Efficient Contextual Bandits with Uninformed Feedback Graphs
This work addresses a gap in online learning for real-world applications like bidding where feedback graphs are not known in advance, offering a novel solution with practical impact.
The paper tackles the problem of contextual bandits with uninformed feedback graphs, where the graph is revealed after decisions or not at all, by developing the first efficient algorithm via reduction to online regression over losses and graphs, showing that using log loss for graph learning yields favorable regret guarantees and demonstrating empirical effectiveness on bidding applications.
Bandits with feedback graphs are powerful online learning models that interpolate between the full information and classic bandit problems, capturing many real-life applications. A recent work by Zhang et al. (2023) studies the contextual version of this problem and proposes an efficient and optimal algorithm via a reduction to online regression. However, their algorithm crucially relies on seeing the feedback graph before making each decision, while in many applications, the feedback graph is uninformed, meaning that it is either only revealed after the learner makes her decision or even never fully revealed at all. This work develops the first contextual algorithm for such uninformed settings, via an efficient reduction to online regression over both the losses and the graphs. Importantly, we show that it is critical to learn the graphs using log loss instead of squared loss to obtain favorable regret guarantees. We also demonstrate the empirical effectiveness of our algorithm on a bidding application using both synthetic and real-world data.