Advancing Trajectory Optimization with Approximate Inference: Exploration, Covariance Control and Adaptive Risk

Discrete-time stochastic optimal control remains a challenging problem for\ngeneral, nonlinear systems under significant uncertainty, with practical\nsolvers typically relying on the certainty equivalence assumption, replanning\nand/or extensive regularization. Control as inference is an approach that\nframes stochastic control as an equivalent inference problem, and has\ndemonstrated desirable qualities over existing methods, namely in exploration\nand regularization. We look specifically at the input inference for control\n(i2c) algorithm, and derive three key characteristics that enable advanced\ntrajectory optimization: An `expert' linear Gaussian controller that combines\nthe benefits of open-loop optima and closed-loop variance reduction when\noptimizing for nonlinear systems, inherent adaptive risk sensitivity from the\ninference formulation, and covariance control functionality with only a minor\nalgorithmic adjustment.\n