Title: Algorithmic Chaining and the Role of Partial Feedback in Online Nonparametric Learning,
Abstract: We investigate contextual online learning with nonparametric (Lipschitz)
comparison classes under different assumptions on losses and feedback
information. For full information feedback and Lipschitz losses, we design the
first explicit algorithm achieving the minimax regret rate (up to log factors).
In a partial feedback model motivated by second-price auctions, we obtain
algorithms for Lipschitz and semi-Lipschitz losses with regret bounds improving
on the known bounds for standard bandit feedback. Our analysis combines novel
results for contextual second-price auctions with a novel algorithmic approach
based on chaining. When the context space is Euclidean, our chaining approach
is efficient and delivers an even better regret bound.