Parameter-Free Algorithms for Performative Regret Minimization under Decision-Dependent Distributions

We consider the general case where the per-formative risk can be non-convex, for which we develop efficient parameter-free optimistic optimization-based methods. Our algorithms significantly improve upon the existing Lips-chitz 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.