Safe non-smooth black-box optimization with application to policy search

For safety-critical black-box optimization tasks, observations of the constraints and the objective are often noisy and available only inside the feasible set. We propose an approach based on log barriers to find a local solution of a non-convex non-smooth black-box optimization problem $\min f^0(x)$ subject to $f^i(x)\leq 0,~ i = 1,\ldots, m$, at the same time, guaranteeing constraint satisfaction while learning with high probability. Starting from a conservative safe point, the proposed algorithm safely improves it by iteratively making observations, and converging to an approximate local stationary point. We prove the convergence rate and safety of our algorithm and demonstrate its performance in an application to an iterative control design problem.