Every Call is Precious: Global Optimization of Black-Box Functions with Unknown Lipschitz Constants
This addresses the challenge of costly function evaluations in global optimization for applications like hyperparameter tuning or engineering design, though it appears incremental as it builds on existing Lipschitz-based methods.
The paper tackled the problem of optimizing expensive black-box functions with unknown Lipschitz constants by introducing the ECP algorithm, which strategically minimizes unpromising evaluations and eliminates the need to estimate the Lipschitz constant, resulting in outperformance over 10 benchmark algorithms across 30 synthetic and real-world problems.
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.