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We develop an algorithm that combines model-based and model-free methods forsolving a nonlinear optimal control problem with a quadratic cost in which thesystem model is given by a linear state-space model with a small additivenonlinear perturbation. We decompose the cost into a sum of two functions, onehaving an explicit form obtained from the approximate linear model, the otherbeing a black-box model representing the unknown modeling error. Thedecomposition allows us to formulate the problem as a composite optimizationproblem. To solve the optimization problem, our algorithm performs gradientdescent using the gradient obtained from the approximate linear model untilbacktracking line search fails, upon which the model-based gradient is comparedwith the exact gradient obtained from a model-free algorithm. The differencebetween the model gradient and the exact gradient is then used for compensatingfuture gradient-based updates. Our algorithm is shown to decrease the number offunction evaluations compared with traditional model-free methods both intheory and in practice.

Accelerating Model-Free Policy Optimization Using Model-Based Gradient: A Composite Optimization Perspective