Maximizing acquisition functions for Bayesian optimization
This work addresses a key bottleneck in Bayesian optimization for practitioners, offering incremental improvements in optimization efficiency.
The paper tackles the challenge of fully maximizing acquisition functions in Bayesian optimization, especially in parallel query settings where these functions are non-convex and intractable, by showing that Monte Carlo-estimated acquisition functions are amenable to gradient-based optimization and identifying a family of functions that justify greedy approaches.
Bayesian optimization is a sample-efficient approach to global optimization that relies on theoretically motivated value heuristics (acquisition functions) to guide its search process. Fully maximizing acquisition functions produces the Bayes' decision rule, but this ideal is difficult to achieve since these functions are frequently non-trivial to optimize. This statement is especially true when evaluating queries in parallel, where acquisition functions are routinely non-convex, high-dimensional, and intractable. We first show that acquisition functions estimated via Monte Carlo integration are consistently amenable to gradient-based optimization. Subsequently, we identify a common family of acquisition functions, including EI and UCB, whose properties not only facilitate but justify use of greedy approaches for their maximization.