Parameterized input inference for approximate stochastic optimal control

Probabilistic inference approaches to stochastic optimal control have attracted significant interest from researchers in the past decade. Existing inference-based optimal control approaches are limited to linear controllers in a finite-horizon model-based setting. Since nonlinear systems typically admit nonlinear optimal controllers, linear controllers may yield sub-optimal trajectories when applied to nonlinear systems. In this paper, we propose a new Expectation-Maximization (EM) based inference algorithm for stochastic optimal control. The algorithm employs nonlinear basis functions to infer nonlinear controllers. We formulate the estimation problem of optimal control as a parameter inference problem. We demonstrate the effectiveness of the algorithm on a simulated nonlinear oscillator system for nonlinear control and a linear thermal system for structured control.