镜像流可实现渐进式学习，自动聚焦于新数据的可行解集。
Incremental Learning in Mirror Flows
- 通过镜像势能边界初始化，轨迹随时间演化逼近极限流
- 最终解在时变假设集中最小化损失，对应子微分支撑函数
- 适用于在线学习场景，尤其适合动态约束优化问题
我们研究由凸二次损失和一般凸下半连续镜像势能生成的镜像流。当初始点靠近镜像势能定义域边界时，其缩放后的轨迹收敛到一个极限镜像流，该流的势能为定义域的指示函数。在此极限下，原变量在时变假设集中最小化损失：即定义域支撑函数在对偶变量处的子微分。这一表征为镜像流中的渐进式学习提供了通用机制。
原文摘要 · Abstract (English)
We study mirror flows generated by a convex quadratic loss and a general convex lower semicontinuous mirror potential. We show that, when initialized near the boundary of the domain of the mirror potential, their rescaled trajectories converge to a limiting mirror flow whose potential is the indicator function of the domain. In this limit, the primal variable minimizes the loss over a time-dependent hypothesis set: the subdifferential of the support function of the domain, evaluated at the dual variable. This characterization provides a general mechanism for incremental learning in mirror flows.
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