Dynamic Regret Bounds for Online Omniprediction with Long Term Constraints

2025-10-08

AI Summary

This paper studies online full-information learning with long-term constraints: a learner produces a single prediction per round, which multiple downstream decision-makers independently use to make decisions in a dynamic, adversarial environment. The objective is to simultaneously guarantee dynamic regret bounds for all decision-makers while minimizing cumulative constraint violations. Existing approaches typically require each agent to maintain internal state or solve complex multi-round optimization problems. In contrast, this work introduces the first stateless algorithm—relying solely on a single-round prediction to solve the constrained optimization problem, without inter-agent communication or storage of historical states. Theoretical analysis establishes that the algorithm achieves joint asymptotic optimality in both dynamic regret and constraint violation, thereby significantly enhancing scalability and practical applicability.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Machine Learning: Online Learning & Bandits

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

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.

Problem

• Achieving dynamic regret bounds for online omniprediction
• Ensuring vanishing constraint violations for all agents
• Providing worst-case utility guarantees to downstream decision makers

Innovation

• Dynamic regret bounds for online omniprediction
• Simultaneous guarantees for multiple decision makers
• Ensures vanishing constraint violation without state