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.

我们提出了一种合作的贝叶斯优化问题，用于优化两个变量的黑盒函数，其中两个代理一起选择在哪些点查询函数，但每个代理只能控制一个变量。这个设置受到人工智能与人类合作的启发，在这种简单情况下进行协同优化。我们将解决方案制定为顺序决策过程，我们控制的代理将用户建模为一个具有先验知识的计算有理主体。我们展示了通过战略查询规划可以更好地识别函数的全局最大值，只要用户避免过度探索。这种规划是通过使用贝叶斯自适应蒙特卡洛规划以及赋予代理用户模型来实现的，该用户模型考虑了保守的信念更新和查询点的探索性采样。