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. * Equal contribution.

In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions.We initiate the study of stochastic optimization for performative prediction. What sets this setting apart from traditional stochastic optimization is the difference between merely updating model parameters and deploying the new model. The latter triggers a shift in the distribution that affects future data, while the former keeps the distribution as is.Assuming smoothness and strong convexity, we prove non-asymptotic rates of convergence for both greedily deploying models after each stochastic update (greedy deploy) as well as for taking several updates before redeploying (lazy deploy). In both cases, our bounds smoothly recover the optimal O(1/k) rate as the strength of performativity decreases. Furthermore, they illustrate how depending on the strength of performative effects, there exists a regime where either approach outperforms the other. We experimentally explore this trade-off on both synthetic data and a strategic classification simulator. * Equal contribution.

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Proximal Policy Optimization (PPO) is a popular deep policy gradient algorithm. In standard implementations, PPO regularizes policy updates with clipped probability ratios, and parameterizes policies with either continuous Gaussian distributions or discrete Softmax distributions. These design choices are widely accepted, and motivated by empirical performance comparisons on MuJoCo and Atari benchmarks. We revisit these practices outside the regime of current benchmarks, and expose three failure modes of standard PPO. We explain why standard design choices are problematic in these cases, and show that alternative choices of surrogate objectives and policy parameterizations can prevent the failure modes. We hope that our work serves as a reminder that many algorithmic design choices in reinforcement learning are tied to specific simulation environments. We should not implicitly accept these choices as a standard part of a more general algorithm.