Stochastic Optimal Control as Approximate Input Inference
This work addresses the problem of stable convergence in robot learning for stochastic optimal control, offering a novel probabilistic approach that is incremental over existing duality-based methods.
The paper tackles the challenge of optimal control for stochastic nonlinear dynamical systems by developing a probabilistic formulation that views optimal control as input inference, which iteratively infers optimal input distributions by minimizing an upper bound of the control cost. The result is a framework that incorporates uncertainty quantification, effective initialization through priors, and principled regularization, deriving the maximum entropy linear quadratic optimal control law for deterministic linearized systems.
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.