Reproduce “Maximizing acquisition functions for Bayesian optimization” on OpenResearch

About this paper

James T. Wilson, Frank Hutter, Marc Peter Deisenroth

This paper presents methods for efficiently maximizing acquisition functions within Bayesian Optimization, a critical step often overlooked in practice. It shows how Monte Carlo estimated acquisition functions can be optimized using gradient-based methods via the reparameterization trick, and proves that a common family of acquisition functions is submodular, enabling efficient greedy maximization for parallel queries. These approaches consistently yield improved performance on black-box optimization tasks.

Key insights

• Monte Carlo estimated acquisition functions, even those with discrete events, are differentiable and can be optimized with gradient-based methods using the reparameterization trick and continuous approximations.
• A common family of acquisition functions, termed "myopic maximal" (e.g., EI, PI, UCB), inherently possesses submodular properties, justifying the use of efficient greedy maximization algorithms for parallel queries.
• Rigorously optimizing the acquisition function, often overlooked, directly improves the overall performance and efficiency of Bayesian Optimization.

Summary by alphaXiv.