Performative Prediction

Many social applications of machine learning exhibit performative effects: population behavior changes in response to deployed models. Performative prediction studies this interaction through a distribution map that relates each model to the population distribution it induces. One of the main results in this framework showed that repeated risk minimization (RRM), which updates models by retraining on the most recent data, can converge to a stable model that minimizes risk on its own induced distribution. However, existing analyses typically assume access to the complete distributions of features and labels after model deployment, ignoring the possibility of selective labels: observing labels only for the accepted subset of the population. In this work, we formalize performative prediction with selective labels and show that retraining only on observed data can misguide the retraining procedure and undermine the guarantees of convergence to a stable solution. We then propose a worst-case objective based on knowledge of a confidence interval on the probability of a positive label. Applying RRM to this objective permits us to remain within a bounded distance to the true stable point. Under a sensitivity assumption on the conditional label distribution, we further show how previously accepted data can tighten these confidence intervals over time. Experiments in a lending application with fairness regularization show that our robust optimization approach closely matches the performance of RRM with complete label access.

Privacy-preserving learning is often motivated by the idea that protecting users' data can preserve trust and thus participation, improving utility in the long term. However, this claim has not been formalized so far. In parallel, performative learning provides a framework for studying learning systems whose deployment affects the data they later observe. In this work, we bring these two perspectives together and introduce performative privacy, where data leakage reduces future participation. We study a simple model where agents repeatedly contribute data for mean estimation but may leave the system when their data is leaked. Privacy is implemented through differentially private mechanisms, creating a trade-off between estimation noise and future participation. We show, through a theoretical study of the dynamics and numerical experiments, that a finite privacy budget can outperform non-private estimation in the long term when the feedback loop between leakage and participation is sufficiently strong. This provides first evidence that differential privacy can be optimal not only as a protection mechanism, but also from the perspective of long-term utility.

Algorithmic recourse aims to provide individuals with actionable changes to improve their predicted outcomes in high-stakes classification settings, such as loan and mortgage applications. However, most existing approaches focus only on flipping a model's prediction, without accounting for whether the recommended changes lead to genuine improvement in an individual's true qualifications or merely enable strategic gaming of the classifier. Consequently, deployed recourse policies can induce behavioral responses that degrade predictive accuracy and become ineffective after model retraining. In this work, we formalize this failure mode through a causal performative framework for recourse. We model how recourse actions propagate through a structural causal model, capturing interactions among features as well as their effect on the true label. These causal responses induce a non-convex optimization problem, even under standard convex losses. We characterize conditions under which performatively stable solutions exist and can be efficiently computed via simple iterative dynamics. Our analysis reveals that recourse policies that ignore causal structure can induce large, misaligned behavioral responses, whereas causal recourse leads to stable equilibria that reduce incentives for gaming. Experiments on both semi-synthetic and real credit datasets demonstrate that our approach consistently outperforms standard empirical risk minimization while reducing the need for repeated model retraining to accommodate distribution shifts caused by strategic agent behavior.

In many domains such as Palliative Care, Credit Assignment and Recommender Systems, predictions may causally influence the outcomes they predict. This phenomena is known as Outcome Performativity. This paper formalises an approach for detecting Outcome Performativity using prediction intervention called Outcome Performativity A/B Detection (OPAB). OPAB enables the detection of Outcome Performativity by assessing the dissimilarity in outcome distributions produced by different predictions groups (interventions). If that dissimilarity is significant, Outcome Performativity is detected. We derive sample complexity bounds for OPAB under various Outcome Performative assumption classes which we empirically validate. Results show that detecting Outcome Performativity using OPAB is achievable in numerous cases. Results also show the presence of regions of indistinguishability which describe settings where the allotted number of interventions are insufficient for detecting Outcome Performativity. The results of which have broader practical implications for the detectability of Outcome Performativity in settings where samples are scarce, cost-prohibitive or potentially unethical to obtain. The paper concludes with a case study on the efficacy of OPAB on the Open Bandits dataset, and provides directions for future work.

