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The two expected average costs used in the theory of semi-Markov control processes with a Borel state space are considered. Under some stochastic stability conditions, we prove that the two criteria are equivalent in the sense that they…

Optimization and Control · Mathematics 2013-09-20 Anna Jaśkiewicz

Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…

Logic in Computer Science · Computer Science 2017-05-11 Tim Quatmann , Sebastian Junges , Joost-Pieter Katoen

Long-run average optimization problems for Markov decision processes (MDPs) require constructing policies with optimal steady-state behavior, i.e., optimal limit frequency of visits to the states. However, such policies may suffer from…

Multiagent Systems · Computer Science 2023-12-20 David Klaška , Antonín Kučera , Vojtěch Kůr , Vít Musil , Vojtěch Řehák

In this paper, we consider a Markov decision process (MDP) with a Borel state space $\textbf{X}\cup\{\Delta\}$, where $\Delta$ is an absorbing state (cemetery), and a Borel action space $\textbf{A}$. We consider the space of finite…

Optimization and Control · Mathematics 2023-07-07 Alexey Piunovskiy , Yi Zhang

We study optimal control of Markov processes with age-dependent transition rates. The control policy is chosen continuously over time based on the state of the process and its age. We study infinite horizon discounted cost and infinite…

Optimization and Control · Mathematics 2014-09-16 Mrinal K. Ghosh , Subhamay Saha

The main goal of this paper is to derive sufficient conditions for the existence of an optimal control strategy for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a…

Probability · Mathematics 2008-12-05 O. L. V. Costa , F. Dufour

We consider robust Markov Decision Processes with Borel state and action spaces, unbounded cost and finite time horizon. Our formulation leads to a Stackelberg game against nature. Under integrability, continuity and compactness assumptions…

Optimization and Control · Mathematics 2025-10-16 Nicole Bäuerle , Alexander Glauner

We show that combinations of optimal (stationary) policies in unichain Markov decision processes are optimal. That is, let M be a unichain Markov decision process with state space S, action space A and policies \pi_j^*: S -> A (1\leq j\leq…

Combinatorics · Mathematics 2007-05-23 Ronald Ortner

For time-inconsistent stochastic controls in discrete time and finite horizon, an open problem in Bj\"ork and Murgoci (Finance Stoch, 2014) is the existence of an equilibrium control. A nonrandomized Borel measurable Markov equilibrium…

Optimization and Control · Mathematics 2023-12-18 Erhan Bayraktar , Bingyan Han

This paper provides conditions under which total-cost and average-cost Markov decision processes (MDPs) can be reduced to discounted ones. Results are given for transient total-cost MDPs with tran- sition rates whose values may be greater…

Optimization and Control · Mathematics 2017-05-04 Eugene A. Feinberg , Jefferson Huang

This work concerns controlled Markov chains with finite state and action spaces. The transition law satisfies the simultaneous Doeblin condition, and the performance of a control policy is measured by the (long-run) risk-sensitive average…

Probability · Mathematics 2007-05-23 Rolando Cavazos-Cadena , Daniel Hernandez-Hernandez

We consider an absorbing Markov decision process with Borel state and action spaces. We study conditions under which the MDP is uniformly absorbing and the set of occupation measures of the MDP is compact in the usual weak topology. These…

Probability · Mathematics 2024-04-30 François Dufour , Tomás Prieto-Rumeau

In this paper, we consider the discounted continuous-time Markov decision process (CTMDP) with a lower bounding function. In this model, the negative part of each cost rate is bounded by the drift function, say $w$, whereas the positive…

Optimization and Control · Mathematics 2016-12-05 Xin Guo , Alexey Piunovskiy , Yi Zhang

In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…

Optimization and Control · Mathematics 2020-06-23 Jinghai Shao , Kun Zhao

We present some hardness results on finding the optimal policy for the static formulation of distributionally robust Markov decision processes. We construct problem instances such that when the considered policy class is Markovian and…

Optimization and Control · Mathematics 2026-05-08 Yan Li

We analyze the infinite horizon minimax average cost Markov Control Model (MCM), for a class of controlled process conditional distributions, which belong to a ball, with respect to total variation distance metric, centered at a known…

Optimization and Control · Mathematics 2015-12-22 Ioannis Tzortzis , Charalambos D. Charalambous , Themistoklis Charalambous

We show that for several variations of partially observable Markov decision processes, polynomial-time algorithms for finding control policies are unlikely to or simply don't have guarantees of finding policies within a constant factor or a…

Artificial Intelligence · Computer Science 2011-06-02 J. Goldsmith , C. Lusena , M. Mundhenk

In this paper, we study discrete-time absorbing Markov Decision Processes (MDP) with measurable state space and Borel action space with a given initial distribution. For such models, solutions to the characteristic equation that are not…

Optimization and Control · Mathematics 2025-10-10 François Dufour , Tomás Prieto-Rumeau

In this paper, we consider the finite-state approximation of a discrete-time constrained Markov decision process (MDP) under the discounted and average cost criteria. Using the linear programming formulation of the constrained discounted…

Optimization and Control · Mathematics 2018-07-10 Naci Saldi

We consider infinite-horizon stationary $\gamma$-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. Using Value and Policy Iteration with some error $\epsilon$ at each iteration, it is…

Machine Learning · Computer Science 2012-11-30 Bruno Scherrer , Boris Lesner