Top-$k$ Ranking Bayesian Optimization
This work addresses the problem of efficiently finding top-k rankings in scenarios with preferential observations, which is relevant for researchers and practitioners in areas like recommender systems and experimental design. It offers an incremental improvement over existing preferential BO methods.
This paper introduces a new Bayesian optimization approach for top-k ranking problems, which can handle tie/indifference observations. It proposes a novel information-theoretic acquisition function, multinomial predictive entropy search (MPES), which outperforms existing greedy acquisition functions.
This paper presents a novel approach to top-$k$ ranking Bayesian optimization (top-$k$ ranking BO) which is a practical and significant generalization of preferential BO to handle top-$k$ ranking and tie/indifference observations. We first design a surrogate model that is not only capable of catering to the above observations, but is also supported by a classic random utility model. Another equally important contribution is the introduction of the first information-theoretic acquisition function in BO with preferential observation called multinomial predictive entropy search (MPES) which is flexible in handling these observations and optimized for all inputs of a query jointly. MPES possesses superior performance compared with existing acquisition functions that select the inputs of a query one at a time greedily. We empirically evaluate the performance of MPES using several synthetic benchmark functions, CIFAR-$10$ dataset, and SUSHI preference dataset.