Tian Xie

Tian Xie, Ding Zhu, Jia Liu et al.

Performative prediction (PP) is an algorithmic framework for optimizing machine learning (ML) models where the model's deployment affects the distribution of the data it is trained on. Compared to traditional ML with fixed data, designing algorithms in PP converging to a stable point -- known as a stationary performative stable (SPS) solution -- is more challenging than the counterpart in conventional ML tasks due to the model-induced distribution shifts. While considerable efforts have been made to find SPS solutions using methods such as repeated gradient descent (RGD) and greedy stochastic gradient descent (SGD-GD), most prior studies assumed a strongly convex loss until a recent work established $O(1/\sqrt{T})$ convergence of SGD-GD to SPS solutions under smooth, non-convex losses. However, this latest progress is still based on the restricted bounded variance assumption in stochastic gradient estimates and yields convergence bounds with a non-vanishing error neighborhood that scales with the variance. This limitation motivates us to improve convergence rates and reduce error in stochastic optimization for PP, particularly in non-convex settings. Thus, we propose a new algorithm called stochastic performative prediction with variance reduction (SPRINT) and establish its convergence to an SPS solution at a rate of $O(1/T)$. Notably, the resulting error neighborhood is independent of the variance of the stochastic gradients. Experiments on multiple real datasets with non-convex models demonstrate that SPRINT outperforms SGD-GD in both convergence rate and stability.

Xue Zheng, Tian Xie, Xuwei Tan et al.

Performative prediction is a framework that captures distribution shifts that occur during the training of machine learning models due to their deployment. As the trained model is used, data generation causes the model to evolve, leading to deviations from the original data distribution. The impact of such model-induced distribution shifts in federated learning is increasingly likely to transpire in real-life use cases. A recently proposed approach extends performative prediction to federated learning with the resulting model converging to a performative stable point, which may be far from the performative optimal point. Earlier research in centralized settings has shown that the performative optimal point can be achieved under model-induced distribution shifts, but these approaches require the performative risk to be convex and the training data to be noiseless, assumptions often violated in realistic federated learning systems. This paper overcomes all of these shortcomings and proposes Performative Robust Optimal Federated Learning, an algorithm that finds performative optimal points in federated learning from noisy and contaminated data. We present the convergence analysis under the Polyak-Lojasiewicz condition, which applies to non-convex objectives. Extensive experiments on multiple datasets demonstrate the advantage of Robust Optimal Federated Learning over the state-of-the-art.

Kun Jin, Tian Xie, Yang Liu et al.

In many real-world applications of machine learning such as recommendations, hiring, and lending, deployed models influence the data they are trained on, leading to feedback loops between predictions and data distribution. The performative prediction (PP) framework captures this phenomenon by modeling the data distribution as a function of the deployed model. While prior work has focused on finding performative stable (PS) solutions for robustness, their societal impacts, particularly regarding fairness, remain underexplored. We show that PS solutions can lead to severe polarization and prediction performance disparities, and that conventional fairness interventions in previous works often fail under model-dependent distribution shifts due to failing the PS criteria. To address these challenges in PP, we introduce novel fairness mechanisms that provably ensure both stability and fairness, validated by theoretical analysis and empirical results.