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Performance limits of stochastic sub-gradient learning, part Ⅱ: Multi-agent case

机译：随机次梯度学习的性能极限，第二部分：多主体案例

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Highlights•A novel sub-gradient assumption is proposed.•New convergence and steady-state performance is been proved.•Multiple examples with this new assumption has been investigated.AbstractIn this work and the supporting Part II [1], we examine the performance of stochastic sub-gradient learning strategies under weaker conditions than usually considered in the literature. The new conditions are shown to be automatically satisfied by several important cases of interest including SVM, LASSO, and Total-Variation denoising formulations. In comparison, these problems do not satisfy the traditional assumptions used in prior analyses and, therefore, conclusions derived from these earlier treatments are not directly applicable to these problems. The results in this article establish that stochastic sub-gradient strategies can attain linear convergence rates, as opposed to sub-linear rates, to the steady-state regime. A realizable exponential-weighting procedure is employed to smooth the intermediate iterates and guarantee useful performance bounds in terms of convergence rate and excessive risk performance. Part I of this work focuses on single-agent scenarios, which are common in stand-alone learning applications, while Part II [1] extends the analysis to networked learners. The theoretical conclusions are illustrated by several examples and simulations, including comparisons with the FISTA procedure.
机译： 突出显示 • 提出了一种新颖的次梯度假设。 • 证明了新的收敛性和稳态性能。 • 已经有了具有此新假设的多个示例 摘要 在本工作和第二部分的支持部分[1]中，我们研究了在较弱的条件下随机次梯度学习策略的性能比文献中通常考虑的条件。几个重要的关注案例（包括SVM，LASSO和Total-Variation去噪公式）自动满足了新条件。相比之下，这些问题不能满足先前分析中使用的传统假设，因此，从这些较早处理中得出的结论并不直接适用于这些问题。本文的结果证明，对于亚稳态策略，随机次梯度策略可以获得相对于次线性率的线性收敛速度。采用可实现的指数加权程序来平滑中间迭代，并确保收敛速度和过度风险表现方面的有用性能界限。这项工作的第一部分着重于单代理场景，这在独立学习应用程序中很常见，而第二部分[1]将分析扩展到网络学习者。通过几个示例和仿真，包括与FISTA程序的比较，说明了理论结论。

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