Adaptive Model Design for Markov Decision Process

In a Markov decision process (MDP), an agent interacts with the environment via perceptions and actions. During this process, the agent aims to maximize its own gain. Hence, appropriate regulations are often required, if we hope to take the external costs/benefits of its actions into consideration. In this paper, we study how to regulate such an agent by redesigning model parameters that can affect the rewards and/or the transition kernels. We formulate this problem as a bilevel program, in which the lower-level MDP is regulated by the upper-level model designer. To solve the resulting problem, we develop a scheme that allows the designer to iteratively predict the agent's reaction by solving the MDP and then adaptively update model parameters based on the predicted reaction. The algorithm is first theoretically analyzed and then empirically tested on several MDP models arising in economics and robotics.