直推式与学习增强型在线回归
Transductive and Learning-Augmented Online Regression
- University of Michigan（密歇根大学）
- Texas A&M University（德克萨斯农工大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对可获取未来样本预测的在线回归场景，刻画了直推式在线学习的最小最大期望后悔值，提出适配不完美预测的学习增强在线学习器，实现预测质量相关的性能提升，拓展了可学习类别范围。
AI中文摘要：
受现实数据流可预测特性的启发，我们研究了学习器可获取未来样本预测信息时的在线回归问题。在被称为直推式在线学习的极端场景中，样本序列会在博弈开始前就向学习器全部披露。针对该场景，我们通过胖粉碎维数（fat-shattering dimension）完整刻画了最小最大期望后悔值，明确了直推式在线回归与（对抗式）在线回归之间的差异。随后，我们将该场景推广至允许未来样本预测存在噪声或“不完美”的情况。借助直推式在线场景下的研究结果，我们设计了一种在线学习器，其最小最大期望后悔值与最坏情况后悔值相匹配，且会随预测质量提升而平滑下降；当未来样本预测较为精准时，其性能显著优于最坏情况后悔值，可达到与直推式在线学习器相近的表现。该研究让此前不可学习的类别在可预测样本场景下具备了可学习性，契合更广泛的学习增强模型范式。
英文摘要：
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.
