图 书 馆
基于熵对偶的广义可混性Generalized Mixability via Entropic Duality |
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| 课程网址: | https://videolectures.net/videos/colt2015_reid_entropic_duality |
| 主讲教师: | Mark Reid |
| 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: | Mixability is a property of a loss which characterizes when fast convergence is possible in the game of prediction with expert advice. We show that a key property of mixability generalizes, and the $\exp$ and $\log$ operations present in the usual theory are not as special as one might have thought. In doing so we introduce a more general notion of $\Phi$-mixability where $\Phi$ is a general entropy (\ie, any convex function on probabilities). We show how a property shared by the convex dual of any such entropy yields a natural algorithm (the minimizer of a regret bound) which, analogous to the classical Aggregating Algorithm, is guaranteed a constant regret when used with $\Phi$-mixable losses. We characterize which $\Phi$ have non-trivial $\Phi$-mixable losses and relate $\Phi$-mixability and its associated Aggregating Algorithm to potential-based methods, a Blackwell-like condition, mirror descent, and risk measures from finance. We also define a notion of ``dominance'' between different entropies in terms of bounds they guarantee and conjecture that classical mixability gives optimal bounds, for which we provide some supporting empirical evidence. |
| 关 键 词: | 可混合性概念; 遗憾界的最小化器; 最优界限 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2025-03-30：zsp |
| 最后编审: | 2025-03-30：zsp |
| 阅读次数: | 2 |