This paper studies performative risk minimization, a formulation of
stochastic optimization under decision-dependent distributions. We consider the
general case where the performative risk can be non-convex, for which we
develop efficient parameter-free optimistic optimization-based methods. Our
algorithms significantly improve upon the existing Lipschitz bandit-based
method in many aspects. In particular, our framework does not require knowledge
about the sensitivity parameter of the distribution map and the Lipshitz
constant of the loss function. This makes our framework practically favorable,
together with the efficient optimistic optimization-based tree-search
mechanism. We provide experimental results that demonstrate the numerical
superiority of our algorithms over the existing method and other black-box
optimistic optimization methods.

本文研究了行为风险最小化，这是一种在决策依赖分布下的随机优化方法。我们考虑了一般情况下的非凸型行为风险，在此基础上，我们提出了高效的无参数乐观优化方法。我们的算法在许多方面显著优于现有的利普希茨贝叶斯方法。特别是，我们的框架不需要关于分布映射的敏感性参数和损失函数的利普希茨常数的知识。这使得我们的框架在实践中更有优势，结合高效的基于乐观优化方法的树搜索机制。通过实验证据，我们展示了我们的算法在数值上优于现有方法和其他黑箱乐观优化方法。