On Convex Data-Driven Inverse Optimal Control for Nonlinear,
  Non-stationary and Stochastic Systems
Emiland Garrabe Hozefa Jesawada Carmen Del Vecchio Giovanni Russo
This paper is concerned with a finite-horizon inverse control problem, which
has the goal of inferring, from observations, the possibly non-convex and
non-stationary cost driving the actions of an agent. In this context, we
present a result that enables cost estimation 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. For this problem, we give an explicit
expression for the optimal solution. Moreover, we turn our findings into
algorithmic procedures and we show the effectiveness of our approach via both
in-silico and experimental validations with real hardware. All the experiments
confirm the effectiveness of our approach.