Cross-learning for performative prediction with changing objectives.

We study contextual performative prediction, where, given side information, a learner repeatedly chooses a model to deploy and incurs a context-dependent loss. Deploying a model influences the distribution of the resulting outcomes, but this influence is independent of the current context. Consequently, observing the outcome of deploying a model in one context also provides information about its behavior in other contexts. We formalize this structure through continuous-armed bandits with cross-learning and introduce the cross-context zooming dimension, a new complexity measure that captures the difficulty of learning across contexts. We establish a lower bound on the regret in terms of this dimension and design matching algorithms, first for the general cross-learning setting and then tailored to contextual performative prediction.