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Related papers: Yet Another Distributional Bellman Equation

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We present a hierarchical reinforcement learning framework that formulates each task in the hierarchy as a special type of Markov decision process for which the Bellman equation is linear and has analytical solution. Problems of this type,…

Artificial Intelligence · Computer Science 2016-03-11 Anders Jonsson , Vicenç Gómez

Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not…

Artificial Intelligence · Computer Science 2017-10-26 Dimitri Scheftelowitsch , Peter Buchholz , Vahid Hashemi , Holger Hermanns

Solving Markov Decision Processes (MDPs) remains a central challenge in sequential decision-making, especially when dealing with large state spaces and long-term optimization criteria. A key step in Bellman dynamic programming algorithms is…

Optimization and Control · Mathematics 2025-08-04 Youssef Ait El Mahjoub , Jean-Michel Fourneau , Salma Alouah

The linear Markov Decision Process (MDP) framework offers a principled foundation for reinforcement learning (RL) with strong theoretical guarantees and sample efficiency. However, its restrictive assumption-that both transition dynamics…

Machine Learning · Statistics 2025-06-03 Sinian Zhang , Kaicheng Zhang , Ziping Xu , Tianxi Cai , Doudou Zhou

We study the convergence of Markov Decision Processes made of a large number of objects to optimization problems on ordinary differential equations (ODE). We show that the optimal reward of such a Markov Decision Process, satisfying a…

Artificial Intelligence · Computer Science 2011-05-20 Nicolas Gast , Bruno Gaujal , Jean-Yves Le Boudec

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

The goal of a traditional Markov decision process (MDP) is to maximize expected cumulative reward over a defined horizon (possibly infinite). In many applications, however, a decision maker may be interested in optimizing a specific…

Artificial Intelligence · Computer Science 2025-10-16 Xiaocheng Li , Huaiyang Zhong , Margaret L. Brandeau

We propose solution methods for previously-unsolved constrained MDPs in which actions can continuously modify the transition probabilities within some acceptable sets. While many methods have been proposed to solve regular MDPs with large…

Artificial Intelligence · Computer Science 2013-09-27 Marek Petrik , Dharmashankar Subramanian , Janusz Marecki

Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to…

Optimization and Control · Mathematics 2022-12-19 Hoang Nam Nguyen , Abdel Lisser , Vikas Vikram Singh

Markov Decision Process (MDP) presents a mathematical framework to formulate the learning processes of agents in reinforcement learning. MDP is limited by the Markovian assumption that a reward only depends on the immediate state and…

Machine Learning · Computer Science 2024-06-04 Bohao Qu , Xiaofeng Cao , Jielong Yang , Hechang Chen , Chang Yi , Ivor W. Tsang , Yew-Soon Ong

We study infinite-horizon Markov Decision Processes (MDPs) with a continuum of heterogeneous agents interacting through a common noise, without assuming exchangeability. We introduce the framework of Conditional Non-Exchangeable Mean Field…

Optimization and Control · Mathematics 2026-03-03 Samy Mekkaoui , Huyên Pham

In reinforcement learning (RL), aligning agent behavior with specific objectives typically requires careful design of the reward function, which can be challenging when the desired objectives are complex. In this work, we propose an…

Machine Learning · Computer Science 2025-09-05 Yuting Tang , Yivan Zhang , Johannes Ackermann , Yu-Jie Zhang , Soichiro Nishimori , Masashi Sugiyama

In this paper, we show the convergence rates of posterior distributions of the model dynamics in a MDP for both episodic and continuous tasks. The theoretical results hold for general state and action space and the parameter space of the…

Statistics Theory · Mathematics 2019-07-23 Zhen Li , Eric Laber

Discrete time stochastic optimal control problems and Markov decision processes (MDPs), respectively, serve as fundamental models for problems that involve sequential decision making under uncertainty and as such constitute the theoretical…

Optimization and Control · Mathematics 2023-03-08 Christian Beck , Arnulf Jentzen , Konrad Kleinberg , Thomas Kruse

We develop an exhaustive study of Markov decision process (MDP) under mean field interaction both on states and actions in the presence of common noise, and when optimization is performed over open-loop controls on infinite horizon. Such…

Optimization and Control · Mathematics 2021-09-10 Médéric Motte , Huyên Pham

We present the first finite-sample analysis of policy evaluation in robust average-reward Markov Decision Processes (MDPs). Prior work in this setting have established only asymptotic convergence guarantees, leaving open the question of…

Machine Learning · Statistics 2025-12-11 Yang Xu , Washim Uddin Mondal , Vaneet Aggarwal

We propose a general framework for entropy-regularized average-reward reinforcement learning in Markov decision processes (MDPs). Our approach is based on extending the linear-programming formulation of policy optimization in MDPs to…

Machine Learning · Computer Science 2017-05-23 Gergely Neu , Anders Jonsson , Vicenç Gómez

We propose a diffusion approximation method to the continuous-state Markov Decision Processes (MDPs) that can be utilized to address autonomous navigation and control in unstructured off-road environments. In contrast to most…

Robotics · Computer Science 2024-02-08 Junhong Xu , Kai Yin , Zheng Chen , Jason M. Gregory , Ethan A. Stump , Lantao Liu

In this paper, we investigate the concentration properties of cumulative reward in Markov Decision Processes (MDPs), focusing on both asymptotic and non-asymptotic settings. We introduce a unified approach to characterize reward…

Machine Learning · Computer Science 2025-12-04 Borna Sayedana , Peter E. Caines , Aditya Mahajan

Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Mean payoff (or long-run average reward) provides a mathematically elegant formalism to express performance related…

Performance · Computer Science 2017-09-08 Jan Křetínský , Tobias Meggendorfer