  Performative distribution shift captures the setting where the choice of
which ML model is deployed changes the data distribution. For example, a bank
which uses the number of open credit lines to determine a customer's risk of
default on a loan may induce customers to open more credit lines in order to
improve their chances of being approved. Because of the interactions between
the model and data distribution, finding the optimal model parameters is
challenging. Works in this area have focused on finding stable points, which
can be far from optimal. Here we introduce performative gradient descent
(PerfGD), which is the first algorithm which provably converges to the
performatively optimal point. PerfGD explicitly captures how changes in the
model affects the data distribution and is simple to use. We support our
findings with theory and experiments.
