Parameter-Free Algorithms for Performative Regret Minimization under Decision-Dependent Distributions
This work addresses optimization challenges in dynamic environments where decisions influence data distributions, offering a more practical approach for applications like adaptive systems, though it is incremental in improving upon prior Lipschitz bandit methods.
The paper tackles performative risk minimization under decision-dependent distributions with non-convex risks by developing parameter-free optimistic optimization algorithms that do not require prior knowledge of sensitivity parameters or Lipschitz constants, resulting in improved performance over existing methods as shown in experiments.
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.