The meta model seeks to answer "what would the outcome be if we were to deploy a different

Machine learning aims to generalize models trained on given datasets to make accurate predictions or decisions on new, unseen data (El Naqa and Murphy, 2015). The effectiveness of those models depends on the alignment between the training datasets and deployment environments (Quinonero-Candela et al.,2008).

Performative predictions influence the very outcomes they aim to forecast. We study performative predictions that affect a sample (e.g., only existing users of an app) and/or the whole population (e.g., all potential app users). This raises the question of how well models generalize under performativity. For example, how well can we draw insights about new app users based on existing users when both of them react to the app's predictions? We address this question by embedding performative predictions into statistical learning theory. We prove generalization bounds under performative effects on the sample, on the population, and on both. A key intuition behind our proofs is that in the worst case, the population negates predictions, while the sample deceptively fulfills them. We cast such self-negating and self-fulfilling predictions as min-max and min-min risk functionals in Wasserstein space, respectively. Our analysis reveals a fundamental trade-off between performatively changing the world and learning from it: the more a model affects data, the less it can learn from it. Moreover, our analysis results in a surprising insight on how to improve generalization guarantees by retraining on performatively distorted samples. We illustrate our bounds in a case study on prediction-informed assignments of unemployed German residents to job trainings, drawing upon administrative labor market records from 1975 to 2017 in Germany.

Predictions about people, such as their expected educational achievement or their credit risk, can be performative and shape the outcome that they are designed to predict. Understanding the causal effect of predictions on the eventual outcomes is crucial for foreseeing the implications of future predictive models and selecting which models to deploy. However, this causal estimation task poses unique challenges: model predictions are usually deterministic functions of input features and highly correlated with outcomes, which can make the causal effects of predictions on outcomes impossible to disentangle from the direct effect of the covariates. We study this problem through the lens of causal identifiability. Despite the hardness of this problem in full generality, we highlight three natural scenarios where the causal effect of predictions can be identified from observational data: randomization in predictions, overparameterization of the predictive model deployed during data collection, and discrete prediction outputs. Empirically we show that given our identifiability conditions hold, standard variants of supervised learning that predict from predictions by treating the prediction as an input feature can find transferable functional relationships that allow for conclusions about newly deployed predictive models. These positive results fundamentally rely on model predictions being recorded during data collection, bringing forward the importance of rethinking standard data collection practices to enable progress towards a better understanding of social outcomes and performative feedback loops.

Distribution variations in machine learning, driven by the dynamic nature of deployment environments, significantly impact the performance of learning models. This paper explores endogenous distribution shifts in learning systems, where deployed models influence environments and subsequently alter data distributions. This phenomenon is formulated by a decision-dependent distribution mapping within the recently proposed framework of performative prediction (PP) Perdomo et al. (2020). We investigate the performative effect in a decentralized noncooperative game, where players aim to minimize private cost functions while simultaneously managing coupled inequality constraints. Under performativity, we examine two equilibrium concepts for the studied game: performative stable equilibrium (PSE) and Nash equilibrium (NE), and establish sufficient conditions for their existence and uniqueness. Notably, we provide the first upper bound on the distance between the PSE and NE in the literature, which is challenging to evaluate due to the absence of strong convexity on the joint cost function. Furthermore, we develop a decentralized stochastic primal-dual algorithm for efficiently computing the PSE point. By carefully bounding the performative effect in theoretical analysis, we prove that the proposed algorithm achieves sublinear convergence rates for both performative regrets and constraint violation and maintains the same order of convergence rate as the case without performativity.

In performative learning, the data distribution reacts to the deployed model - for example, because strategic users adapt their features to game it - which creates a more complex dynamic than in classical supervised learning. One should thus not only optimize the model for the current data but also take into account that the model might steer the distribution in a new direction, without knowing the exact nature of the potential shift. We explore how regularization can help cope with performative effects by studying its impact in high-dimensional ridge regression. We show that, while performative effects worsen the test risk in the population setting, they can be beneficial in the over-parameterized regime where the number of features exceeds the number of samples. We show that the optimal regularization scales with the overall strength of the performative effect, making it possible to set the regularization in anticipation of this effect. We illustrate this finding through empirical evaluations of the optimal regularization parameter on both synthetic and real-world datasets.

The meta model seeks to answer "what would the outcome be if we were to deploy a different

Performativity of predictions refers to the phenomena that prediction-informed decisions may influence the target they aim to predict, which is widely observed in policy-making in social sciences and economics. In this paper, we initiate the study of statistical inference under performativity. Our contribution is two-fold. First, we build a central limit theorem for estimation and inference under performativity, which enables inferential purposes in policy-making such as constructing confidence intervals or testing hypotheses. Second, we further leverage the derived central limit theorem to investigate prediction-powered inference (PPI) under performativity, which is based on a small labeled dataset and a much larger dataset of machine-learning predictions. This enables us to obtain more precise estimation and improved confidence regions for the model parameter (i.e., policy) of interest in performative prediction. We demonstrate the power of our framework by numerical experiments. To the best of our knowledge, this paper is the first one to establish statistical inference under performativity, which brings up new challenges and inference settings that we believe will add significant values to policy-making, statistics, and machine learning.

Calibrating blackbox machine learning models to achieve risk control is crucial to ensure reliable decision-making. A rich line of literature has been studying how to calibrate a model so that its predictions satisfy explicit finite-sample statistical guarantees under a fixed, static, and unknown data-generating distribution. However, prediction-supported decisions may influence the outcome they aim to predict, a phenomenon named performativity of predictions, which is commonly seen in social science and economics. In this paper, we introduce Performative Risk Control, a framework to calibrate models to achieve risk control under performativity with provable theoretical guarantees. Specifically, we provide an iteratively refined calibration process, where we ensure the predictions are improved and risk-controlled throughout the process. We also study different types of risk measures and choices of tail bounds. Lastly, we demonstrate the effectiveness of our framework by numerical experiments on the task of predicting credit default risk. To the best of our knowledge, this work is the first one to study statistically rigorous risk control under performativity, which will serve as an important safeguard against a wide range of strategic manipulation in decision-making processes.

Distribution variations in machine learning, driven by the dynamic nature of deployment environments, significantly impact the performance of learning models. This paper explores endogenous distribution shifts in learning systems, where deployed models influence environments and subsequently alter data distributions. This phenomenon is formulated by a decision-dependent distribution mapping within the recently proposed framework of performative prediction (PP) Perdomo et al. (2020). We investigate the performative effect in a decentralized noncooperative game, where players aim to minimize private cost functions while simultaneously managing coupled inequality constraints. Under performativity, we examine two equilibrium concepts for the studied game: performative stable equilibrium (PSE) and Nash equilibrium (NE), and establish sufficient conditions for their existence and uniqueness.