Event-based optimization with lagged state information

Event-based optimization (EBO) has provided a general framework for many control, decision-making, and optimization problems, where the actions can be taken only when certain events occur. In many large-scale networked systems, the sensors periodically report the system state to a remote center. The long-distant wireless communication usually suffers from random or deterministic delay. It is thus of great practical interest to understand how to solve EBO with such lagged state information. We consider this important problem in this paper, and make the following major contributions. First, we mathematically formulate finite-stage EBO with lagged state information (EBOLSI). Second, we prove that such an EBOLSI can be converted to a partially observable Markov decision process (POMDP) with lagged state information. Then existing exact and approximate solution methods can be applied. Third, we use numerical experiments on evacuation problems to demonstrate the impact of information delay on the performance of the simulation-based policy improvement method in EBOLSI. We hope this work sheds insight on EBOLSI in more general situations.