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The Gaussian process bandit is a problem in which we want to find a maximizerof a black-box function with the minimum number of function evaluations. If theblack-box function varies with time, then time-varying Bayesian optimization isa promising framework. However, a drawback with current methods is in theassumption that the evaluation time for every observation is constant, whichcan be unrealistic for many practical applications, e.g., recommender systemsand environmental monitoring. As a result, the performance of current methodscan be degraded when this assumption is violated. To cope with this problem, wepropose a novel time-varying Bayesian optimization algorithm that caneffectively handle the non-constant evaluation time. Furthermore, wetheoretically establish a regret bound of our algorithm. Our bound elucidatesthat a pattern of the evaluation time sequence can hugely affect the difficultyof the problem. We also provide experimental results to validate the practicaleffectiveness of the proposed method.

Time-varying Gaussian Process Bandit Optimization with Non-constant Evaluation Time