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.

Based on our theoretical analysis, we propose an active learning algorithm that employs regret minimization to minimize the FIR.

Bwk work Liu et al. (2022), we do not require a bounded global variation.

There aretwointeresting andwell-studied computational paradigms aimed attackling uncertainty.

This gives rise to a rich collection oftopological relationships and conditions under which VE models are optimal for planning. Despite this effort, relatively little is known about the planning performance of models that fail to satisfy these conditions.