Title: Dynamic Regret Bounds for Online Omniprediction with Long Term Constraints
Primary area: learning theory
Keywords: omniprediction, online learning, dynamic regret, long-term constraints

Abstract: We present an algorithm guaranteeing dynamic regret bounds for online omniprediction with long term constraints. The goal in this recently introduced problem is for a learner to generate a sequence of predictions which are broadcast to a collection of downstream decision makers. Each decision maker has their own utility function, as well as a vector of constraint functions, each mapping their actions and an adversarially selected state to reward or constraint violation terms.  The downstream decision makers select actions ``as if'' the state predictions are correct, and the goal of the learner is to produce predictions such that all downstream decision makers choose actions that give them worst-case utility guarantees while minimizing worst-case constraint violation. Within this framework, we give the first algorithm that obtains simultaneous \emph{dynamic regret} guarantees for all of the agents --- where regret for each agent is measured against a potentially changing sequence of actions across rounds of interaction, while also ensuring vanishing constraint violation for each agent. Our results do not require the agents themselves to maintain any state --- they only solve one-round constrained optimization problems defined by the prediction made at that round.