Stochastic Online Linear Regression: the Forward Algorithm to Replace Ridge
This work addresses the need for more accurate and robust online regression algorithms in machine learning, particularly for applications like linear bandits, though it appears incremental as it builds on existing methods.
The paper tackles the problem of online linear regression in stochastic settings by deriving high-probability regret bounds for ridge regression and the forward algorithm, showing that the forward algorithm provides better bounds and robustness to regularization parameters. It demonstrates this improvement in linear bandit settings with enhanced regret bounds and numerical experiments.
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.