ECPv2: Fast, Efficient, and Scalable Global Optimization of Lipschitz Functions

2025-11-20

AI Summary

This paper addresses efficient global optimization of Lipschitz-continuous functions with unknown Lipschitz constants, aiming to overcome key limitations of Extremal Curvature-based (ECP) methods—namely, high computational overhead and overly conservative initial sampling. The proposed approach introduces three core innovations: (1) an adaptive lower-bound mechanism coupled with a Worst-m memory structure to dynamically expand the effective sampling region; (2) fixed random projection to drastically accelerate distance computations and candidate screening; and (3) theory-guided hyperparameter design with memory-constrained strategies, ensuring optimal finite-time convergence. Evaluated on multiple high-dimensional nonconvex benchmark problems, the method matches or surpasses state-of-the-art performance while reducing empirical runtime significantly. It exhibits strong scalability and maintains rigorous theoretical guarantees.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

We propose ECPv2, a scalable and theoretically grounded algorithm for global optimization of Lipschitz-continuous functions with unknown Lipschitz constants. Building on the Every Call is Precious (ECP) framework, which ensures that each accepted function evaluation is potentially informative, ECPv2 addresses key limitations of ECP, including high computational cost and overly conservative early behavior. ECPv2 introduces three innovations: (i) an adaptive lower bound to avoid vacuous acceptance regions, (ii) a Worst-m memory mechanism that restricts comparisons to a fixed-size subset of past evaluations, and (iii) a fixed random projection to accelerate distance computations in high dimensions. We theoretically show that ECPv2 retains ECP's no-regret guarantees with optimal finite-time bounds and expands the acceptance region with high probability. We further empirically validate these findings through extensive experiments and ablation studies. Using principled hyperparameter settings, we evaluate ECPv2 across a wide range of high-dimensional, non-convex optimization problems. Across benchmarks, ECPv2 consistently matches or outperforms state-of-the-art optimizers, while significantly reducing wall-clock time.

Problem

• Optimizes Lipschitz functions with unknown constants efficiently
• Reduces computational cost and conservative behavior in global optimization
• Accelerates high-dimensional non-convex optimization while maintaining guarantees

Innovation

• Adaptive lower bound for non-vacuous acceptance regions
• Worst-m memory mechanism for fixed-size comparisons
• Fixed random projection for high-dimensional acceleration