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In this paper, we consider an integrated MSP-MDP framework which captures features of Markov decision process (MDP) and multistage stochastic programming (MSP). The integrated framework allows one to study a dynamic decision-making process…

In the Markov decision process model, policies are usually evaluated by expected cumulative rewards. As this decision criterion is not always suitable, we propose in this paper an algorithm for computing a policy optimal for the quantile…

This paper deals with the infinite-horizon optimal control problem for Boolean control networks (BCNs) with a discounted-cost criterion. This problem has been investigated in existing studies with algorithms characterized by high…

The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…

We present a technique for speeding up the convergence of value iteration for partially observable Markov decisions processes (POMDPs). The underlying idea is similar to that behind modified policy iteration for fully observable Markov…

We introduce a new method, stepwise method for solving optimal con- trol problems. Our first motivation for new approach emanate from limi- tations on continuous time control functions in PMP. Practically in most of the real world models,…

Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition…

We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…

Constrained Markov decision processes (CMDPs) are used as a decision-making framework to study the long-run performance of a stochastic system. It is well-known that a stationary optimal policy of a CMDP problem under discounted cost…

The present paper considers the constrained optimal control problem with total undiscounted criteria for a continuous-time Markov decision process (CTMDP) in Borel state and action spaces. Under the standard compactness and continuity…

We present existence and discrete-time approximation results on optimal control policies for continuous-time stochastic control problems under a variety of information structures. These include fully observed models, partially observed…

We consider the problem of designing policies for partially observable Markov decision processes (POMDPs) with dynamic coherent risk objectives. Synthesizing risk-averse optimal policies for POMDPs requires infinite memory and thus…

This papers deals with the constrained discounted control of piecewise deterministic Markov process (PDMPs) in general Borel spaces. The control variable acts on the jump rate and transition measure, and the goal is to minimize the total…

We study policy optimization problems for deterministic Markov decision processes (MDPs) with metric state and action spaces, which we refer to as Metric Policy Optimization Problems (MPOPs). Our goal is to establish theoretical results on…

This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…

Partially Observable Markov Decision Processes (POMDPs) provide an efficient way to model real-world sequential decision making processes. Motivated by the problem of maintenance and inspection of a group of infrastructure components with…

This paper is concerned with the error analysis of two types of sampling algorithms, namely model predictive path integral (MPPI) and an interacting particle system (\IPS) algorithm, that have been proposed in the literature for numerical…

This paper considers a risk-constrained infinite-horizon optimal control problem and proposes to solve it in an iterative manner. Each iteration of the algorithm generates a trajectory from the starting point to the target equilibrium state…

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…

One often encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for controlled Markov chains. In this paper, we provide a method to construct sub-optimal policies along with a bound…