Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization
We provide a theoretical analysis of Adam under non-stationary stochastic objectives, separating two regimes: Euclidean tracking under adaptive strong monotonicity of the Adam-preconditioned mean-gradient operator, and high-probability projected stationarity guarantees under general $L$-smooth objectives. In the tracking regime, we derive finite-time expected and high-probability bounds that decompose sharply into four components: initialization, objective drift, a first-moment tracking error governed by $β_1$, and a preconditioner perturbation governed by $β_2$. We characterize the burn-in time required for the transient terms to decay to the asymptotic tracking bound under constant and ...
| Authors | Sharan Sahu, Abir Sarkar, Cameron J. Hogan et al. |
|---|---|
| Primary category | stat.ML |
| Published | 5 May 2026 |
| Last updated at source | 11 September 2026 |
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