Bayesian optimization (BO) is a powerful framework to optimize black-box expensive-to-evaluate functions via sequential interactions. In several important problems (e.g. drug discovery, circuit design, neural architecture search, etc.), though, such functions are defined over large spaces. This makes existing BO algorithms not feasible due to the intractable maximization of the acquisition function over these domains. To address this issue, we propose , a novel game-theoretical approach to combinatorial BO. establishes a cooperative game between the different optimization variables, and selects points that are game of an upper confidence bound acquisition function. These are stable configurations from which no variable has an incentive to deviate analog to local optima in continuous domains. Crucially, this allows us to efficiently break down the complexity of the combinatorial domain into individual decision sets, making scalable to large combinatorial spaces. We demonstrate the application of to the challenging problem and validate its performance on four real-world protein datasets. Each protein can take up to possible configurations, where is the length of a protein, making standard BO methods infeasible. Instead, our approach iteratively selects informative protein configurations and very quickly discovers highly active protein variants compared to other baselines.
View on arXiv@article{bal2025_2409.18582,
title={ Optimistic Games for Combinatorial Bayesian Optimization with Application to Protein Design },
author={ Melis Ilayda Bal and Pier Giuseppe Sessa and Mojmir Mutny and Andreas Krause },
journal={arXiv preprint arXiv:2409.18582},
year={ 2025 }
}