Related papers: Reducing Blackwell and Average Optimality to Disco…
Markov Decision Problems (MDPs) provide a foundational framework for modelling sequential decision-making across diverse domains, guided by optimality criteria such as discounted and average rewards. However, these criteria have inherent…
Robust Markov Decision Processes (RMDPs) are a widely used framework for sequential decision-making under parameter uncertainty. RMDPs have been extensively studied when the objective is to maximize the discounted return, but little is…
In robust Markov decision processes (MDPs), the uncertainty in the transition kernel is addressed by finding a policy that optimizes the worst-case performance over an uncertainty set of MDPs. While much of the literature has focused on…
Although average gain optimality is a commonly adopted performance measure in Markov Decision Processes (MDPs), it is often too asymptotic. Further incorporating measures of immediate losses leads to the hierarchy of bias optimalities, all…
In this paper we provide faster algorithms for approximately solving discounted Markov Decision Processes in multiple parameter regimes. Given a discounted Markov Decision Process (DMDP) with $|S|$ states, $|A|$ actions, discount factor…
In this paper we consider the problem of computing an $\epsilon$-optimal policy of a discounted Markov Decision Process (DMDP) provided we can only access its transition function through a generative sampling model that given any…
N-discount optimality was introduced as a hierarchical form of policy- and value-function optimality, with Blackwell optimality lying at the top level of the hierarchy Veinott (1969); Blackwell (1962). We formalize notions of myopic…
This work provides a novel interpretation of Markov Decision Processes (MDP) from the online optimization viewpoint. In such an online optimization context, the policy of the MDP is viewed as the decision variable while the corresponding…
This paper provides conditions under which total-cost and average-cost Markov decision processes (MDPs) can be reduced to discounted ones. Results are given for transient total-cost MDPs with tran- sition rates whose values may be greater…
This paper studies convergence properties of optimal values and actions for discounted and average-cost Markov Decision Processes (MDPs) with weakly continuous transition probabilities and applies these properties to the stochastic…
In this paper, we consider the finite-state approximation of a discrete-time constrained Markov decision process (MDP) under the discounted and average cost criteria. Using the linear programming formulation of the constrained discounted…
Markov decision processes (MDPs) are the defacto frame-work for sequential decision making in the presence ofstochastic uncertainty. A classical optimization criterion forMDPs is to maximize the expected discounted-sum pay-off, which…
We investigate refinements of the mean-payoff criterion in two-player zero-sum perfect-information stochastic games. A strategy is Blackwell optimal if it is optimal in the discounted game for all discount factors sufficiently close to $1$.…
This note describes sufficient conditions under which total-cost and average-cost Markov decision processes (MDPs) with general state and action spaces, and with weakly continuous transition probabilities, can be reduced to discounted MDPs.…
Reinforcement learning (RL) agents have traditionally been tasked with maximizing the value function of a Markov decision process (MDP), either in continuous settings, with fixed discount factor $\gamma < 1$, or in episodic settings, with…
Although in recent years reinforcement learning has become very popular the number of successful applications to different kinds of operations research problems is rather scarce. Reinforcement learning is based on the well-studied dynamic…
We consider a dynamic programming (DP) approach to approximately solving an infinite-horizon constrained Markov decision process (CMDP) problem with a fixed initial-state for the expected total discounted-reward criterion with a…
We study discrete-time Markov Decision Processes (MDPs) on finite state-action spaces and analyze the stability of optimal policies and value functions in the long-run discounted risk-sensitive objective setting. Our analysis addresses…
In this technical note, we establish an upper-bound on the threshold on the discount factor starting from which all discounted-optimal deterministic policies are gain-optimal, that we prove to be tight on an example. To address…
This paper is devoted to studying constrained continuous-time Markov decision processes (MDPs) in the class of randomized policies depending on state histories. The transition rates may be unbounded, the reward and costs are admitted to be…