Linear Bandits in High Dimension and Recommendation Systems

I recently stumbled on a presentation by Andrea Montanari on Collaborative Filtering: Models and Algorithms where I learned that his team won the 2011 CAMrA competition 

If an AMP beat the netflix winner, I wonder if another AMP instance could beat SVDFeature at the latest KDD cups ? The seocnd part of the presentation is provided in more detail in Linear Bandits in High Dimension and Recommendation Systems by Yash Deshpande and Andrea Montanari

A large number of online services provide automated recommendations to help users to navigate through a large collection of items. New items (products, videos, songs, advertisements) are suggested on the basis of the user’s past history and –when available– her demographic profile. Recommendations have to satisfy the dual goal of helping the user to explore the space of available items, while allowing the system to probe the user’s preferences.We model this trade-off using linearly parametrized multi-armed bandits, propose a policy and prove upper and lower bounds on the cumulative “reward” that coincide up to constants in the data poor(high-dimensional) regime. Prior work on linear bandits has focused on the data rich (low-dimensional)regime and used cumulative “risk” as the figure of merit. For this data rich regime, we provide a simple modification for our policy that achieves near-optimal risk performance under more restrictive assumptions on the geometry of the problem. We test (a variation of) the scheme used for establishing achievability on the Netflix and MovieLens datasets and obtain good agreement with the qualitative predictions of the theory we develop.

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