GraphDR-LinUCB Improves Contextual Bandit Performance with Dimensionality Reduction.

Contextual bandit problems, common in recommendation systems and advertising, often involve items with inherent graph structures where connected items tend to share similar reward signals. Traditional dimensionality reduction techniques fail to leverage this structure, leading to higher exploration costs. Researchers have developed GraphDR-LinUCB, an innovative approach that projects arm features onto the graph's low-frequency spectral subspace. This method effectively reduces the problem's dimensionality from 'd' to 'k', leading to more efficient exploration. The new method demonstrates significant improvements, achieving a regret bound of \wtO(k\sqrt{T}), a substantial reduction compared to previous methods. The study also extends its applicability to noisy graphs, accounting for reward-smoothness mismatch and graph-estimation errors. A key theoretical insight is that high-frequency reward components do not necessarily incur a worst-case linear penalty, but rather a cost dependent on their impact along the chosen path. Empirical evaluations across synthetic and six real-world datasets, including MovieLens and Amazon, show GraphDR-LinUCB reducing cumulative regret by 15 times over full-dimensional LinUCB and outperforming most competing graph-aware methods. A simple spectral comparison metric, \Gamma_k, accurately predicts the method's success, highlighting its practical utility.