Online learning with noisy side observations
This work provides a unified framework and efficient algorithm for online learning with noisy feedback, generalizing previous models and achieving near-optimal regret bounds.
The paper introduces a new partial-observability model for online learning with noisy side observations, represented by a weighted directed graph. The proposed algorithm achieves a regret of Õ(√(α* T)) without requiring knowledge of the graph property α*.
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.