Bayesian Optimization with a Finite Budget: An Approximate Dynamic Programming Approach

Part of Advances in Neural Information Processing Systems 29 (NIPS 2016)

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Remi Lam, Karen Willcox, David H. Wolpert


We consider the problem of optimizing an expensive objective function when a finite budget of total evaluations is prescribed. In that context, the optimal solution strategy for Bayesian optimization can be formulated as a dynamic programming instance. This results in a complex problem with uncountable, dimension-increasing state space and an uncountable control space. We show how to approximate the solution of this dynamic programming problem using rollout, and propose rollout heuristics specifically designed for the Bayesian optimization setting. We present numerical experiments showing that the resulting algorithm for optimization with a finite budget outperforms several popular Bayesian optimization algorithms.