Related papers: On the Complexity of Reachability in Parametric Ma…
Markov Decision Processes (MDPs) are stochastic optimization problems that model situations where a decision maker controls a system based on its state. Partially observed Markov decision processes (POMDPs) are generalizations of MDPs where…
We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases…
Markov Decision Processes (MDPs) are a classical model for decision making in the presence of uncertainty. Often they are viewed as state transformers with planning objectives defined with respect to paths over MDP states. An increasingly…
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…
We propose a new approach to the problem of searching a space of policies for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP), given a model. Our approach is based on the following observation: Any…
Markov decision processes (MDPs) in queues and networks have been an interesting topic in many practical areas since the 1960s. This paper provides a detailed overview on this topic and tracks the evolution of many basic results. Also, this…
Given Markov chains and Markov decision processes (MDPs) whose transitions are labelled with non-negative integer costs, we study the computational complexity of deciding whether the probability of paths whose accumulated cost satisfies a…
Constrained Markov Decision Processes (CMDPs) are notably more complex to solve than standard MDPs due to the absence of universally optimal policies across all initial state distributions. This necessitates re-solving the CMDP whenever the…
Solving partially observable Markov decision processes (POMDPs) is highly intractable in general, at least in part because the optimal policy may be infinitely large. In this paper, we explore the problem of finding the optimal policy from…
Decision-making problems in uncertain or stochastic domains are often formulated as Markov decision processes (MDPs). Policy iteration (PI) is a popular algorithm for searching over policy-space, the size of which is exponential in the…
Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision making under uncertainty. The classical approaches for solving MDPs are well known and have been widely studied, some of which rely on…
Markov decision processes (MDPs) are a fundamental model for decision making under uncertainty. They exhibit non-deterministic choice as well as probabilistic uncertainty. Traditionally, verification algorithms assume exact knowledge of the…
We consider risk-sensitive Markov decision processes (MDPs), where the MDP model is influenced by a parameter which takes values in a compact metric space. We identify sufficient conditions under which small perturbations in the model…
We consider large-scale Markov decision processes (MDPs) with parameter uncertainty, under the robust MDP paradigm. Previous studies showed that robust MDPs, based on a minimax approach to handle uncertainty, can be solved using dynamic…
Probabilistic model checking aims to prove whether a Markov decision process (MDP) satisfies a temporal logic specification. The underlying methods rely on an often unrealistic assumption that the MDP is precisely known. Consequently,…
Computing reachability probabilities is at the heart of probabilistic model checking. All model checkers compute these probabilities in an iterative fashion using value iteration. This technique approximates a fixed point from below by…
This paper studies the computation of robust deterministic policies for Markov Decision Processes (MDPs) in the Lightning Does Not Strike Twice (LDST) model of Mannor, Mebel and Xu (ICML '12). In this model, designed to provide robustness…
We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the…
This paper studies Markov Decision Processes under parameter uncertainty. We adapt the distributionally robust optimization framework, and assume that the uncertain parameters are random variables following an unknown distribution, and…
We prove new upper and lower bounds for sample complexity of finding an $\epsilon$-optimal policy of an infinite-horizon average-reward Markov decision process (MDP) given access to a generative model. When the mixing time of the…