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We provide a unifying approximate dynamic programming framework that appliesto a broad variety of problems involving sequential estimation. We considerfirst the construction of surrogate cost functions for the purposes ofoptimization, and we focus on the special case of Bayesian optimization, usingthe rollout algorithm and some of its variations. We then discuss the moregeneral case of sequential estimation of a random vector using optimalmeasurement selection, and its application to problems of stochastic andadaptive control. We distinguish between adaptive control of deterministic andstochastic systems: the former are better suited for the use of rollout, whilethe latter are well suited for the use of rollout with certainty equivalenceapproximations. As an example of the deterministic case, we discuss sequentialdecoding problems, and a rollout algorithm for the approximate solution of theWordle and Mastermind puzzles, recently developed in the paper [BBB22].

Rollout Algorithms and Approximate Dynamic Programming for Bayesian Optimization and Sequential Estimation