Title: Zeroth-Order Constrained Optimization from a Control Perspective via Feedback Linearization
Primary area: optimization
Keywords: Zeroth Order Optimization, Constrained Optimization, Control and Optimization, Feedback Linearization

Abstract: Designing safe derivative-free optimization algorithms under unknown constraints is a fundamental challenge in modern learning and control. Most existing zeroth-order (ZO) approaches typically assume white-box constraints or focus on convex settings, leaving the general case of nonconvex optimization with black-box constraints largely open. We propose a control-theoretic framework for ZO constrained optimization that enforces feasibility without relying on solving costly convex subproblems. Leveraging feedback linearization, we introduce a family of ZO feedback linearization (ZOFL) algorithms applicable to both equality and inequality constraints. Our method requires only noisy, sample-based gradient estimates yet provably guarantees constraint satisfaction under mild regularity conditions. We establish finite-time bounds on constraint violation and further present a midpoint discretization variant that further improves feasibility without sacrificing optimality. Empirical results demonstrate that ZOFL consistently outperforms standard ZO baselines, achieving competitive objective values while maintaining feasibility.

TL;DR: We propose a control-theoretic framework for zeroth-order constrained optimization, based on which we develop ZOFL algorithms that are efficient, guarantee constraint satisfaction even in nonconvex problems, and achieve strong empirical performance.