Stochastic Heavy Ball with Polyak Step Size and Armijo Line Search: A General Convergence Analysis
Polyak step size (PS) and Armijo line search (ALS) have received increasing attention in stochastic optimization, with encouraging empirical performance and theoretical guarantees. However, their convergence theory for stochastic heavy ball (SHB) methods remains limited. In this work, we develop a unified convergence analysis for SHB equipped with PS and ALS. To this end, we introduce a modified Armijo rule that closely parallels the Polyak step size, together with a decoupling analysis that isolates the historical dependence induced by momentum. For SHB with standard PS and ALS, we establish expected convergence for strongly convex, convex, and non-convex objectives without interpolation...
| Authors | Jiawei Zhang, Qitan Shi, Yuantao Gu |
|---|---|
| Primary category | cs.LG |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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