English
Related papers

Related papers: B\"uchi Objectives in Countable MDPs

200 papers

We study countably infinite stochastic 2-player games with reachability objectives. Our results provide a complete picture of the memory requirements of $\varepsilon$-optimal (resp. optimal) strategies. These results depend on the size of…

Computer Science and Game Theory · Computer Science 2024-07-03 Stefan Kiefer , Richard Mayr , Mahsa Shirmohammadi , Patrick Totzke

We consider discrete-time Markov decision processes in which the decision maker is interested in long but finite horizons. First we consider reachability objective: the decision maker's goal is to reach a specific target state with the…

Optimization and Control · Mathematics 2019-11-14 Galit Ashkenazi-Golan , János Flesch , Arkadi Predtetchinski , Eilon Solan

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

We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…

Systems and Control · Electrical Eng. & Systems 2022-07-13 Kush Grover , Jan Křetínský , Tobias Meggendorfer , Maximilian Weininger

It is well known that for any finite state Markov decision process (MDP) there is a memoryless deterministic policy that maximizes the expected reward. For partially observable Markov decision processes (POMDPs), optimal memoryless policies…

Optimization and Control · Mathematics 2016-02-16 Guido Montufar , Keyan Ghazi-Zahedi , Nihat Ay

We present metrics for measuring state similarity in Markov decision processes (MDPs) with infinitely many states, including MDPs with continuous state spaces. Such metrics provide a stable quantitative analogue of the notion of…

Artificial Intelligence · Computer Science 2012-07-09 Norman Ferns , Prakash Panangaden , Doina Precup

Optimal policies for partially observed Markov decision processes (POMDPs) are history-dependent: Decisions are made based on the entire history of observation. Memoryless policies, which take decisions based on the last observation only,…

Optimization and Control · Mathematics 2022-05-06 Victor Cohen , Axel Parmentier

We propose an algorithm for deterministic continuous Markov Decision Processes with sparse rewards that computes the optimal policy exactly with no dependency on the size of the state space. The algorithm has time complexity of $O( |R|^3…

Machine Learning · Computer Science 2018-05-21 Joshua R. Bertram , Peng Wei

We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with k limit-average functions, in the…

Computer Science and Game Theory · Computer Science 2015-07-01 Tomáš Brázdil , Václav Brožek , Krishnendu Chatterjee , Vojtěch Forejt , Antonín Kučera

Models of many real-life applications, such as queuing models of communication networks or computing systems, have a countably infinite state-space. Algorithmic and learning procedures that have been developed to produce optimal policies…

Systems and Control · Electrical Eng. & Systems 2024-03-19 Saghar Adler , Vijay Subramanian

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 study time-bounded reachability in continuous-time Markov decision processes for time-abstract scheduler classes. Such reachability problems play a paramount role in dependability analysis and the modelling of manufacturing and queueing…

Formal Languages and Automata Theory · Computer Science 2010-06-29 Markus Rabe , Sven Schewe

We study infinite-horizon Markov decision processes (MDPs) where the decision maker evaluates each of her strategies by aggregating the infinite stream of expected stage-rewards. The crucial feature of our approach is that the aggregation…

Optimization and Control · Mathematics 2026-03-05 János Flesch , Arkadi Predtetchinski , William D Sudderth , Xavier Venel

We consider infinite-state Markov decision processes (MDPs) that are induced by extensions of vector addition systems with states (VASS). Verification conditions for these MDPs are described by reachability and Buchi objectives w.r.t. given…

Logic in Computer Science · Computer Science 2016-01-14 Parosh Aziz Abdulla , Radu Ciobanu , Richard Mayr , Arnaud Sangnier , Jeremy Sproston

A standard model that arises in several applications in sequential decision making is partially observable Markov decision processes (POMDPs) where a decision-making agent interacts with an uncertain environment. A basic objective in such…

Computational Complexity · Computer Science 2025-06-16 Ali Asadi , Krishnendu Chatterjee , Raimundo Saona , Ali Shafiee

Calculating optimal policies is known to be computationally difficult for Markov decision processes (MDPs) with Borel state and action spaces. This paper studies finite-state approximations of discrete time Markov decision processes with…

Optimization and Control · Mathematics 2016-09-23 Naci Saldi , Serdar Yüksel , Tamás Linder

This paper investigates MDPs with intermittent state information. We consider a scenario where the controller perceives the state information of the process via an unreliable communication channel. The transmissions of state information…

Artificial Intelligence · Computer Science 2025-02-17 Gongpu Chen , Soung-Chang Liew

The goal of a traditional Markov decision process (MDP) is to maximize expected cumulative reward over a defined horizon (possibly infinite). In many applications, however, a decision maker may be interested in optimizing a specific…

Artificial Intelligence · Computer Science 2025-10-16 Xiaocheng Li , Huaiyang Zhong , Margaret L. Brandeau

We consider partially observable Markov decision processes (POMDPs) with {\omega}-regular conditions specified as parity objectives. The class of {\omega}-regular languages extends regular languages to infinite strings and provides a robust…

Logic in Computer Science · Computer Science 2013-09-12 Krishnendu Chatterjee , Martin Chmelik , Mathieu Tracol

What are the functionals of the reward that can be computed and optimized exactly in Markov Decision Processes?In the finite-horizon, undiscounted setting, Dynamic Programming (DP) can only handle these operations efficiently for certain…

Artificial Intelligence · Computer Science 2024-02-20 Alexandre Marthe , Aurélien Garivier , Claire Vernade