We introduce a cooperative Bayesian optimization problem for optimizing black-box functions of two variables where two agents choose together at which points to query the function but have only control over one variable each. This setting is inspired by human-AI teamwork, where an AI-assistant helps its human user solve a problem, in this simplest case, collaborative optimization. We formulate the solution as sequential decision-making, where the agent we control models the user as a computationally rational agent with prior knowledge about the function. We show that strategic planning of the queries enables better identification of the global maximum of the function as long as the user avoids excessive exploration. This planning is made possible by using Bayes Adaptive Monte Carlo planning and by endowing the agent with a user model that accounts for conservative belief updates and exploratory sampling of the points to query.

翻译：我们提出了一种协作贝叶斯优化问题，用于优化两个变量的黑箱函数。在该问题中，两个智能体共同选择查询函数的点，但各自仅能控制其中一个变量。这一设定受人类-人工智能团队协作的启发，即AI助手协助人类用户解决问题——在此最简情形中表现为协作优化。我们将该问题的解决方案建模为序贯决策过程，其中被我们控制的智能体将用户视为具备函数先验知识的计算理性智能体。研究表明，只要用户避免过度探索，通过策略性地规划查询点，能够更有效地识别函数的全局最大值。该规划的实现依赖于贝叶斯自适应蒙特卡洛规划方法，并通过赋予智能体一个用户模型来实现——该模型需考虑保守信念更新及对查询点的探索性采样。