Multisection: Parallelized bisection

Abstract

We consider a one-dimensional bisection method for finding the zero of a function, where function evaluations can be performed asynchronously in a parallel computing environment. Using dynamic programming, we characterize the Bayes-optimal policy for sequentially choosing points at which to query the function. In choosing these points, we face a trade-off between aggressively reducing the search space in the short term, and maintaining a desirable spread of queries in the long-term. Our results provide insight on how this trade-off is affected by function evaluation times, risk preferences, and computational budget.