We study optimization under performative prediction, where deploying a model affects the future data distribution. For this setting, several gradient-based approaches have been proposed. However, they typically assume specific data distributions or loss functions, which limit their practical applicability. To overcome these limitations, we propose a gradient-based optimization method with convergence guarantees under substantially weaker assumptions. Our method explicitly estimates the induced distribution shift through finite differences. It enables higher-dimensional optimization across broader classes of loss functions and data distributions. We also propose a practical variant that reduces the number of samples required. Numerical experiments demonstrate that our proposed algorithms converge faster and more consistently than existing ones.

Predictive models deployed at scale influence future data, a phenomenon called performativity. And there is always one way to cope: Train the model on new data, deploy it again, and repeat. This process, called retraining or repeated risk minimization, creates a feedback loop between model and data that real-world learning systems can't avoid. Results on performative prediction shed light on this dynamic: If the model's influence on the data is small, retraining reaches a fixed point. What remains open is why fixed points should naturally exist, and what governs retraining when the model's influence is strong. In this work we develop a new perspective on retraining -- the stable signal principle -- that addresses these questions. We start from the assumption that the prediction target has at least some small model-independent component, a stable signal, such as the intrinsic quality of an item. We prove that when a nonzero stable signal exists, repeated risk minimization, suitably regularized, converges geometrically to the direction of this stable signal. This is true even if the model's influence on the target is arbitrarily large relative to the stable signal. Regularization emerges naturally as a force to control performativity, rather than to promote generalization, revealing a new facet of an old concept. We extend the analysis to a broad family of affine retraining operators under arbitrary model-induced feature changes, heterogeneous time-varying effects, and nonlinear responses. The stable signal perspective also applies to data feedback loops in language modeling, providing new explanations for the stability of language model training from model-generated data.

A non-agentic "oracle" that reports probabilities of future events is performative: once its answer is learned and acted upon, it can change the very probability it was asked to report. Performativity is not in itself the difficulty -- one consults an oracle precisely in order to be informed, and hence influenced, by it. The difficulty is agency. The requirement that a report be self-consistent, still holding once announced, may be met by many different values -- the classical non-uniqueness of self-fulfilling prophecies -- and any rule the system uses to choose among them is a lever for goal-directed steering. We remove the choice rather than the performativity. Reporting a credal set instead of a single probability distribution, we lift the reaction to an isotone operator on the complete lattice of closed credal sets, whose fixed points are self-consistent, and report its Knaster--Tarski least fixed point as a canonical, rule-determined answer; a variant reports instead the least fixed point that contains every self-consistent point estimate. We prove existence, self-consistency, and nonemptiness; show that the construction reduces to the classical point answer when the question is non-performative; and show that for a binary event the answer is, under a natural hull-factoring assumption, an interval.

Federated bilevel optimization is widely used for nested learning problems across distributed clients, such as federated hyperparameter tuning and meta-learning under privacy and communication constraints. Most existing formulations assume fixed client data distributions, which can be violated by performativity, where deployed decisions reshape client behavior and data collection, inducing client-specific, decision-dependent distribution shift. We study federated bilevel performative prediction, where both upper-level (UL) and lower-level (LL) objectives are evaluated under client-dependent, decision-dependent distributions. We formalize the federated bilevel performatively stable (FBPS) point under a decoupled-risk perspective and provide sufficient conditions for its existence and uniqueness. We then develop two federated methods to compute the FBPS solution: FBi-RRM, which converges linearly under a contraction condition, and FBi-SGD, a communication-efficient stochastic method based on federated hypergradient estimation with convergence guarantees under diminishing step sizes when sensitivities are sufficiently small. Experiments on strategic regression and meta strategic classification validate the predicted stability thresholds and demonstrate improved meta-generalization over non-performative baselines, and CNN-based classification further demonstrates the practical effectiveness of the proposed methods in nonconvex neural network settings.

