多智能体优化中，通过受限通信图提升采样效率。
Distributed Thompson sampling under constrained communication
- 各智能体基于邻居采样点，用高斯过程建模目标函数。
- 理论证明平均与简单遗憾随通信图连通性加快收敛。
- 适合分布式优化场景，尤其通信受限的协同任务。
在贝叶斯优化中，通过代理模型最大化黑箱函数。本文采用分布式汤普森采样，以高斯过程作为代理模型，解决多智能体贝叶斯优化问题。在实现中，每个智能体接收来自邻近智能体的采样点，通信结构由图编码；每个智能体使用独立的高斯过程建模目标函数。我们推导了贝叶斯平均遗憾和贝叶斯简单遗憾的理论界，该界依赖于通信图的结构。与批量贝叶斯优化不同，此界适用于智能体间通信受限的情况。只要通信图连通，相比串行单智能体汤普森采样，我们的方法在时间上能更快收敛。通过经典测试函数的数值模拟验证了算法有效性，证明图连通性对遗憾收敛有显著促进作用。
原文摘要 · Abstract (English)
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 average regret and Bayesian simple 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, demonstrating the significance of graph connectivity on improving regret convergence.
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