Combining diffusion strategies with complementary properties enables enhanced performance when they can be run simultaneously. In this article, we first propose two schemes for the convex combination of two diffusion strategies, namely, the power-normalized scheme and the sign-regressor scheme. Then, we conduct theoretical analysis for one of the schemes, i.e., the power-normalized one. An analysis of universality shows that it cannot perform worse than any of its component strategies in terms of the excess mean-square-error (EMSE) at steady state, and sometimes even better. An analysis of stability also reveals that it is more stable than affine combination schemes already proposed by the authors in the literature. Next, several adjustments are proposed to further improve the performance of convex combination schemes. A discussion about the computational and communication complexity is provided, as well as a comparison between convex and affine combination schemes. Finally, simulation results are shown to demonstrate their effectiveness, the accuracy of the theoretical results, and the improved stability of the convex power-normalized scheme over the affine one.

中文翻译：

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网络上扩散策略的凸组合

当扩散策略可以同时运行时，将扩散策略与互补属性结合起来可以提高性能。在本文中，我们首先针对两种扩散策略的凸组合提出两种方案，即功率归一化方案和正负回归方案。然后，我们对其中一种方案进行了理论分析，即功率归一化方案。对普遍性的分析表明，就稳定状态下的均方误差（EMSE）而言，它的表现不会比其任何组件策略都要差，甚至有时甚至更好。对稳定性的分析还表明，它比文献中作者已经提出的仿射组合方案更稳定。接下来，提出了一些调整以进一步提高凸组合方案的性能。提供了有关计算和通信复杂性的讨论，以及凸和仿射组合方案之间的比较。最后，仿真结果显示了其有效性，理论结果的准确性以及凸幂归一化方案相对于仿射方案的改进稳定性。