We study finite-sum distributed optimization problems with $n$-clients under popular $\delta$-similarity condition and $\mu$-strong convexity. We propose two new algorithms: SVRS and AccSVRS motivated by previous works. The non-accelerated SVRS method combines the techniques of gradient-sliding and variance reduction, which achieves superior communication complexity $\tilde{\gO}(n {+} \sqrt{n}\delta/\mu)$ compared to existing non-accelerated algorithms. Applying the framework proposed in Katyusha X, we also build a direct accelerated practical version named AccSVRS with totally smoothness-free $\tilde{\gO}(n {+} n^{3/4}\sqrt{\delta/\mu})$ communication complexity that improves upon existing algorithms on ill-conditioning cases. Furthermore, we show a nearly matched lower bound to verify the tightness of our AccSVRS method.

翻译：我们研究了在流行的$\delta$-相似性条件和$\mu$-强凸性下，基于$n$个客户端的有限和分布式优化问题。受前人工作启发，我们提出了两种新算法：SVRS和AccSVRS。非加速的SVRS方法结合了梯度滑动与方差缩减技术，相较于现有非加速算法，实现了更优的通信复杂度$\tilde{\gO}(n {+} \sqrt{n}\delta/\mu)$。通过应用Katyusha X中提出的框架，我们进一步构建了直接加速的实用版本AccSVRS，其完全无光滑性依赖的通信复杂度为$\tilde{\gO}(n {+} n^{3/4}\sqrt{\delta/\mu})$，在病态情形下优于现有算法。此外，我们给出了近乎匹配的下界以验证AccSVRS方法的紧致性。