High-Probability PL-SGD with Markovian Noise: Optimal Mixing and Tail Dependence
We study first-order methods for smooth objectives satisfying the Polyak-Łojasiewicz (PL) condition when gradient samples are generated by an exogenous Markov chain. In the light-tailed setting, prior uniform-in-time high-probability bounds for ordinary Stochastic Gradient Descent (SGD) under a standard growth envelope scale as $\widetilde{O}(t_{mix}^2/k)$, leaving a gap with the $\widetilde{O}(t_{mix}/k)$ expectation bounds. We close this gap using a lag-blocking argument to establish a uniform high-probability guarantee with a leading stochastic term of $\widetilde{O}(t_{mix}/(k+K_0))$ under geometric mixing. We prove this linear dependence on the mixing time is optimal via a matching $...
| Authors | Dhruv Sarkar, Aprameyo Chakrabartty, Vaneet Aggarwal |
|---|---|
| Primary category | cs.LG |
| Published | 24 June 2026 |
| Last updated at source | 24 June 2026 |
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