Efficient Rollout Strategies for Bayesian Optimization
This work addresses efficiency issues in Bayesian optimization for researchers and practitioners, but it is incremental as it builds on existing rollout strategies.
The paper tackles the computational expense of non-myopic acquisition functions in Bayesian optimization, which involve high-dimensional integrals, by proposing methods like quasi-Monte Carlo and policy-search to reduce costs and eliminate optimization needs, achieving significant computational savings.
Bayesian optimization (BO) is a class of sample-efficient global optimization methods, where a probabilistic model conditioned on previous observations is used to determine future evaluations via the optimization of an acquisition function. Most acquisition functions are myopic, meaning that they only consider the impact of the next function evaluation. Non-myopic acquisition functions consider the impact of the next $h$ function evaluations and are typically computed through rollout, in which $h$ steps of BO are simulated. These rollout acquisition functions are defined as $h$-dimensional integrals, and are expensive to compute and optimize. We show that a combination of quasi-Monte Carlo, common random numbers, and control variates significantly reduce the computational burden of rollout. We then formulate a policy-search based approach that removes the need to optimize the rollout acquisition function. Finally, we discuss the qualitative behavior of rollout policies in the setting of multi-modal objectives and model error.