# A Parameter-Free Stochastic LineseArch Method (SLAM) for Minimizing Expectation Residuals

arXiv: https://arxiv.org/abs/2512.14979 · HTML: https://mlsanity.com/paper/2512.14979/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2025.

## Built on by (most cited first, 1 of 1)

- [Stochastic Auto-conditioned Fast Gradient Methods with Optimal Rates](https://mlsanity.com/paper/2604.06525/) (2026)

## Abstract (arXiv)

Most existing rate and complexity guarantees for stochastic gradient methods in L-smooth settings mandates that such sequences be non-adaptive, non-increasing, and upper bounded by tfracaL for a > 0. This requires knowledge of L and may preclude larger steps. Motivated by these shortcomings, we present an Armijo-enabled stochastic linesearch framework with standard stochastic zeroth- and first-order oracles. The resulting steplength sequence is non-monotone and requires neither knowledge of L nor any other problem parameters. We then prove that the expected stationarity residual diminishes at a rate of O(1/√K), where K denotes the iteration budget. Furthermore, the resulting iteration and sample complexities for computing an ε-stationary point are O(ε-2) and Oleft(ε-4right). The proposed method allows for a simple nonsmooth convex component in the objective, addressed through proximal gradient updates. Analogous guarantees are provided in the Polyak-Lojasiewicz (PL) setting and convex regimes. Preliminary numerical experiments are seen to be promising.