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Register a new userStochastic Control through Approximate Bayesian Input Inference
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Joe Watson
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Optimal control under uncertainty is a prevailing challenge in control, due to the difficulty in producing tractable solutions for the stochastic optimization problem. By framing the control problem as one of input estimation, advanced approximate inference techniques can be used to handle the statistical approximations in a principled and practical manner. Analyzing the Gaussian setting, we present a solver capable of several stochastic control methods, and was found to be superior to popular baselines on nonlinear simulated tasks. We draw connections that relate this inference formulation to previous approaches for stochastic optimal control, and outline several advantages that this inference view brings due to its statistical nature.
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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.
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