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In this paper we provide faster algorithms for approximately solving discounted Markov Decision Processes in multiple parameter regimes. Given a discounted Markov Decision Process (DMDP) with $|S|$ states, $|A|$ actions, discount factor…

Data Structures and Algorithms · Computer Science 2020-12-24 Aaron Sidford , Mengdi Wang , Xian Wu , Yinyu Ye

The standard version of the policy iteration (PI) algorithm fails for semicontinuous models, that is, for models with lower semicontinuous one-step costs and weakly continuous transition law. This is due to the lack of continuity properties…

Optimization and Control · Mathematics 2023-07-17 Óscar Vega-Amaya , Fernando Luque-Vásquez

We present the first finite time global convergence analysis of policy gradient in the context of infinite horizon average reward Markov decision processes (MDPs). Specifically, we focus on ergodic tabular MDPs with finite state and action…

Machine Learning · Computer Science 2024-03-12 Navdeep Kumar , Yashaswini Murthy , Itai Shufaro , Kfir Y. Levy , R. Srikant , Shie Mannor

We study the sample complexity of learning an $\varepsilon$-optimal policy in an average-reward Markov decision process (MDP) under a generative model. We establish the complexity bound $\widetilde{O}\left(SA\frac{H}{\varepsilon^2}…

Machine Learning · Computer Science 2024-03-21 Matthew Zurek , Yudong Chen

We consider Markov Decision Processes (MDPs) in which every stationary policy induces the same graph structure for the underlying Markov chain and further, the graph has the following property: if we replace each recurrent class by a node,…

Machine Learning · Computer Science 2021-03-10 Joseph Lubars , Anna Winnicki , Michael Livesay , R. Srikant

We consider infinite-horizon $\gamma$-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. We consider the algorithm Value Iteration and the sequence of policies $\pi_1,...,\pi_k$ it…

Artificial Intelligence · Computer Science 2012-04-02 Bruno Scherrer

Unique Sink Orientations (USOs) are an appealing abstraction of several major optimization problems of applied mathematics such as for instance Linear Programming (LP), Markov Decision Processes (MDPs) or 2-player Turn Based Stochastic…

Discrete Mathematics · Computer Science 2015-01-12 Romain Hollanders , Balázs Gerencsér , Jean-Charles Delvenne , Raphaël M. Jungers

We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on Policy Search algorithms, that compute an approximately optimal policy by following the standard Policy Iteration (PI)…

Artificial Intelligence · Computer Science 2013-06-04 Bruno Scherrer

Consider the problem of approximating the optimal policy of a Markov decision process (MDP) by sampling state transitions. In contrast to existing reinforcement learning methods that are based on successive approximations to the nonlinear…

Machine Learning · Computer Science 2017-10-18 Mengdi Wang

In this paper we consider the problem of computing an $\epsilon$-optimal policy of a discounted Markov Decision Process (DMDP) provided we can only access its transition function through a generative sampling model that given any…

Optimization and Control · Mathematics 2019-06-07 Aaron Sidford , Mengdi Wang , Xian Wu , Lin F. Yang , Yinyu Ye

In this paper we propose an on-line policy iteration (PI) algorithm for finite-state infinite horizon discounted dynamic programming, whereby the policy improvement operation is done on-line, only for the states that are encountered during…

Optimization and Control · Mathematics 2021-06-03 Dimitri Bertsekas

We revisit the problem of finding optimal strategies for deterministic Markov Decision Processes (DMDPs), and a closely related problem of testing feasibility of systems of $m$ linear inequalities on $n$ real variables with at most two…

Data Structures and Algorithms · Computer Science 2021-10-29 Adam Karczmarz

Value iteration is a commonly used and empirically competitive method in solving many Markov decision process problems. However, it is known that value iteration has only pseudo-polynomial complexity in general. We establish a somewhat…

Artificial Intelligence · Computer Science 2013-01-07 Omid Madani

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

We study policy optimization in an infinite horizon, $\gamma$-discounted constrained Markov decision process (CMDP). Our objective is to return a policy that achieves large expected reward with a small constraint violation. We consider the…

Machine Learning · Computer Science 2022-04-12 Arushi Jain , Sharan Vaswani , Reza Babanezhad , Csaba Szepesvari , Doina Precup

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

This work considers the sample complexity of obtaining an $\varepsilon$-optimal policy in an average reward Markov Decision Process (AMDP), given access to a generative model (simulator). When the ground-truth MDP is weakly communicating,…

Machine Learning · Computer Science 2022-12-02 Jinghan Wang , Mengdi Wang , Lin F. Yang

We study the sample complexity of learning an $\varepsilon$-optimal policy in an average-reward Markov decision process (MDP) under a generative model. For weakly communicating MDPs, we establish the complexity bound…

Machine Learning · Computer Science 2025-02-25 Matthew Zurek , Yudong Chen

Markov decision processes (MDPs) is viewed as an optimization of an objective function over certain linear operators over general function spaces. A new existence result is established for the existence of optimal policies in general MDPs,…

Machine Learning · Computer Science 2026-04-01 Abhishek Gupta , Aditya Mahajan

This note provides upper bounds on the number of operations required to compute by value iterations a nearly optimal policy for an infinite-horizon discounted Markov decision process with a finite number of states and actions. For a given…

Optimization and Control · Mathematics 2020-01-29 Eugene A. Feinberg , Gaojin He