces a fundamental stability-recency tradeoff: slower…

Machine Learning · Computer Science 2026-05-20 Leonard S. Pleiss , James Harrison , Maximilian Schiffer