2021/11/02 by Reda Ouhamma, Ouhamma, Reda, Odalric Maillard +3 · 1 citation
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Cognitive Radio Networks and Spectrum Sensing #Distributed Sensor Networks and Detection Algorithms #cs.LG
paper · pdf · doi:10.48550/arxiv.2111.01602
11+12 pages. To be published in the proceedings of NeurIPS 2021
arxiv created 2021/11/02 · arxiv updated 2021/11/03
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.