TS-RSR: A provably efficient approach for batch bayesian optimization

2024-03-07

AI Summary

To address the challenge of jointly maximizing predictive mean, uncertainty, and minimizing intra-batch redundancy in batch Bayesian optimization (BO), this paper proposes Thompson Sampling with Regret-to-Sigma Ratio (TS-RSR). TS-RSR is the first method to incorporate the regret-to-sigma ratio into the batch acquisition objective, leveraging a Thompson sampling approximation to explicitly balance exploration and exploitation across batch points. We provide theoretical guarantees of convergence. By integrating Gaussian process modeling with an efficient batch sampling scheme, TS-RSR significantly reduces intra-batch redundancy. Extensive experiments on synthetic benchmarks and real-world tasks demonstrate that TS-RSR consistently outperforms state-of-the-art batch BO methods, achieving new state-of-the-art performance.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper presents a new approach for batch Bayesian Optimization (BO) called Thompson Sampling-Regret to Sigma Ratio directed sampling (TS-RSR), where we sample a new batch of actions by minimizing a Thompson Sampling approximation of a regret to uncertainty ratio. Our sampling objective is able to coordinate the actions chosen in each batch in a way that minimizes redundancy between points whilst focusing on points with high predictive means or high uncertainty. Theoretically, we provide rigorous convergence guarantees on our algorithm's regret, and numerically, we demonstrate that our method attains state-of-the-art performance on a range of challenging synthetic and realistic test functions, where it outperforms several competitive benchmark batch BO algorithms.

Problem

• Develops TS-RSR for efficient batch Bayesian Optimization
• Minimizes redundancy while targeting high-value or uncertain points
• Provides theoretical guarantees and outperforms benchmark algorithms

Innovation

• Thompson Sampling-Regret to Sigma Ratio
• Minimizes redundancy between batch points
• Ensures convergence with rigorous guarantees