Safe Primal-Dual Optimization with a Single Smooth Constraint

TL;DR

This paper introduces a novel primal-dual optimization algorithm for safe black-box optimization with a single smooth constraint, ensuring safety and improved convergence rates in applications like robotics.

Contribution

It presents the first primal-dual method guaranteeing safe updates and extends to multiple constraints, outperforming existing techniques in convergence and safety.

Findings

Achieves faster convergence than current methods.

Guarantees safety of primal and dual sequences.

Demonstrates effectiveness through simulations.

Abstract

This paper addresses the problem of safe optimization under a single smooth constraint, a scenario that arises in diverse real-world applications such as robotics and autonomous navigation. The objective of safe optimization is to solve a black-box minimization problem while strictly adhering to a safety constraint throughout the learning process. Existing methods often suffer from high sample complexity due to their noise sensitivity or poor scalability with number of dimensions, limiting their applicability. We propose a novel primal-dual optimization method that, by carefully adjusting dual step-sizes and constraining primal updates, ensures the safety of both primal and dual sequences throughout the optimization. Our algorithm achieves a convergence rate that significantly surpasses current state-of-the-art techniques. Furthermore, to the best of our knowledge, it is the first primal-dual approach to guarantee safe updates. Simulations corroborate our theoretical findings, demonstrating the practical benefits of our method. We also show how the method can be extended to multiple constraints.