Dynamic Regret Bounds for Online Omniprediction with Long Term Constraints
Yahav Bechavod, Jiuyao Lu, Aaron Roth
TL;DR
This work studies online omniprediction with long-term constraints, where a single forecaster broadcasts predictions for downstream decision makers who each optimize under their own linear utilities and constraint functions. The authors introduce a purely prediction-based, stateless decision rule and a calibration framework (decision calibration and infeasibility calibration) built on an Unbiased-Prediction backbone to obtain simultaneous dynamic regret and constraint-violation guarantees for many agents. They prove that cumulative constraint violations and swap-based regrets over arbitrary subsequences can be bounded with polylogarithmic dependence on the number of subsequences, enabling strong dynamic regret results (dynamic swap regret) and reducing to dynamic regret bounds for standard benchmarks. The approach yields practical benefits: downstream agents can operate without maintaining history, simply solving a one-round constrained optimization using the predicted outcome, while the forecaster guarantees diminishing regret and constraint violations across changing environments, making it well-suited for adversarial settings with multiple stakeholders.
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.