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最小最大固定设计线性回归Minimax Fixed-Design Linear Regression |
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| 课程网址: | https://videolectures.net/videos/colt2015_malek_linear_regression |
| 主讲教师: | Alan Malek |
| 开课单位: | 信息不详。欢迎您在右侧留言补充。 |
| 开课时间: | 2025-02-04 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | We consider a linear regression game in which the covariates are known in advance: at each round, the learner predicts a real-value, the adversary reveals a label, and the learner incurs a squared error loss. The aim is to minimize the regret with respect to linear predictions. For a variety of constraints on the adversary's labels, we show that the minimax optimal strategy is linear, with a parameter choice that is reminiscent of ordinary least squares (and as easy to compute). The predictions depend on all covariates, past and future, with a particular weighting assigned to future covariates corresponding to the role that they play in the minimax regret. We study two families of label sequences: box constraints (under a covariate compatibility condition), and a weighted 2-norm constraint that emerges naturally from the analysis. The strategy is adaptive in the sense that it requires no knowledge of the constraint set. We obtain an explicit expression for the minimax regret for these games. For the case of uniform box constraints, we show that, with worst case covariate sequences, the regret is $O(d\log T)$, with no dependence on the scaling of the covariates. |
| 关 键 词: | 线性回归博弈; 协变量：线性预测 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2025-03-28：zsp |
| 最后编审: | 2025-03-28：zsp |
| 阅读次数: | 4 |