Stochastic Online Linear Regression: the Forward Algorithm to Replace Ridge

Reda Ouhamma (1, 2, 3, 4) , Odalric Maillard (4, 1, 2) , Vianney Perchet (5)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 Inria Lille - Nord Europe
3 Université de Lille
4 Scool - Scool
5 CREST - Centre de Recherche en Economie et Statistique [Bruz]

We consider the problem of online linear regression in the stochastic setting. We derive high probability regret bounds for online ridge regression and the 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.

Domaines: Informatique [cs]; Mathématiques [math]

Reda Ouhamma, Odalric Maillard, Vianney Perchet. Stochastic Online Linear Regression: the Forward Algorithm to Replace Ridge. NeurIPS 2021 - 35th International Conference on Neural Information Processing Systems, Dec 2021, Virtual, Canada. ⟨hal-03410901⟩