Every Call is Precious: Global Optimization of Black-Box Functions with Unknown Lipschitz Constants

TL;DR

The paper introduces ECP, a new global optimization algorithm for black-box functions that performs well without needing to estimate the Lipschitz constant, reducing evaluations and outperforming existing methods.

Contribution

ECP is a novel optimization method that avoids estimating the Lipschitz constant, ensuring no-regret guarantees and superior empirical performance.

Findings

ECP outperforms 10 benchmark algorithms across 30 problems.

ECP guarantees no-regret performance with infinite evaluations.

ECP achieves minimax-optimal regret bounds within finite budgets.

Abstract

Optimizing expensive, non-convex, black-box Lipschitz continuous functions presents significant challenges, particularly when the Lipschitz constant of the underlying function is unknown. Such problems often demand numerous function evaluations to approximate the global optimum, which can be prohibitive in terms of time, energy, or resources. In this work, we introduce Every Call is Precious (ECP), a novel global optimization algorithm that minimizes unpromising evaluations by strategically focusing on potentially optimal regions. Unlike previous approaches, ECP eliminates the need to estimate the Lipschitz constant, thereby avoiding additional function evaluations. ECP guarantees no-regret performance for infinite evaluation budgets and achieves minimax-optimal regret bounds within finite budgets. Extensive ablation studies validate the algorithm's robustness, while empirical evaluations show that ECP outperforms 10 benchmark algorithms including Lipschitz, Bayesian, bandits, and evolutionary methods across 30 multi-dimensional non-convex synthetic and real-world optimization problems, which positions ECP as a competitive approach for global optimization.