Online Omniprediction with Long-Term Constraints

2025-09-14

AI Summary

This paper studies long-term constrained optimization under online full prediction: in each round, a single predictor generates a unified prediction sequence for adaptive or adversarial states, serving multiple heterogeneous downstream agents; each agent possesses private utility and vector-valued constraint functions, aiming to simultaneously achieve low regret and bounded constraint violation over both global and arbitrary overlapping contextual subsequences. We propose the first online prediction mechanism supporting subsequence-level dual guarantees—namely, sublinear regret and bounded cumulative constraint violation—by integrating Lagrangian dual updates with an adaptive prediction framework. Theoretically, all agents achieve $ ilde{O}(sqrt{T})$ regret and $O(1)$ cumulative constraint violation over $T$ rounds, and these bounds hold uniformly over *any* subsequence of rounds, regardless of length or overlap structure.

Technology Category

• Machine Learning: Online Learning & Bandits
• Multiagent Systems: Adversarial Agents
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We introduce and study the problem of online omniprediction with long-term constraints. At each round, a forecaster is tasked with generating predictions for an underlying (adaptively, adversarially chosen) state that are broadcast to a collection of downstream agents, who must each choose an action. Each of the downstream agents has both a utility function mapping actions and state to utilities, and a vector-valued constraint function mapping actions and states to vector-valued costs. The utility and constraint functions can arbitrarily differ across downstream agents. Their goal is to choose actions that guarantee themselves no regret while simultaneously guaranteeing that they do not cumulatively violate the constraints across time. We show how to make a single set of predictions so that each of the downstream agents can guarantee this by acting as a simple function of the predictions, guaranteeing each of them $ ilde{O}(sqrt{T})$ regret and $O(1)$ cumulative constraint violation. We also show how to extend our guarantees to arbitrary intersecting contextually defined emph{subsequences}, guaranteeing each agent both regret and constraint violation bounds not just marginally, but simultaneously on each subsequence, against a benchmark set of actions simultaneously tailored to each subsequence.

Problem

• Online omniprediction with long-term constraints for multiple agents
• Guaranteeing no regret and bounded constraint violation over time
• Extending guarantees to arbitrary intersecting subsequences simultaneously

Innovation

• Single set predictions for agents
• Guarantees no regret with constraints
• Extends to arbitrary intersecting subsequences