Policy teaching through reward function learning

Policy teaching considers a Markov Decision Process setting in which an interested party aims to influence an agent's decisions by providing limited incentives. In this paper, we consider the specific objective of inducing a pre-specified desired policy. We examine both the case in which the agent's reward function is known and unknown to the interested party, presenting a linear program for the former case and formulating an active, indirect elicitation method for the latter. We provide conditions for logarithmic convergence, and present a polynomial time algorithm that ensures logarithmic convergence with arbitrarily high probability. We also offer practical elicitation heuristics that can be formulated as linear programs, and demonstrate their effectiveness on a policy teaching problem in a simulated ad-network setting. We extend our methods to handle partial observations and partial target policies, and provide a game-theoretic interpretation of our methods for handling strategic agents.