Related papers: Methods for computing state similarity in Markov D…
We present a general framework for applying learning algorithms and heuristical guidance to the verification of Markov decision processes (MDPs). The primary goal of our techniques is to improve performance by avoiding an exhaustive…
In this paper, we present a novel iterative Monte Carlo method for approximating the stationary probability of a single state of a positive recurrent Markov chain. We utilize the characterization that the stationary probability of a state…
In many practical sequential decision-making problems, tracking the state of the environment incurs a sensing/communication/computation cost. In these settings, the agent's interaction with its environment includes the additional component…
Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to…
For a Markov decision process with countably infinite states, the optimal value may not be achievable in the set of stationary policies. In this paper, we study the existence conditions of an optimal stationary policy in a countable-state…
Within the framework of probably approximately correct Markov decision processes (PAC-MDP), much theoretical work has focused on methods to attain near optimality after a relatively long period of learning and exploration. However,…
Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods. A PDMP is…
We study an approximation method for partially observed Markov decision processes (POMDPs) with continuous spaces. Belief MDP reduction, which has been the standard approach to study POMDPs requires rigorous approximation methods for…
We develop a qualitative theory of Markov Decision Processes (MDPs) and Partially Observable MDPs that can be used to model sequential decision making tasks when only qualitative information is available. Our approach is based upon an…
For infinite-horizon average-cost criterion problems, there exist relatively few rigorous approximation and reinforcement learning results. In this paper, for Markov Decision Processes (MDPs) with standard Borel spaces, (i) we first provide…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…
The online Markov decision process (MDP) is a generalization of the classical Markov decision process that incorporates changing reward functions. In this paper, we propose practical online MDP algorithms with policy iteration and…
We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The…
We consider a finite number of $N$ statistically equal agents, each moving on a finite set of states according to a continuous-time Markov Decision Process (MDP). Transition intensities of the agents and generated rewards depend not only on…
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…
We consider probability measures on $\mathbb{R}^{\infty}$ and study optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include 1) quasi-product measures, 2) measures with certain symmetric…
We describe a generalization of the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) which is able to encode prior information that state transitions are more likely between "nearby" states. This is accomplished by defining a…
We consider synchronizing properties of Markov decision processes (MDP), viewed as generators of sequences of probability distributions over states. A probability distribution is p-synchronizing if the probability mass is at least p in some…
In this work we introduce new approximate similarity relations that are shown to be key for policy (or control) synthesis over general Markov decision processes. The models of interest are discrete-time Markov decision processes, endowed…
Analyzing the Markov decision process (MDP) with continuous state spaces is generally challenging. A recent interesting work \cite{shah2018q} solves MDP with bounded continuous state space by a nearest neighbor $Q$ learning approach, which…