A General Approach to Environment Design with One Agent

Abstract

The problem of environment design considers a setting in which an interested party aims to influence an agent's decisions by making limited changes to the agent's environment. Zhang and Parkes [2008] first introduced the environment design concept for a specific problem in the Markov Decision Process setting. In this paper, we present a general framework for the formulation and solution of environment design problems with one agent. We consider both the case in which the agent's local decision model is known and partially unknown to the interested party, and illustrate the framework and results on a linear programming setting. For the latter problem, we formulate an active, indirect elicitation method and provide conditions for convergence and logarithmic convergence. We relate to the problem of inverse optimization and also offer a game-theoretic interpretation of our methods.