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Poster
Stochastic Online Linear Regression: the Forward Algorithm to Replace Ridge
reda None ouhamma · Odalric-Ambrym Maillard · Vianney Perchet

Tue Dec 07 08:30 AM -- 10:00 AM (PST) @ None #None
We consider the problem of online linear regression in the stochastic setting. We derive high probability regret bounds for online $\textit{ridge}$ regression and the $\textit{forward}$ algorithm. This enables us to compare online regression algorithms more accurately and eliminate assumptions of bounded observations and predictions. Our study advocates for the use of the forward algorithm in lieu of ridge due to its enhanced bounds and robustness to the regularization parameter. Moreover, we explain how to integrate it in algorithms involving linear function approximation to remove a boundedness assumption without deteriorating theoretical bounds. We showcase this modification in linear bandit settings where it yields improved regret bounds. Last, we provide numerical experiments to illustrate our results and endorse our intuitions.

Author Information

reda None ouhamma (Université de Lille)
Odalric-Ambrym Maillard (INRIA Lille Nord Europe)
Vianney Perchet (ENSAE & Criteo AI Lab)

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