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 $\textit{combinatorial and unstructured}$ 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 $\textbf{GameOpt}$, a novel game-theoretical approach to combinatorial BO. $\textbf{GameOpt}$ establishes a cooperative game between the different optimization variables, and selects points that are game $\textit{equilibria}$ 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 $\textbf{GameOpt}$ scalable to large combinatorial spaces. We demonstrate the application of $\textbf{GameOpt}$ to the challenging $\textit{protein design}$ problem and validate its performance on four real-world protein datasets. Each protein can take up to $20^{X}$ possible configurations, where $X$ 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.

翻译：贝叶斯优化（BO）是一种通过顺序交互来优化评估成本高昂的黑箱函数的强大框架。然而，在若干重要问题（例如药物发现、电路设计、神经架构搜索等）中，此类函数定义在庞大的 $\textit{组合且非结构化}$ 空间上。由于在这些域上获取函数的最大化难以处理，这使得现有的BO算法不可行。为解决此问题，我们提出 $\textbf{GameOpt}$，一种新颖的博弈论方法用于组合贝叶斯优化。$\textbf{GameOpt}$ 在不同的优化变量之间建立了一个合作博弈，并选择作为上置信界获取函数的博弈 $\textit{均衡}$ 的点。这些是稳定的配置，其中没有变量有动机偏离$-$类似于连续域中的局部最优解。至关重要的是，这使我们能够有效地将组合域的复杂性分解为各个决策集，使得 $\textbf{GameOpt}$ 能够扩展到大型组合空间。我们展示了 $\textbf{GameOpt}$ 在具有挑战性的 $\textit{蛋白质设计}$ 问题中的应用，并在四个真实世界的蛋白质数据集上验证了其性能。每个蛋白质最多可具有 $20^{X}$ 种可能的配置，其中 $X$ 是蛋白质的长度，这使得标准BO方法不可行。相比之下，我们的方法迭代地选择信息丰富的蛋白质配置，并与其他基线方法相比，能够非常快速地发现高活性蛋白质变体。