On Provably Robust Meta-Bayesian Optimization

Zhongxiang Dai, YIZHOU CHEN, Haibin Yu, Bryan Kian Hsiang Low, Patrick Jaillet

Keywords: Bayesian Optimization, Gaussian Processes

TL;DR: We introduce two provably robust meta-BO algorithms, RM-GP-UCB and RM-GP-TS. We show that RM-GP-UCB is more robust both theoretically and empirically, and RM-GP-TS works effectively in some settings and is more computationally efficient.

Abstract: Bayesian optimization (BO) has become popular for sequential optimization of black-box functions. When BO is used to optimize a target function, we often have access to previous evaluations of potentially related functions. This begs the question as to whether we can leverage these previous experiences to accelerate the current BO task through meta-learning (meta-BO), while ensuring robustness against potentially harmful dissimilar tasks that could sabotage the convergence of BO. This paper introduces two scalable and provably robust meta-BO algorithms: robust meta-Gaussian process-upper confidence bound (RM-GP-UCB) and RM-GP-Thompson sampling (RM-GP-TS). We prove that both algorithms are asymptotically no-regret even when some or all previous tasks are dissimilar to the current task, and show that RM-GP-UCB enjoys a better theoretical robustness than RM-GP-TS. We also exploit the theoretical guarantees to optimize the weights assigned to individual previous tasks through regret minimization via online learning, which diminishes the impact of dissimilar tasks and hence further enhances the robustness. Empirical evaluations show that (a) RM-GP-UCB performs effectively and consistently across various applications, and (b) RM-GP-TS, despite being less robust than RM-GP-UCB both in theory and in practice, performs competitively in some scenarios with less dissimilar tasks and is more computationally efficient.

Community Implementations: [ 4 code implementations](https://www.catalyzex.com/paper/arxiv:2206.06872/code)