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We study the never-worse relation (NWR) for Markov decision processes with an infinite-horizon reachability objective. A state q is never worse than a state p if the maximal probability of reaching the target set of states from p is at most…
This article presents the complexity of reachability decision problems for parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a…
The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the…
This paper studies parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters. Fixing values for all parameters…
The paper addresses two variants of the stochastic shortest path problem ('optimize the accumulated weight until reaching a goal state') in Markov decision processes (MDPs) with integer weights. The first variant optimizes partial expected…
We introduce the notion of quantum Markov decision process (qMDP) as a semantic model of nondeterministic and concurrent quantum programs. It is shown by examples that qMDPs can be used in analysis of quantum algorithms and protocols. We…
Parametric Markov chains (pMC) are used to model probabilistic systems with unknown or partially known probabilities. Although (universal) pMC verification for reachability properties is known to be coETR-complete, there have been efforts…
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…
Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for…
Recent research in decision theoretic planning has focussed on making the solution of Markov decision processes (MDPs) more feasible. We develop a family of algorithms for structured reachability analysis of MDPs that are suitable when an…
We introduce and study constrained Markov Decision Processes (cMDPs) with anytime constraints. An anytime constraint requires the agent to never violate its budget at any point in time, almost surely. Although Markovian policies are no…
Computing optimal conditional reachability probabilities in Markov decision processes (MDPs) is tractable by a reduction to reachability probabilities. Yet, this reduction yields cyclic, challenging MDPs that are often notoriously hard to…
Value iteration is a well-known method of solving Markov Decision Processes (MDPs) that is simple to implement and boasts strong theoretical convergence guarantees. However, the computational cost of value iteration quickly becomes…
We study the computational complexity of the infinite-horizon discounted-reward Markov Decision Problem (MDP) with a finite state space $|\mathcal{S}|$ and a finite action space $|\mathcal{A}|$. We show that any randomized algorithm needs a…
Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
We introduce a mesh-type approach for tackling discrete-time, finite-horizon Markov Decision Processes (MDPs) characterized by state and action spaces that are general, encompassing both finite and infinite (yet suitably regular) subsets of…
Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process's probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal…
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…
Markov decision processes (MDPs) describe sequential decision-making processes; MDP policies return for every state in that process an advised action. Classical algorithms can efficiently compute policies that are optimal with respect to,…