On Solving Optimal Policies for Finite-Stage Event-Based Optimization

Event-based optimization (EBO) has been developed to model a specific type of problems, in which decisions can be made only when certain events occur. Because the event sequence usually is not Markovian, how to solve optimal policies for EBOs remains open in general. Motivated by real applications, we focus on finite-stage EBOs with discrete state space in this technical note and make two contributions. First, we show that this EBO can be converted to a partially observable Markov decision process (POMDP). Based on this connection, existing exact and approximate solution methodologies for POMDPs can then be applied to EBOs. Second, we develop the performance difference and derivative formulas and the potential-based policy iteration algorithm, which converges to the global optimum. This algorithm is then applied to a node activation problem in wireless sensor network.