Stochastic Optimal Control as Approximate Input Inference

TL;DR

This paper presents a probabilistic framework for stochastic optimal control by formulating it as an input inference problem, enabling uncertainty quantification and principled regularization.

Contribution

It introduces a novel probabilistic approach using Expectation Maximization and message passing to infer optimal control inputs, unifying control and inference perspectives.

Findings

Incorporates uncertainty quantification into control inference.

Derives maximum entropy LQG control law for linearized systems.

Provides a detailed derivation and comparison with existing methods.

Abstract

Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization techniques, that heavily rely on heuristics for regularization in order to achieve stable convergence. By building upon the duality between inference and control, we develop the view of Optimal Control as Input Estimation, devising a probabilistic stochastic optimal control formulation that iteratively infers the optimal input distributions by minimizing an upper bound of the control cost. Inference is performed through Expectation Maximization and message passing on a probabilistic graphical model of the dynamical system, and time-varying linear Gaussian feedback controllers are extracted from the joint state-action distribution. This perspective incorporates uncertainty quantification, effective initialization through priors, and the principled regularization inherent to the Bayesian treatment. Moreover, it can be shown that for deterministic linearized systems, our framework derives the maximum entropy linear quadratic optimal control law. We provide a complete and detailed derivation of our probabilistic approach and highlight its advantages in comparison to other deterministic and probabilistic solvers.