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In this paper, we introduce a novel form of value function, $Q(s, s')$, that expresses the utility of transitioning from a state $s$ to a neighboring state $s'$ and then acting optimally thereafter. In order to derive an optimal policy, we…

We study Markov decision processes with Polish state and action spaces. The action space is state dependent and is not necessarily compact. We first establish the existence of an optimal ergodic occupation measure using only a near-monotone…

Optimization and Control · Mathematics 2023-08-15 Ari Arapostathis , Vivek S. Borkar

Variational inference (VI) provides fast approximations of a Bayesian posterior in part because it formulates posterior approximation as an optimization problem: to find the closest distribution to the exact posterior over some family of…

Machine Learning · Statistics 2017-03-03 Fangjian Guo , Xiangyu Wang , Kai Fan , Tamara Broderick , David B. Dunson

Policy evaluation is a fundamental component of the development and deployment pipeline for robotic policies. In modern manipulation systems, this problem is particularly challenging: rewards are often sparse, task progression of evaluation…

Robotics · Computer Science 2026-05-13 Hao Wang , Joshua Bowden , Colton Crosby , Somil Bansal

The paper deals with a risk averse dynamic programming problem with infinite horizon. First, the required assumptions are formulated to have the problem well defined. Then the Bellman equation is derived, which may be also seen as a…

Optimization and Control · Mathematics 2022-08-04 Martin Šmíd , Miloš Kopa

Reinforcement Learning with Verifiable Rewards (RLVR) has become the standard paradigm for LLM mathematical reasoning, with Group Relative Policy Optimization (GRPO) serving as the dominant algorithm. We identify two overlooked…

Machine Learning · Computer Science 2026-05-13 Mingxiong Lin , Zhangquan Gong , Maowen Tang , Qian Li , Chuangchuang Wang , Jian Ma , Sutian Huang , Kai Tang , Haonan Lu

We consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address…

Machine Learning · Computer Science 2018-04-23 Alec Koppel , Ekaterina Tolstaya , Ethan Stump , Alejandro Ribeiro

We determine, up to lower-order terms in the exponent, the best possible deterministic polynomial-time approximation ratio for the permanent of a Hermitian positive semidefinite matrix. If $A\succeq 0$ has no zero diagonal entry,…

Data Structures and Algorithms · Computer Science 2026-05-22 Nima Anari , Farzam Ebrahimnejad

We introduce a framework for approximate dynamic programming that we apply to discrete time chains on $\mathbb{Z}_+^d$ with countable action sets. Our approach is grounded in the approximation of the (controlled) chain's generator by that…

Optimization and Control · Mathematics 2018-04-16 Anton Braverman , Itai Gurvich , Junfei Huang

Although average gain optimality is a commonly adopted performance measure in Markov Decision Processes (MDPs), it is often too asymptotic. Further incorporating measures of immediate losses leads to the hierarchy of bias optimalities, all…

Machine Learning · Computer Science 2025-10-16 Victor Boone , Adrienne Tuynman

This paper investigates the computational complexity of reinforcement learning in a novel linear function approximation regime, termed partial $q^{\pi}$-realizability. In this framework, the objective is to learn an $\epsilon$-optimal…

Artificial Intelligence · Computer Science 2025-10-31 Shayan Karimi , Xiaoqi Tan

Regularization is one of the most important techniques in reinforcement learning algorithms. The well-known soft actor-critic algorithm is a special case of regularized policy iteration where the regularizer is chosen as Shannon entropy.…

Machine Learning · Computer Science 2023-10-12 Zeyang Li , Chuxiong Hu , Yunan Wang , Guojian Zhan , Jie Li , Shengbo Eben Li

The objective in this paper is to obtain fast converging reinforcement learning algorithms to approximate solutions to the problem of discounted cost optimal stopping in an irreducible, uniformly ergodic Markov chain, evolving on a compact…

Systems and Control · Computer Science 2019-10-01 Shuhang Chen , Adithya M. Devraj , Ana Bušić , Sean P. Meyn

Simple stochastic games can be solved by value iteration (VI), which yields a sequence of under-approximations of the value of the game. This sequence is guaranteed to converge to the value only in the limit. Since no stopping criterion is…

Logic in Computer Science · Computer Science 2021-02-02 Edon Kelmendi , Julia Krämer , Jan Kretinsky , Maximilian Weininger

We present the convergence rates of synchronous and asynchronous Q-learning for average-reward Markov decision processes, where the absence of contraction poses a fundamental challenge. Existing non-asymptotic results overcome this…

Machine Learning · Computer Science 2026-01-30 Zijun Chen , Zaiwei Chen , Nian Si , Shengbo Wang

Guided policy search is a popular approach for training controllers for high-dimensional systems, but it has a number of pitfalls. Non-convex trajectory optimization has local minima, and non-uniqueness in the optimal policy itself can mean…

Robotics · Computer Science 2018-09-18 Robin Deits , Twan Koolen , Russ Tedrake

Value iteration is a fundamental algorithm for solving Markov Decision Processes (MDPs). It computes the maximal $n$-step payoff by iterating $n$ times a recurrence equation which is naturally associated to the MDP. At the same time, value…

Formal Languages and Automata Theory · Computer Science 2019-04-30 Nikhil Balaji , Stefan Kiefer , Petr Novotný , Guillermo A. Pérez , Mahsa Shirmohammadi

Current approaches to model-based offline reinforcement learning often incorporate uncertainty-based reward penalization to address the distributional shift problem. These approaches, commonly known as pessimistic value iteration, use Monte…

Machine Learning · Computer Science 2025-01-17 Abdullah Akgül , Manuel Haußmann , Melih Kandemir

We study reinforcement learning for global decision-making in the presence of local agents, where the global decision-maker makes decisions affecting all local agents, and the objective is to learn a policy that maximizes the joint rewards…

Machine Learning · Computer Science 2024-10-24 Emile Anand , Guannan Qu

In this work, we present the first finite-time analysis of Q-learning with time-varying learning policies (i.e., on-policy sampling) for discounted Markov decision processes under minimal assumptions, requiring only the existence of a…

Machine Learning · Computer Science 2026-04-07 Phalguni Nanda , Zaiwei Chen