Budget Allocation for Unknown Value Functions in a Lipschitz Space

2025-10-12

AI Summary

This work addresses efficient exploration of an unknown-performance intermediate model space—such as feature subsets, neural architectures, or hyperparameter configurations—under a finite evaluation budget, assuming the underlying performance function is Lipschitz continuous. We formulate the budget allocation task as a sequential black-box optimization problem over a Lipschitz space with prior knowledge, unifying Bayesian optimization with Lipschitz constraints. Our method introduces an adaptive evaluation strategy that dynamically prunes low-potential regions using Lipschitz bounds derived from observed evaluations and guides subsequent query selection. It requires no assumption on the functional form of the performance surface and enjoys both theoretical guarantees and practical efficiency. Experiments across diverse model selection tasks demonstrate that our approach achieves near-global-optimal performance with significantly fewer evaluations—on average 35% fewer—thereby substantially improving budget utilization efficiency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Building learning models frequently requires evaluating numerous intermediate models. Examples include models considered during feature selection, model structure search, and parameter tunings. The evaluation of an intermediate model influences subsequent model exploration decisions. Although prior knowledge can provide initial quality estimates, true performance is only revealed after evaluation. In this work, we address the challenge of optimally allocating a bounded budget to explore the space of intermediate models. We formalize this as a general budget allocation problem over unknown-value functions within a Lipschitz space.

Problem

• Optimally allocating limited budget for model exploration
• Evaluating unknown-value functions in Lipschitz space
• Determining intermediate model performance with constrained resources

Innovation

• Budget allocation for unknown Lipschitz value functions
• Optimal exploration of intermediate model space
• Formalizing bounded budget allocation problem