Optimistic Games for Combinatorial Bayesian Optimization with Application to Protein Design

2024-09-27

arXiv.org

AI Summary

Bayesian optimization (BO) struggles with expensive black-box function optimization in combinatorial and unstructured high-dimensional discrete spaces—e.g., protein design—due to the intractability of global acquisition function maximization. Method: We propose GameOpt, the first combinatorial BO framework integrating cooperative game theory: sequence positions are modeled as rational players; instead of global acquisition maximization, it seeks a UCB-based Nash equilibrium for stable, decentralized, and scalable local coordination. The method synergistically combines cooperative games, Nash equilibrium computation, UCB-style acquisition, and combinatorial space decomposition. Results: On four real-world protein engineering benchmarks, GameOpt significantly outperforms existing baselines in sample efficiency and wall-clock time, discovering high-activity variants rapidly. It successfully navigates combinatorial spaces of length up to数十 and size up to 20^X, thereby overcoming fundamental scalability bottlenecks in discrete, high-dimensional BO.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Game Theory and Economic Paradigms: Cooperative Game Theory
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 $ extit{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 $ extbf{GameOpt}$, a novel game-theoretical approach to combinatorial BO. $ extbf{GameOpt}$ establishes a cooperative game between the different optimization variables, and selects points that are game $ extit{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 $ extbf{GameOpt}$ scalable to large combinatorial spaces. We demonstrate the application of $ extbf{GameOpt}$ to the challenging $ extit{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.

Problem

• Addresses combinatorial Bayesian optimization challenges
• Proposes GameOpt for large unstructured spaces
• Applies GameOpt to scalable protein design

Innovation

• Game-theoretical approach for BO
• Breaks down combinatorial complexity
• Efficient protein design optimization