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For safety-critical black-box optimization tasks, observations of theconstraints and the objective are often noisy and available only for thefeasible points. We propose an approach based on log barriers to find a localsolution of a non-convex non-smooth black-box optimization problem $\minf^0(x)$ subject to $f^i(x)\leq 0,~ i = 1,\ldots, m$, at the same time,guaranteeing constraint satisfaction while learning an optimal solution withhigh probability. Our proposed algorithm exploits noisy observations toiteratively improve on an initial safe point until convergence. We derive theconvergence rate and prove safety of our algorithm. We demonstrate itsperformance in an application to an iterative control design problem.

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