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Policy Iteration (PI) is a widely used family of algorithms to compute optimal policies for Markov Decision Problems (MDPs). We derive upper bounds on the running time of PI on Deterministic MDPs (DMDPs): the class of MDPs in which every…

Discrete Mathematics · Computer Science 2023-10-10 Ritesh Goenka , Eashan Gupta , Sushil Khyalia , Pratyush Agarwal , Mulinti Shaik Wajid , Shivaram Kalyanakrishnan

In this paper we present a review of the connections between classical algorithms for solving Markov Decision Processes (MDPs) and classical gradient-based algorithms in convex optimization. Some of these connections date as far back as the…

Optimization and Control · Mathematics 2021-11-29 Julien Grand-Clément

Model checking undiscounted reachability and expected-reward properties on Markov decision processes (MDPs) is key for the verification of systems that act under uncertainty. Popular algorithms are policy iteration and variants of value…

Logic in Computer Science · Computer Science 2023-01-25 Arnd Hartmanns , Sebastian Junges , Tim Quatmann , Maximilian Weininger

Constrained decision-making is essential for designing safe policies in real-world control systems, yet simulated environments often fail to capture real-world adversities. We consider the problem of learning a policy that will maximize the…

Machine Learning · Computer Science 2026-02-10 Sourav Ganguly , Kishan Panaganti , Arnob Ghosh , Adam Wierman

Standard Markov decision process (MDP) and reinforcement learning algorithms optimize the policy with respect to the expected gain. We propose an algorithm which enables to optimize an alternative objective: the probability that the gain is…

Machine Learning · Computer Science 2023-03-06 Vincent Corlay , Jean-Christophe Sibel

Robust Markov decision processes (MDPs) allow to compute reliable solutions for dynamic decision problems whose evolution is modeled by rewards and partially-known transition probabilities. Unfortunately, accounting for uncertainty in the…

Machine Learning · Computer Science 2020-06-18 Chin Pang Ho , Marek Petrik , Wolfram Wiesemann

We propose a new simple and natural algorithm for learning the optimal Q-value function of a discounted-cost Markov Decision Process (MDP) when the transition kernels are unknown. Unlike the classical learning algorithms for MDPs, such as…

Optimization and Control · Mathematics 2019-01-31 Dileep Kalathil , Vivek S. Borkar , Rahul Jain

This note re-visits the rolling-horizon control approach to the problem of a Markov decision process (MDP) with infinite-horizon discounted expected reward criterion. Distinguished from the classical value-iteration approach, we develop an…

Optimization and Control · Mathematics 2022-06-07 Hyeong Soo Chang

One of the most widely used methods for solving average cost MDP problems is the value iteration method. This method, however, is often computationally impractical and restricted in size of solvable MDP problems. We propose acceleration…

Optimization and Control · Mathematics 2008-06-03 Oleksandr Shlakhter , Chi-Guhn Lee

While there is an extensive body of research on the analysis of Value Iteration (VI) for discounted cumulative-reward MDPs, prior work on analyzing VI for (undiscounted) average-reward MDPs has been limited, and most prior results focus on…

Optimization and Control · Mathematics 2026-02-10 Jongmin Lee , Ernest K. Ryu

Howard's Policy Iteration (HPI) is a classic algorithm for solving Markov Decision Problems (MDPs). HPI uses a "greedy" switching rule to update from any non-optimal policy to a dominating one, iterating until an optimal policy is found.…

Artificial Intelligence · Computer Science 2025-05-05 Dibyangshu Mukherjee , Shivaram Kalyanakrishnan

Robust Markov Decision Processes (RMDPs) have recently been recognized as a valuable and promising approach to discovering a policy with creditable performance, particularly in the presence of a dynamic environment and estimation errors in…

Optimization and Control · Mathematics 2024-06-04 Zhenwei Lin , Chenyu Xue , Qi Deng , Yinyu Ye

We consider approximate dynamic programming for the infinite-horizon stationary $\gamma$-discounted optimal control problem formalized by Markov Decision Processes. While in the exact case it is known that there always exists an optimal…

Optimization and Control · Mathematics 2013-04-23 Boris Lesner , Bruno Scherrer

Markov decision processes (MDPs) are a fundamental model in sequential decision making. Robust MDPs (RMDPs) extend this framework by allowing uncertainty in transition probabilities and optimizing against the worst-case realization of that…

Artificial Intelligence · Computer Science 2026-02-02 Ali Asadi , Krishnendu Chatterjee , Ehsan Goharshady , Mehrdad Karrabi , Alipasha Montaseri , Carlo Pagano

While Value Iteration (VI) is one of the most fundamental algorithms in Reinforcement Learning, its theoretical convergence guarantees still exhibit a persistent mismatch with empirical behavior. In the discounted-reward case, classical…

Machine Learning · Computer Science 2026-03-12 Arsenii Mustafin , Xinyi Sheng , Dominik Baumann

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

A basic model in sequential decision making is the Markov decision process (MDP), which is extended to Robust MDPs (RMDPs) by allowing uncertainty in transition probabilities and optimizing against the worst-case transition probabilities…

Computational Complexity · Computer Science 2026-05-11 Ali Asadi , Krishnendu Chatterjee , Alipasha Montaseri , Ali Shafiee

We consider inexact policy iteration methods for large-scale infinite-horizon discounted MDPs with finite spaces, a variant of policy iteration where the policy evaluation step is implemented inexactly using an iterative solver for linear…

Optimization and Control · Mathematics 2024-04-10 Matilde Gargiani , Robin Sieber , Efe Balta , Dominic Liao-McPherson , John Lygeros

Markov decision problems (MDPs) provide the foundations for a number of problems of interest to AI researchers studying automated planning and reinforcement learning. In this paper, we summarize results regarding the complexity of solving…

Artificial Intelligence · Computer Science 2013-02-21 Michael L. Littman , Thomas L. Dean , Leslie Pack Kaelbling

Algorithms developed under stationary Markov Decision Processes (MDPs) often face challenges in non-stationary environments, and infinite-horizon formulations may not directly apply to finite-horizon tasks. To address these limitations, we…

Machine Learning · Computer Science 2025-12-03 Zhizuo Chen , Theodore T. Allen