Why Non-myopic Bayesian Optimization is Promising and How Far Should We Look-ahead? A Study via Rollout

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Xubo Yue, Raed AL Kontar ;
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2808-2818, 2020.

Abstract

Lookahead, also known as non-myopic, Bayesian optimization (BO) aims to find optimal sampling policies through solving a dynamic programming (DP) formulation that maximizes a long-term reward over a rolling horizon. Though promising, lookahead BO faces the risk of error propagation through its increased dependence on a possibly mis-specified model. In this work we focus on the rollout approximation for solving the intractable DP. We first prove the improving nature of rollout in tackling lookahead BO and provide a sufficient condition for the used heuristic to be rollout improving. We then provide both a theoretical and practical guideline to decide on the rolling horizon stagewise. This guideline is built on quantifying the negative effect of a mis-specified model. To illustrate our idea, we provide case studies on both single and multi-information source BO. Empirical results show the advantageous properties of our method over several myopic and non-myopic BO algorithms.

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