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This note describes sufficient conditions under which total-cost and average-cost Markov decision processes (MDPs) with general state and action spaces, and with weakly continuous transition probabilities, can be reduced to discounted MDPs.…

Optimization and Control · Mathematics 2017-11-21 Eugene A. Feinberg , Jefferson Huang

We introduce and study the infinite dimensional linear programming problem which along with its dual allows one to characterize the optimal value of the deterministic long-run average optimal control problem in the general case when the…

Optimization and Control · Mathematics 2018-05-08 Vivek S. Borkar , Vladimir Gaitsgory

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

Computational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of an irreducible Markov chain, are developed using perturbations. The derivation of these…

Probability · Mathematics 2016-10-12 Jeffrey J. Hunter

We are interested in risk constraints for infinite horizon discrete time Markov decision processes (MDPs). Starting with average reward MDPs, we show that increasing concave stochastic dominance constraints on the empirical distribution of…

Optimization and Control · Mathematics 2012-06-21 William B. Haskell , Rahul Jain

We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…

Optimization and Control · Mathematics 2026-04-21 Yuchao Li , Dimitri Bertsekas

We formulate and study the infinite dimensional linear programming (LP) problem associated with the deterministic discrete time long-run average criterion optimal control problem. Along with its dual, this LP problem allows one to…

Optimization and Control · Mathematics 2019-05-29 Vivek S. Borkar , Vladimir Gaitsgory , Ilya Shvartsman

There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both…

Artificial Intelligence · Computer Science 2026-02-24 Donghwan Lee , Hyukjun Yang , Bum Geun Park

Robust Markov decision processes (MDPs) aim to handle changing or partially known system dynamics. To solve them, one typically resorts to robust optimization methods. However, this significantly increases computational complexity and…

Machine Learning · Computer Science 2023-03-14 Esther Derman , Yevgeniy Men , Matthieu Geist , Shie Mannor

We consider challenging dynamic programming models where the associated Bellman equation, and the value and policy iteration algorithms commonly exhibit complex and even pathological behavior. Our analysis is based on the new notion of…

Optimization and Control · Mathematics 2016-09-13 Dimitri P. Bertsekas

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

In Markov Decision Processes (MDPs) with intermittent state information, decision-making becomes challenging due to periods of missing observations. Linear programming (LP) methods can play a crucial role in solving MDPs, in particular,…

Optimization and Control · Mathematics 2025-09-09 Konstantin Avrachenkov , Madhu Dhiman , Veeraruna Kavitha

We study a class of infinite-horizon average-cost Markov Decision Processes (MDPs) whose reward and transition structures are nearly separable. For the totally separable baseline (that is, with no perturbation), we derive an explicit…

Optimization and Control · Mathematics 2025-10-28 Dhairya Kantawala

The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we…

Systems and Control · Computer Science 2018-10-10 Zhi Chen , Pengqian Yu , William B. Haskell

We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…

Logic in Computer Science · Computer Science 2015-12-17 Michael Bukatin , Steve Matthews

Markov decision processes (MDPs) are the defacto frame-work for sequential decision making in the presence ofstochastic uncertainty. A classical optimization criterion forMDPs is to maximize the expected discounted-sum pay-off, which…

Artificial Intelligence · Computer Science 2020-02-28 Tomas Brazdil , Krishnendu Chatterjee , Petr Novotny , Jiri Vahala

It is common to address the curse of dimensionality in Markov decision processes (MDPs) by exploiting low-rank representations. This motivates much of the recent theoretical study on linear MDPs. However, most approaches require a given…

Machine Learning · Computer Science 2022-12-09 Tianjun Zhang , Tongzheng Ren , Mengjiao Yang , Joseph E. Gonzalez , Dale Schuurmans , Bo Dai

The paper aims at the development of tools for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems with long run average optimality criteria. The idea that we exploit is to first…

Optimization and Control · Mathematics 2014-08-20 Vladimir Gaitsgory , Ludmila Manic , Sergey Rossomakhine

Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the…

Computer Science and Game Theory · Computer Science 2022-09-29 Krishnendu Chatterjee , Raimundo Saona , Bruno Ziliotto

We consider the constrained optimal control problem for the gradual-impulsive CTMDP model with the performance criteria being the expected total undiscounted costs (from the running cost and the cost from each time an impulse being…

Optimization and Control · Mathematics 2022-04-07 Alexey Piunovskiy , Yi Zhang