Transductive and Learning-Augmented Online Regression
This work addresses the problem of making online regression more efficient when predictions about future data are available, which is incremental within the learning-augmented model paradigm.
The paper tackles online regression with access to predictions about future examples, establishing that the minimax expected regret in transductive online learning (where all examples are known in advance) is characterized by the fat-shattering dimension, showing a separation from adversarial online regression. It then develops an online learner that matches worst-case regret, improves with prediction quality, and achieves near-transductive performance with precise predictions, enabling learnability for previously unlearnable classes.
Motivated by the predictable nature of real-life in data streams, we study online regression when the learner has access to predictions about future examples. In the extreme case, called transductive online learning, the sequence of examples is revealed to the learner before the game begins. For this setting, we fully characterize the minimax expected regret in terms of the fat-shattering dimension, establishing a separation between transductive online regression and (adversarial) online regression. Then, we generalize this setting by allowing for noisy or \emph{imperfect} predictions about future examples. Using our results for the transductive online setting, we develop an online learner whose minimax expected regret matches the worst-case regret, improves smoothly with prediction quality, and significantly outperforms the worst-case regret when future example predictions are precise, achieving performance similar to the transductive online learner. This enables learnability for previously unlearnable classes under predictable examples, aligning with the broader learning-augmented model paradigm.