Search

This paper is concerned with the problem of minimizing the expected finite-horizon cost for piecewise deterministic Markov decision processes. The transition rates may be unbounded, and the cost functions are allowed to be unbounded from above and from below. The optimality is over the general history-dependent policies, where the control is continuously acting in time. The infinitesimal approach is employed to establish the associated Hamilton-Jacobi-Bellman equation, via which the existence of optimal policies is proved. An example is provided to verify all the assumptions proposed. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the risk probability criteria for finite horizon semi-Markov decision processes. The goal is to find an optimal policy with the minimum risk probability that the total reward produced by a system during a finite horizon does not exceed a reward level, where the optimality is over the class of all randomized historic policies which include states, planning horizons and also reward levels. Under mild conditions, the optimality equation and the existence of optimal policies are established, and in addition, an iteration algorithm for solving optimal policies is developed. Our main results are applied to a manufacturing system. [Copyright &y& Elsevier]

Abstract: This paper studies the risk minimization problem in semi-Markov decision processes with denumerable states. The criterion to be optimized is the risk probability (or risk function) that a first passage time to some target set doesn''t exceed a threshold value. We first characterize such risk functions and the corresponding optimal value function, and prove that the optimal value function satisfies the optimality equation by using a successive approximation technique. Then, we present some properties of optimal policies, and further give conditions for the existence of optimal policies. In addition, a value iteration algorithm and a policy improvement method for obtaining respectively the optimal value function and optimal policies are developed. Finally, two examples are given to illustrate the value iteration procedure and essential characterization of the risk function. [Copyright &y& Elsevier]