Regret-Based $(ε,δ)$-optimal Stopping Criteria for Bayesian Optimization

2026-05-21 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new research paper introduces regret-based (ε,δ)-optimal stopping criteria for Bayesian Optimization (BO), a method widely used for black-box optimization with Gaussian process (GP) surrogate models. Current BO practices often terminate after a fixed evaluation budget, leading to potential unnecessary costs and no guaranteed solution optimality. This work presents provably tighter instantaneous regret bounds for GP Upper Confidence Bound (GP-UCB) at any iteration. Based on these improved bounds, the authors propose novel stopping criteria designed to ensure an ε-optimal solution with a high probability of 1-δ upon termination. Numerical experiments validate the effectiveness and efficiency of these new stopping criteria.

Key takeaway

For AI Scientists deploying Bayesian Optimization for black-box function optimization, adopting these new regret-based (ε,δ)-optimal stopping criteria is crucial. You can achieve guaranteed ε-optimal solutions with high probability 1-δ, significantly improving efficiency by avoiding arbitrary fixed evaluation budgets. This approach ensures better resource allocation and more reliable optimization outcomes for your models.

Key insights

New regret bounds enable provably optimal stopping for Bayesian Optimization, ensuring ε-optimality with high probability.

Principles

• Tighter regret bounds improve theoretical guarantees.
• Fixed evaluation budgets are inefficient.

Method

Propose stopping criteria for GP-UCB based on provably tighter instantaneous regret bounds.

In practice

• Ensure ε-optimal solutions with high probability.
• Reduce unnecessary computational cost.

Topics

• Bayesian Optimization
• Optimal Stopping
• Gaussian Processes
• Regret Bounds
• Black-box Optimization
• GP-UCB

Best for: Research Scientist, AI Scientist

Related on AIssential

• Kernel-based guarantees for nonlinear parametric models in Bayesian optimization — A kernel-based framework provides theoretical guarantees for nonlinear parametric models in adaptive optimization.
• When Does q-error Predict Plan Regret? Three Regimes of Cardinality-Estimation Error — The relationship between q-error and plan regret varies across three error regimes, with ACS-infinity being key for large errors.
• When Does Learning to Stop Help? A Cost-Aware Study of Early Exits in Reasoning Models — Learned stopping rules improve reasoning model efficiency when scalar signals are insufficient, but their value is task-dependent.
• Refined Risk Bounds for Unbounded Losses via Transductive Priors — Transductive priors and exponential weights yield tighter risk bounds for unbounded losses in sequential learning.
• A Gentle Introduction to Stochastic Programming — Stochastic programming integrates uncertainty into linear programs, offering robust, probabilistic, or multi-stage recourse solutions.
• Unleashing LLMs in Bayesian Optimization: Preference-Guided Framework for Scientific Discovery — LGBO integrates LLM semantic reasoning into every BO iteration via a preference mechanism, accelerating scientific discovery.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.