Local and global event-based optimization: Performace and complexity

Markov decision processes (MDPs) provide a general framework for many control, decision-making, and optimization problems. An well-known difficulty in MDPs is that the state and action space increase exponentially with the scale of the problem. The event-based optimization (EBO) provides an alternative approach to solve the large scale MDPs by concentrating on the state transitions with certain common properties. The scale and performance of the EBO problem is affected by the definition of events. In this paper, we demonstrate the relationship between the complexity of the events and the performance of the event-based policies by a multi-room Heating, Ventilation, and Air-Conditioning (HVAC) control problem. First, we formulate the multi-room HVAC control problem as an event-based optimization, and define the global events and local events of the problem. Second, we propose the definition of the complexity performance curve (CPC). A CPC describes the relationship between the complexity of the events and the performance of the best policy under the given complexity. Third, we give the method to estimate the CPC in the certain EBO problem. Fourth, we demonstrate the CPCs of the multi-room HVAC control problem.