Inverse Bayesian Optimization: Learning Human Search Strategies in a Sequential Optimization Task

Bayesian optimization is a popular algorithm for sequential optimization of a latent objective function when sampling from the objective is costly. The search path of the algorithm is governed by the acquisition function, which defines the agent's search strategy. Conceptually, the acquisition function characterizes how the optimizer balances exploration and exploitation when searching for the optimum of the latent objective. In this paper, we explore the inverse problem of Bayesian optimization; we seek to estimate the agent's latent acquisition function based on observed search paths. We introduce a probabilistic solution framework for the inverse problem which provides a principled framework to quantify both the variability with which the agent performs the optimization task as well as the uncertainty around their estimated acquisition function. We illustrate our methods by analyzing human behavior from an experiment which was designed to force subjects to balance exploration and exploitation in search of an invisible target location. We find that while most subjects demonstrate clear trends in their search behavior, there is significant variation around these trends from round to round. A wide range of search strategies are exhibited across the subjects in our study, but upper confidence bound acquisition functions offer the best fit for the majority of subjects. Finally, some subjects do not map well to any of the acquisition functions we initially consider; these subjects tend to exhibit exploration preferences beyond that of standard acquisition functions to capture. Guided by the model discrepancies, we augment the candidate acquisition functions to yield a superior fit to the human behavior in this task.