  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.
