Shuffling the Stochastic Mirror Descent via Dual Lipschitz Continuity and Kernel Conditioning
The global Lipschitz smoothness condition underlies most convergence and complexity analyses via two key consequences: the descent lemma and the gradient Lipschitz continuity. How to study the performance of optimization algorithms in the absence of Lipschitz smoothness remains an active area. The relative smoothness framework from Bauschke-Bolte-Teboulle (2017) and Lu-Freund-Nesterov (2018) provides an extended descent lemma, ensuring convergence of Bregman-based proximal gradient methods and their vanilla stochastic counterparts. However, many widely used techniques (e.g., momentum schemes, random reshuffling, and variance reduction) additionally require the Lipschitz-type bound for gra...
| Authors | Junwen Qiu, Leilei Mei, Junyu Zhang |
|---|---|
| Primary category | math.OC |
| Published | 17 March 2026 |
| Last updated at source | 17 March 2026 |
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