Variable Forward Regularization to Replace Ridge in Online Linear Regression
Keywords: Forward regularization, linear regression, regret bound, continual learning
TL;DR: We propose the Variable Forward regularization and derive its regret bounds for online linear regression, showing better performance than Ridge and Forward in continual learning scenario..
Abstract: Forward regularization (-F) with unsupervised knowledge was proposed to replace canonical Ridge regularization (-R) in online linear learners, which achieves lower relative regret bounds. However, we observe that -F cannot perform as expected in practice, even possibly losing to -R for online learning tasks. We identify two main causes for this: (1) inappropriate intervention penalty; (2) potential non-i.i.d nature in online learning, both of which result in unstable posterior distribution and optima offset of the learner. To improve these, we propose Variable Forward regularization (-$k$F), a more general style with -F intensity modulated by a variable $k$. We further derive -$k$F algorithm to online learning tasks, which shows holistic recursive closed-form updates and superior performance compared to both -R and -F. Moreover, we theoretically establish the relative regrets of -$k$F in online learning, showing that it has a tighter upper bound than -F in adversarial settings. We also introduce an adaptive -$k$F, termed -$k$F-Bayes, to curb unstable penalties caused by non-i.i.d and mitigate intractable tuning of hard $k$ based on Bayesian learning for online learning. In experiments, we adapted -$k$F and -$k$F-Bayes into class incremental scenario, where it realized less forgetting and non-replay. Results distinctly demonstrate the efficacy of using -$k$F and -$k$F-Bayes.
Primary Area: transfer learning, meta learning, and lifelong learning
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Submission Number: 13067
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