Multiple Plans are Better than One: Diverse Stochastic Planning
This work tackles the problem of generating robust and diverse plans for human-robot interaction, where human preferences are difficult to model, benefiting designers of such systems.
This paper addresses the challenge of incomplete objective functions in planning problems, particularly in human-robot interaction, by formulating diverse stochastic planning. It aims to generate a small and diverse set of near-optimal behaviors for systems modeled by Markov decision processes, proposing a solution based on the Frank-Wolfe method that converges to a stationary point.
In planning problems, it is often challenging to fully model the desired specifications. In particular, in human-robot interaction, such difficulty may arise due to human's preferences that are either private or complex to model. Consequently, the resulting objective function can only partially capture the specifications and optimizing that may lead to poor performance with respect to the true specifications. Motivated by this challenge, we formulate a problem, called diverse stochastic planning, that aims to generate a set of representative -- small and diverse -- behaviors that are near-optimal with respect to the known objective. In particular, the problem aims to compute a set of diverse and near-optimal policies for systems modeled by a Markov decision process. We cast the problem as a constrained nonlinear optimization for which we propose a solution relying on the Frank-Wolfe method. We then prove that the proposed solution converges to a stationary point and demonstrate its efficacy in several planning problems.