Performative Prediction (2002.06673v4)

Abstract: When predictions support decisions they may influence the outcome they aim to predict. We call such predictions performative; the prediction influences the target. Performativity is a well-studied phenomenon in policy-making that has so far been neglected in supervised learning. When ignored, performativity surfaces as undesirable distribution shift, routinely addressed with retraining. We develop a risk minimization framework for performative prediction bringing together concepts from statistics, game theory, and causality. A conceptual novelty is an equilibrium notion we call performative stability. Performative stability implies that the predictions are calibrated not against past outcomes, but against the future outcomes that manifest from acting on the prediction. Our main results are necessary and sufficient conditions for the convergence of retraining to a performatively stable point of nearly minimal loss. In full generality, performative prediction strictly subsumes the setting known as strategic classification. We thus also give the first sufficient conditions for retraining to overcome strategic feedback effects.

Overview of "Performative Prediction"

The paper "Performative Prediction" introduces a framework to understand and address the effects of predictions influencing the outcomes they are meant to predict, a concept the authors term as "performativity." This phenomenon has long been recognized in the field of policy-making, but its implications in supervised learning have been underexplored prior to this work. The paper proposes a risk minimization framework by drawing from statistics, game theory, and causality to formalize performative prediction. It also introduces novel concepts such as "performative stability" and provides necessary and sufficient conditions for achieving such stability through retraining.

The paper exposes performativity as a source of distribution shift, often encountered in contexts where models support decision-making that feeds back into the input distribution. Examples include credit risk assessments influencing default rates, traffic predictions altering traffic flow, and recommendation systems shaping consumer preferences. Recognizing the performative effects is crucial as they transform the predictive model from merely a statistical tool to an agent within a feedback loop.

Key Results

1. Performative Risk and Stability: The authors define performative risk as the expectation of loss evaluated on the induced distribution, and propose the concept of performative stability, where a model is optimal for the distribution it induces.
2. Conditions for Stability: The paper's main theoretical result states that if the loss function is both smooth and strongly convex, and the distribution map is sufficiently Lipschitz, retraining through repeated risk minimization will converge linearly to a performatively stable point.
3. Convergence Analysis: They demonstrate that this convergence is robust under certain parameter choices and provide counterexamples showing divergence when these conditions are violated. Notably, strong convexity is highlighted as essential for the guaranteed convergence of such retraining dynamics, a distinction from standard convexity.
4. Closeness of Stable and Optimal Points: Another significant result is that under a strongly convex, Lipschitz loss and a Lipschitz distribution map, performatively stable and optimal points lie close to each other. This implies that reachability of a performatively stable point through such methods ensures near-optimal performative risk reduction.
5. Applicability to Strategic Classification: The illustration of the framework in the context of strategic classification reveals that retraining classifiers in environments where users adaptively respond to the classifier results leads to stable outcomes, thus overcoming strategic feedback loops.

Practical and Theoretical Implications

This work has far-reaching implications for fields that utilize predictive analytics within dynamic and interactive environments. By introducing a robust analytical framework to tackle performativity, it sets the stage for developing predictive models that remain reliably accurate in the presence of feedback-induced distribution shifts. In practical terms, these findings are essential for improving the reliability of predictive systems in finance, policing, marketing, and other domains, where the act of prediction can significantly influence the very system being predicted.

On a theoretical level, the paper expands the frontier of supervised learning by explaining how traditional risk minimization strategies can be adapted or need alteration in performative contexts. It integrates ideas from game theory, suggesting methods traditionally applied in strategic settings as applicable to broader predictive tasks subject to performative effects.

Future Directions

Future research can extend this work by examining alternative methodologies for achieving performative stability in cases where the assumptions of smoothness or strong convexity do not hold. Moreover, further exploration into scenarios with multiple interacting predictors, each subject to performative effects, would provide insights into more complex systems. Finally, real-world application studies to validate this theoretical framework can bridge the gap between theory and practice, ensuring predictive models are robust enough to withstand the dynamics of the environments they aim to predict.