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

TL;DR

This paper introduces a log barrier-based method for safe, non-smooth black-box optimization that guarantees constraint satisfaction and converges to a local solution, demonstrated on a control design task.

Contribution

It presents a novel safe optimization algorithm using log barriers for non-convex, non-smooth problems with noisy observations, ensuring safety and convergence.

Findings

Algorithm guarantees safety with high probability.

Convergence rate is theoretically derived.

Effective in a control design application.

Abstract

For safety-critical black-box optimization tasks, observations of the constraints and the objective are often noisy and available only for the feasible points. 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 an optimal solution with high probability. Our proposed algorithm exploits noisy observations to iteratively improve on an initial safe point until convergence. We derive the convergence rate and prove safety of our algorithm. We demonstrate its performance in an application to an iterative control design problem.