Online learning with noisy side observations

2026-04-15

AI Summary

This work studies a novel partially observable online learning setting in which, beyond observing their own loss, the learner receives noisy feedback on other actions dictated by the problem structure, modeled via a weighted directed graph. The authors introduce a new graph-theoretic quantity—the effective independence number α*—and propose the first fully parameter-free algorithm that requires neither prior knowledge nor estimation of α*. By integrating techniques from online learning and graph theory, the algorithm achieves a regret bound of Õ(√(α* T)) over T rounds. In the special case of binary edge weights, it recovers the best-known results in the literature, substantially advancing the ability to leverage noisy side observations for efficient decision-making.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a new partial-observability model for online learning problems where the learner, besides its own loss, also observes some noisy feedback about the other actions, depending on the underlying structure of the problem. We represent this structure by a weighted directed graph, where the edge weights are related to the quality of the feedback shared by the connected nodes. Our main contribution is an efficient algorithm that guarantees a regret of $\widetilde{O}(\sqrt{α^* T})$ after $T$ rounds, where $α^*$ is a novel graph property that we call the effective independence number. Our algorithm is completely parameter-free and does not require knowledge (or even estimation) of $α^*$. For the special case of binary edge weights, our setting reduces to the partial-observability models of Mannor and Shamir (2011) and Alon et al. (2013) and our algorithm recovers the near-optimal regret bounds.

Problem

• online learning
• noisy side observations
• partial observability
• feedback graph
• regret minimization

Innovation

• online learning
• partial observability
• noisy side observations
• effective independence number
• parameter-free algorithm