  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.
