Bayesian Optimization with Unknown Search Space

TL;DR

This paper introduces a parameter-free Bayesian optimization method with a systematic volume expansion strategy for unknown search spaces, ensuring epsilon-accuracy and outperforming baselines in tests.

Contribution

The authors propose a novel, parameter-free volume expansion strategy for Bayesian optimization in unknown search spaces, with theoretical guarantees and practical effectiveness.

Findings

Achieves epsilon-accuracy after finite iterations

Automatically determines minimal expansion needed

Outperforms baseline methods in benchmarks and hyper-parameter tuning

Abstract

Applying Bayesian optimization in problems wherein the search space is unknown is challenging. To address this problem, we propose a systematic volume expansion strategy for the Bayesian optimization. We devise a strategy to guarantee that in iterative expansions of the search space, our method can find a point whose function value within epsilon of the objective function maximum. Without the need to specify any parameters, our algorithm automatically triggers a minimal expansion required iteratively. We derive analytic expressions for when to trigger the expansion and by how much to expand. We also provide theoretical analysis to show that our method achieves epsilon-accuracy after a finite number of iterations. We demonstrate our method on both benchmark test functions and machine learning hyper-parameter tuning tasks and demonstrate that our method outperforms baselines.