Lookahead Bayesian Optimization via Rollout: Guarantees and Sequential Rolling Horizons

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. 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.