  When an expert operates a perilous dynamic system, ideal constraint
information is tacitly contained in their demonstrated trajectories and
controls. The likelihood of these demonstrations can be computed, given the
system dynamics and task objective, and the maximum likelihood constraints can
be identified. Prior constraint inference work has focused mainly on
deterministic models. Stochastic models, however, can capture the uncertainty
and risk tolerance that are often present in real systems of interest.
  This paper extends maximum likelihood constraint inference to stochastic
applications by using maximum causal entropy likelihoods. Furthermore, we
propose an efficient algorithm that computes constraint likelihood and risk
tolerance in a unified Bellman backup, allowing us to generalize to stochastic
systems without increasing computational complexity.
