On the Expected Total Reward with Unbounded Returns for Markov Decision Processes

Continuous Time Markov Decision Processes with Expected Discounted Total Rewards

Abstract. This paper discusses continuous time Markov decision processes with criterion of expected discounted total rewards, where the state space is countable, the reward rate function is extended real-valued and the discount rate is a real number. Under necessary conditions that the model is well defined, the state space is partitioned into three subsets, on which the optimal value function ...

Markov Decision Processes with Arbitrary Reward Processes

We consider a learning problem where the decision maker interacts with a standard Markov decision process, with the exception that the reward functions vary arbitrarily over time. We show that, against every possible realization of the reward process, the agent can perform as well—in hindsight—as every stationary policy. This generalizes the classical no-regret result for repeated games. Specif...

Splitting Randomized Stationary Policies in Total-Reward Markov Decision Processes

This paper studies a discrete-time total-reward Markov decision process (MDP) with a given initial state distribution. A (randomized) stationary policy can be split on a given set of states if the occupancy measure of this policy can be expressed as a convex combination of the occupancy measures of stationary policies, each selecting deterministic actions on the given set and coinciding with th...

Controlled Markov Decision Processes with AVaR criteria for unbounded costs

In this paper, we consider the control problem with the Average-Value-at-Risk (AVaR) criteria of the possibly unbounded L1-costs in infinite horizon on a Markov Decision Process (MDP). With a suitable state aggregation and by choosing a priori a global variable s heuristically, we show that there exist optimal policies for the infinite horizon problem for possibly unbounded costs. Mathematics S...

On Markov Decision Processes with Pseudo-Boolean Reward Functions