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We introduce the Blackwell discount factor for Markov Decision Processes (MDPs). Classical objectives for MDPs include discounted, average, and Blackwell optimality. Many existing approaches to computing average-optimal policies solve for…

Machine Learning · Computer Science 2024-07-04 Julien Grand-Clément , Marek Petrik

Markov decision processes (MDPs) and simple stochastic games (SSGs) provide a rich mathematical framework to study many important problems related to probabilistic systems. MDPs and SSGs with finite-horizon objectives, where the goal is to…

Computer Science and Game Theory · Computer Science 2012-09-18 Krishnendu Chatterjee , Rasmus Ibsen-Jensen

Informed and robust decision making in the face of uncertainty is critical for robots that perform physical tasks alongside people. We formulate this as Bayesian Reinforcement Learning over latent Markov Decision Processes (MDPs). While…

Robotics · Computer Science 2020-02-11 Gilwoo Lee , Brian Hou , Sanjiban Choudhury , Siddhartha S. Srinivasa

Many dynamic decision problems, such as robotic control, involve a series of tasks, many of which are unknown at training time. Typical approaches for these problems, such as multi-task and meta reinforcement learning, do not generalize…

Machine Learning · Computer Science 2025-05-28 Luise Ge , Michael Lanier , Anindya Sarkar , Bengisu Guresti , Chongjie Zhang , Yevgeniy Vorobeychik

Markov decision processes (MDPs) are used to model stochastic systems in many applications. Several efficient algorithms to compute optimal policies have been studied in the literature, including value iteration (VI) and policy iteration.…

Optimization and Control · Mathematics 2021-08-30 Vineet Goyal , Julien Grand-Clement

Markov Decision Processes (MDPs) are an effective way to formally describe many Machine Learning problems. In fact, recently MDPs have also emerged as a powerful framework to model financial trading tasks. For example, financial MDPs can…

Computational Engineering, Finance, and Science · Computer Science 2021-07-21 Diego Pino , Javier García , Fernando Fernández , Svitlana S Vyetrenko

Contextual Markov decision processes (CMDPs) describe a class of reinforcement learning problems in which the transition kernels and reward functions can change over time with different MDPs indexed by a context variable. While CMDPs serve…

Machine Learning · Computer Science 2024-02-06 Junze Deng , Yuan Cheng , Shaofeng Zou , Yingbin Liang

Policy-based algorithms are among the most widely adopted techniques in model-free RL, thanks to their strong theoretical groundings and good properties in continuous action spaces. Unfortunately, these methods require precise and…

Machine Learning · Computer Science 2023-06-14 Luca Sabbioni , Francesco Corda , Marcello Restelli

We introduce and study constrained Markov Decision Processes (cMDPs) with anytime constraints. An anytime constraint requires the agent to never violate its budget at any point in time, almost surely. Although Markovian policies are no…

Machine Learning · Computer Science 2024-06-14 Jeremy McMahan , Xiaojin Zhu

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

Constrained Markov Decision Process (CMDP) is a natural framework for reinforcement learning tasks with safety constraints, where agents learn a policy that maximizes the long-term reward while satisfying the constraints on the long-term…

Artificial Intelligence · Computer Science 2018-02-20 Qingkai Liang , Fanyu Que , Eytan Modiano

In the Markov decision process model, policies are usually evaluated by expected cumulative rewards. As this decision criterion is not always suitable, we propose in this paper an algorithm for computing a policy optimal for the quantile…

Artificial Intelligence · Computer Science 2016-12-02 Hugo Gilbert , Paul Weng , Yan Xu

We present new algorithms for computing and approximating bisimulation metrics in Markov Decision Processes (MDPs). Bisimulation metrics are an elegant formalism that capture behavioral equivalence between states and provide strong…

Machine Learning · Computer Science 2019-11-22 Pablo Samuel Castro

We study the multiple-policy evaluation problem where we are given a set of $K$ policies and the goal is to evaluate their performance (expected total reward over a fixed horizon) to an accuracy $\epsilon$ with probability at least…

Machine Learning · Computer Science 2026-01-13 Yilei Chen , Aldo Pacchiano , Ioannis Ch. Paschalidis

Large-scale Markov decision processes (MDPs) require planning algorithms with runtime independent of the number of states of the MDP. We consider the planning problem in MDPs using linear value function approximation with only weak…

Machine Learning · Computer Science 2020-07-14 Roshan Shariff , Csaba Szepesvári

Motivated by many application problems, we consider Markov decision processes (MDPs) with a general loss function and unknown parameters. To mitigate the epistemic uncertainty associated with unknown parameters, we take a Bayesian approach…

Machine Learning · Computer Science 2025-10-02 Xiaoshuang Wang , Yifan Lin , Enlu Zhou

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

Decision-making under distribution shift is a central challenge in reinforcement learning (RL), where training and deployment environments differ. We study this problem through the lens of robust Markov decision processes (RMDPs), which…

Machine Learning · Computer Science 2025-10-17 Jingwen Gu , Yiting He , Zhishuai Liu , Pan Xu

We address the challenge of quantifying Bayesian uncertainty and incorporating it in offline use cases of finite-state Markov Decision Processes (MDPs) with unknown dynamics. Our approach provides a principled method to disentangle…

Machine Learning · Computer Science 2024-06-05 Filippo Valdettaro , A. Aldo Faisal

Policy Mirror Descent (PMD) is a general family of algorithms that covers a wide range of novel and fundamental methods in reinforcement learning. Motivated by the instability of policy iteration (PI) with inexact policy evaluation, PMD…

Optimization and Control · Mathematics 2023-11-23 Emmeran Johnson , Ciara Pike-Burke , Patrick Rebeschini
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