  This paper is concerned with a finite-horizon inverse control problem, which
has the goal of reconstructing, from observations, the possibly non-convex and
non-stationary cost driving the actions of an agent. In this context, we
present a result enabling cost reconstruction by solving an optimization
problem that is convex even when the agent cost is not and when the underlying
dynamics is nonlinear, non-stationary and stochastic. To obtain this result, we
also study a finite-horizon forward control problem that has randomized
policies as decision variables. We turn our findings into algorithmic
procedures and show the effectiveness of our approach via in-silico and
hardware validations. All experiments confirm the effectiveness of our
approach.
