提出自适应分布式核岭回归方法，无需通信本地数据即可自动调参。
Lepskii Principle for Distributed Kernel Ridge Regression
- 基于双加权平均合成策略设计自适应算法
- 理论证明可实现最优学习率并适配函数正则性
- 适合隐私保护与分布式场景下的高效建模
在分布式学习中，不通信本地数据的情况下进行参数选择极具挑战性，导致理论分析与实际应用之间存在不一致。受近期提出的 Lepskii 原理及非隐私通信协议启发，本文提出将 Lepskii 原理引入分布式核岭回归（DKRR），并通过双加权平均合成方案构建一种自适应的分布式核岭回归方法（称为 Lep-AdaDKRR）。我们推导了 Lep-AdaDKRR 的最优学习率，并理论上证明该方法能自适应地匹配回归函数的正则性、核函数的有效维度衰减速率以及不同的泛化度量，从而弥合了理论与应用间的鸿沟。
原文摘要 · Abstract (English)
Parameter selection without communicating local data is quite challenging in distributed learning, exhibing an inconsistency between theoretical analysis and practical application of it in tackling distributively stored data. Motivated by the recently developed Lepskii principle and non-privacy communication protocol for kernel learning, we propose a Lepskii principle to equip distributed kernel ridge regression (DKRR) and consequently develop an adaptive DKRR with Lepskii principle (Lep-AdaDKRR for short) by using a double weighted averaging synthesization scheme. We deduce optimal learning rates for Lep-AdaDKRR and theoretically show that Lep-AdaDKRR succeeds in adapting to the regularity of regression functions, effective dimension decaying rate of kernels and different metrics of generalization, which fills the gap of the mentioned inconsistency between theory and application.
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