Top-k Ranking Bayesian Optimization

This paper presents a novel approach to top-k ranking Bayesian optimization (top-k BO) which is practical and significant generalization of preferential BO handle tie/indifference observations. We first design surrogate model that not only capable catering the above observations, but also supported by classic random utility model. Another equally important contribution introduction information-theoretic acquisition function in with observation called multinomial predictive entropy search (MPES) flexible handling these observations optimized for all inputs query jointly. MPES possesses superior performance compared existing functions select one at time greedily. empirically evaluate using several synthetic benchmark functions, CIFAR-10 dataset, SUSHI preference dataset.