让机器人长期影响人类行为，避免过度干预。

Robot actions influence the decisions of nearby humans. Here influence refers to intentional change: robots influence humans when they shift the human's behavior in a way that helps the robot complete its task. Imagine an autonomous car trying to merge; by proactively nudging into the human's lane, the robot causes human drivers to yield and provide space. Influence is often necessary for seamless interaction. However, if influence is left unregulated and uncontrolled, robots will negatively impact the humans around them. Prior works have begun to address this problem by creating a variety of control algorithms that seek to influence humans. Although these methods are effective in the short-term, they fail to maintain influence over time as the human adapts to the robot's behaviors. In this paper we therefore present an optimization framework that enables robots to purposely regulate their influence over humans across both short-term and long-term interactions. Here the robot maintains its influence by reasoning over a dynamic human model which captures how the robot's current choices will impact the human's future behavior. Our resulting framework serves to unify current approaches: we demonstrate that state-of-the-art methods are simplifications of our underlying formalism. Our framework also provides a principled way to generate influential policies: in the best case the robot exactly solves our framework to find optimal, influential behavior. But when solving this optimization problem becomes impractical, designers can introduce their own simplifications to reach tractable approximations. We experimentally compare our unified framework to state-of-the-art baselines and ablations, and demonstrate across simulations and user studies that this framework is able to successfully influence humans over repeated interactions. See videos of our experiments here: https://youtu.be/nPekTUfUEbo