Beyond Performative Prediction: Open-environment Learning with Presence of Corruptions

Performative prediction is a framework to capture the endogenous distribution changes resulting from the reactions of deployed environments to the learner's decision. Existing results require that the collected data are sampled from the clean observed distribution. However, this is often not the case in real-world applications, and even worse, data collected in open environments may include corruption due to various undesirable factors. In this paper, we study the entanglement of endogenous distribution change and corruption in open environments, where data are obtained from a corrupted decision-dependent distribution. The central challenge in this problem is the entangling effects between changing distributions and corruptions, which impede the use of effective gradient-based updates. To overcome this difficulty, we propose a novel recursive formula that decouples the two sources of effects, which allows us to further exploit suitable techniques for handling two decoupled effects and obtaining favorable guarantees. Theoretically, we prove that our proposed algorithm converges to the desired solution under corrupted observations, and simultaneously it can retain a competitive rate in the uncorrupted case. Experimental results also support our theoretical findings.