{"ID":2827804,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.14979","arxiv_id":"2512.14979","title":"A Parameter-Free Stochastic LineseArch Method (SLAM) for Minimizing Expectation Residuals","abstract":"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 $\\tfrac{a}{L}$ for $a \u003e 0$. 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 $\\mathcal{O}(1/\\sqrt{K})$, where $K$ denotes the iteration budget. Furthermore, the resulting iteration and sample complexities for computing an $ε$-stationary point are $\\mathcal{O}(ε^{-2})$ and $\\mathcal{O}\\left(ε^{-4}\\right)$. 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.","short_abstract":"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 $\\tfrac{a}{L}$ for $a \u003e 0$. This requires knowledge of $L$ and may preclude larger steps. Motivated by these shortcomings, we present an...","url_abs":"https://arxiv.org/abs/2512.14979","url_pdf":"https://arxiv.org/pdf/2512.14979v1","authors":"[\"Qi Wang\",\"Uday V. Shanbhag\",\"Yue Xie\"]","published":"2025-12-17T00:22:46Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}