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Lookahead, also known as non-myopic, Bayesian optimization (BO) aims to findoptimal sampling policies through solving a dynamic program (DP) that maximizesa long-term reward over a rolling horizon. Though promising, lookahead BO facesthe risk of error propagation through its increased dependence on a possiblymis-specified model. In this work we focus on the rollout approximation forsolving the intractable DP. We first prove the improving nature of rollout intackling lookahead BO and provide a sufficient condition for the used heuristicto be rollout improving. We then provide both a theoretical and practicalguideline to decide on the rolling horizon stagewise. This guideline is builton quantifying the negative effect of a mis-specified model. To illustrate ouridea, we provide case studies on both single and multi-information source BO.Empirical results show the advantageous properties of our method over severalmyopic and non-myopic BO algorithms.

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