Related papers: Stochastic Online Linear Regression: the Forward Algorithm to Replace Ridge

Stochastic Online Linear Regression: the Forward Algorithm to Replace Ridge

URL: http://arxiv.org/abs/2111.01602v1
Date: Tue, 2 Nov 2021 13:57:53 GMT
Title: Stochastic Online Linear Regression: the Forward Algorithm to Replace Ridge
Authors: Reda Ouhamma, Odalric Maillard, Vianney Perchet
Abstract summary: 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.
Score: 24.880035784304834
License: http://creativecommons.org/licenses/by-nc-sa/4.0/
Abstract: 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.

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