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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.…

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…

We introduce Multi-Environment Markov Decision Processes (MEMDPs) which are MDPs with a set of probabilistic transition functions. The goal in a MEMDP is to synthesize a single controller with guaranteed performances against all…

Recent decision-making systems are increasingly complicated, making it crucial to verify and understand their behavior for a given specification. A promising approach is to comprehensively explain undesired behavior in the systems modeled…

Markov Decision Processes (Mdps) form a versatile framework used to model a wide range of optimization problems. The Mdp model consists of sets of states, actions, time steps, rewards, and probability transitions. When in a given state and…

While there is an extensive body of research on the analysis of Value Iteration (VI) for discounted cumulative-reward MDPs, prior work on analyzing VI for (undiscounted) average-reward MDPs has been limited, and most prior results focus on…

We study a finite time horizon Markov decision process (MDP) consisting of several groups of multi-action finite-state restless bandit processes, which are identical within each group. The bandit processes into different groups can be…

Value decomposition has long been a fundamental technique in multi-agent dynamic programming and reinforcement learning (RL). Specifically, the value function of a global state $(s_1,s_2,\ldots,s_N)$ is often approximated as the sum of…

This paper considers parametric Markov decision processes (pMDPs) whose transitions are equipped with affine functions over a finite set of parameters. The synthesis problem is to find a parameter valuation such that the instantiated pMDP…

In many practical settings control decisions must be made under partial/imperfect information about the evolution of a relevant state variable. Partially Observable Markov Decision Processes (POMDPs) is a relatively well-developed framework…

The key assumption underlying linear Markov Decision Processes (MDPs) is that the learner has access to a known feature map $\phi(x, a)$ that maps state-action pairs to $d$-dimensional vectors, and that the rewards and transitions are…

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…

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure,…

Piecewise-deterministic Markov processes (PDMPs) offer a powerful stochastic modeling framework that combines deterministic trajectories with random perturbations at random times. Estimating their local characteristics (particularly the…

Active classification, i.e., the sequential decision-making process aimed at data acquisition for classification purposes, arises naturally in many applications, including medical diagnosis, intrusion detection, and object tracking. In this…

POMDPs are useful models for systems where the true underlying state is not known completely to an outside observer; the outside observer incompletely knows the true state of the system, and observes a noisy version of the true system…

This study introduces a comparative modeling framework using stationary and non-stationary transition probabilities within a Markov Decision Process (MDP) to assess COVID-19 disease dynamics. Stationary transition probabilities assume…

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…

This paper presents with justifications a technique that is useful for the study of piecewise deterministic Markov decision processes (PDMDPs) with general policies and unbounded transition intensities. This technique produces an auxiliary…

In many operations management problems, we need to make decisions sequentially to minimize the cost while satisfying certain constraints. One modeling approach to study such problems is constrained Markov decision process (CMDP). When…