Dynamic Batch Bayesian Optimization

Bayesian optimization (BO) algorithms try to optimize an unknown function that is expensive to evaluate using minimum number of evaluations/experiments. Most of the proposed algorithms in BO are sequential, where only one experiment is selected at each iteration. This method can be time inefficient when each experiment takes a long time and more than one experiment can be ran concurrently. On the other hand, requesting a fix-sized batch of experiments at each iteration causes performance inefficiency in BO compared to the sequential policies. In this paper, we present an algorithm that asks a batch of experiments at each time step t where the batch size p_t is dynamically determined in each step. Our algorithm is based on the observation that the sequence of experiments selected by the sequential policy can sometimes be almost independent from each other. Our algorithm identifies such scenarios and request those experiments at the same time without degrading the performance. We evaluate our proposed method using the Expected Improvement policy and the results show substantial speedup with little impact on the performance in eight real and synthetic benchmarks.

💡 Research Summary

Bayesian optimization (BO) is a powerful framework for optimizing expensive black‑box functions by iteratively selecting evaluation points based on a probabilistic surrogate model, most commonly a Gaussian Process (GP). Traditional BO operates sequentially: after each experiment the GP posterior is updated and a new point is chosen, typically using an acquisition function such as Expected Improvement (EI). While this approach is sample‑efficient, it can be time‑inefficient when each evaluation is costly and multiple evaluations can be run in parallel. Existing batch BO methods address parallelism by fixing a batch size, but they often sacrifice the performance of the underlying sequential policy because the batch points are only an approximation of the sequential decisions.

The paper “Dynamic Batch Bayesian Optimization” proposes a novel algorithm that determines the batch size adaptively at every iteration. The central observation is that, under a sequential policy like EI, the next few points may be almost independent of each other; if this independence holds, the points can be evaluated concurrently without degrading the quality of the optimization. The authors formalize this intuition using three theoretical results.

1. Theorem 1 shows that, for a GP, the reduction in predictive variance after adding a set of candidate points depends only on their locations, not on the (as‑yet‑unknown) observation values. This permits exact computation of the variance change Δσ² for any prospective batch.

2. Theorem 2 provides an upper bound on the expected absolute change in the predictive mean, E