Performative prediction studies feedback loops that arise when predictive models are deployed in consequential domains. In these settings, deploying a model can change the population whose patterns the model aims to predict, inducing a distribution shift that is endogenous to the learning system. This perspective departs from classical treatments of distribution shift, where shifts are typically modeled as exogenous changes in the data-generating process. Yet, in practice, distribution shift is rarely one or the other. Predictive models may influence future data through the decisions they support, while the world itself continues to drift for reasons beyond the learner's control. We study partially performative prediction, a framework that captures both endogenous and exogenous sources of distribution shift. The framework generalizes performative prediction by allowing the data distribution to evolve both in response to the deployed model and according to an external, time-varying process. We extend the central notions of performative stability and performative optimality to this setting by defining their online analogues that track the evolving partially performative environment. We analyze practical learning heuristics, including repeated retraining, and characterize when they successfully adapt to partially performative environments.

We study off-policy evaluation (OPE) under strategic behavior where decision subjects (or agents) respond to a decision maker's policy by strategically modifying their covariates. Such behavior induces a policy-dependent covariate shift, breaking the standard assumption in existing methods that covariates are exogenous to the policy. Related work addresses this challenge by imposing strong assumptions such as repeated interactions or full knowledge of agents' response behavior, substantially limiting its applicability to OPE. In contrast, we consider a one-shot OPE setting where the decision maker has only partial knowledge of the agents' response behavior. Our key insight is that disclosing local information through post-hoc explanations reveals agents' pre-strategic covariates prior to adaptation, mitigating the information loss induced by strategic behavior. Leveraging this structure, we estimate a statistical model for the agents' responses and construct a doubly robust estimator for policy value. By assuming that the agents' cost sensitivity follows a conditional log-normal distribution, we establish consistency of the proposed estimator and validate our approach empirically. More broadly, our results highlight how interaction design can mitigate information asymmetry by revealing otherwise hidden structure in agents' strategic responses.

Online link recommendation on evolving graphs is performative: by choosing which candidate links to show users, the system changes which links form and what feedback it later observes. Consequently, fairness estimates from logged outcomes can be misleading and may drift after deployment when the recommendation policy is updated. We introduce COPF (Counterfactual Online Performative Fairness), a decision-layer framework for deployment-stable fairness monitoring and control in online link recommendation. COPF (i) defines group-level opportunity gaps over exposure (shown vs. not shown) counterfactuals, (ii) makes them estimable by explicit exploration and by logging the probability (propensity) that each candidate is shown, and (iii) audits and controls fairness using residual outcome indistinguishability (OI) over a configurable auditor family with graph-aware doubly robust (GA-DR) estimators. We provide a noisy transfer theorem showing that Residual-OI on estimated GA-DR residuals implies bounds on exposure-counterfactual group gaps under temporal mixing and bounded local interference, and we instantiate an online multicalibration auditor together with a primal-dual controller. Experiments on two TGB streams and a controlled synthetic bipartite stream show that COPF reduces worst-case spikes in exposure-counterfactual group disparities with modest impact on ranking utility. Our code is available at https://github.com/lsnnnnnnnn/COPF.

In algorithmic markets, predictive models become part of the data-generating process they aim to forecast. Once their outputs are converted into trades, allocations, execution schedules, or risk controls, they change the future data on which they are evaluated. I introduce algometrics, a framework for time series whose evolution depends on the predictive algorithms forecasting them. The framework distinguishes historical risk, measured under passive forecasting, from deployment risk, measured when forecasts drive actions. I prove three results. First, deployment risk is not identifiable from passive historical data alone: even in a one-step linear feedback model, infinitely many algorithm-mediated environments induce the same historical law while implying different deployment risks for the same forecaster. Second, historical model rankings can invert under crowding, so a predictor with lower passive error can have higher deployment error once similar algorithms are adopted. Third, randomized or instrumented actions identify short-horizon linear feedback, and I derive a finite-sample bound for deployment-risk estimation. These results suggest that time-series benchmarks in algorithmic markets should report feedback sensitivity alongside predictive accuracy.