  Decision-makers often act in response to data-driven predictions, with the
goal of achieving favorable outcomes. In such settings, predictions don't
passively forecast the future; instead, predictions actively shape the
distribution of outcomes they are meant to predict. This performative
prediction setting raises new challenges for learning "optimal" decision rules.
In particular, existing solution concepts do not address the apparent tension
between the goals of forecasting outcomes accurately and steering individuals
to achieve desirable outcomes.
  To contend with this concern, we introduce a new optimality concept --
performative omniprediction -- adapted from the supervised (non-performative)
learning setting. A performative omnipredictor is a single predictor that
simultaneously encodes the optimal decision rule with respect to many
possibly-competing objectives. Our main result demonstrates that efficient
performative omnipredictors exist, under a natural restriction of performative
prediction, which we call outcome performativity. On a technical level, our
results follow by carefully generalizing the notion of outcome
indistinguishability to the outcome performative setting. From an appropriate
notion of Performative OI, we recover many consequences known to hold in the
supervised setting, such as omniprediction and universal adaptability.
