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

arXiv: https://arxiv.org/abs/2511.16575 · HTML: https://mlsanity.com/paper/2511.16575/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 32 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Builds on (most cited first, 9 of 9)

- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [Global optimization of Lipschitz functions](https://mlsanity.com/paper/1703.02628/) (2017)
- [Use Your INSTINCT: INSTruction optimization for LLMs usIng Neural bandits Coupled with Transformers](https://mlsanity.com/paper/2310.02905/) (2023)
- [Achieving Human Level Competitive Robot Table Tennis](https://mlsanity.com/paper/2408.03906/) (2024)
- [A simple parameter-free and adaptive approach to optimization under a minimal local smoothness assumption](https://mlsanity.com/paper/1810.00997/) (2018)
- [Global Continuous Optimization with Error Bound and Fast Convergence](https://mlsanity.com/paper/1607.04817/) (2016)
- [Stochastic Q-learning for Large Discrete Action Spaces](https://mlsanity.com/paper/2405.10310/) (2024)
- [LIPO+: Frugal Global Optimization for Lipschitz Functions](https://mlsanity.com/paper/2406.19723/) (2024)
- [ACING: Actor-Critic for Instruction Learning in Black-Box LLMs](https://mlsanity.com/paper/2411.12736/) (2024)

## Built on by (most cited first, 2 of 2)

- [Label-Efficient School Detection from Aerial Imagery via Weakly Supervised Pretraining and Fine-Tuning](https://mlsanity.com/paper/2605.03968/) (2026)
- [Signal from Space: Detecting Schools and Towers to Bridge the Digital Divide](https://mlsanity.com/paper/2607.02724/) (2026)

## Abstract (arXiv)

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.