In Bayesian optimization, a black-box function is maximized via the use of a surrogate model. We apply distributed Thompson sampling, using a Gaussian process as a surrogate model, to approach the multi-agent Bayesian optimization problem. In our distributed Thompson sampling implementation, each agent receives sampled points from neighbors, where the communication network is encoded in a graph; each agent utilizes their own Gaussian process to model the objective function. We demonstrate theoretical bounds on Bayesian simple regret and Bayesian average regret, where the bound depends on the structure of the communication graph. Unlike in batch Bayesian optimization, this bound is applicable in cases where the communication graph amongst agents is constrained. When compared to sequential single-agent Thompson sampling, our bound guarantees faster convergence with respect to time as long as the communication graph is connected. We confirm the efficacy of our algorithm with numerical simulations on traditional optimization test functions, illustrating the significance of graph connectivity on improving regret convergence.

翻译：在贝叶斯优化中，黑箱函数通过代理模型实现最大化。我们采用分布式Thompson采样方法，以高斯过程作为代理模型，处理多智能体贝叶斯优化问题。在该分布式Thompson采样实现中，每个智能体从邻居节点接收采样点，其中通信网络通过图结构进行编码；每个智能体使用独立的高斯过程对目标函数进行建模。我们证明了贝叶斯简单遗憾和贝叶斯平均遗憾的理论界，该界限取决于通信图的结构特征。与批量贝叶斯优化不同，该理论界适用于智能体间通信图受约束的场景。相较于顺序单智能体Thompson采样，只要通信图保持连通性，我们的理论界能保证算法在时间维度上具有更快的收敛速度。通过在传统优化测试函数上的数值模拟，我们验证了算法的有效性，并阐明了图连通性对改善遗憾收敛的重要作用。