{"ID":2898181,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.04133","arxiv_id":"2507.04133","title":"Online Convex Optimization with Switching Cost with Only One Single Gradient Evaluation","abstract":"Online convex optimization with switching cost is considered under the frugal information setting where at time $t$, before action $x_t$ is taken, only a single function evaluation and a single gradient is available at the previously chosen action $x_{t-1}$ for either the current cost function $f_t$ or the most recent cost function $f_{t-1}$. When the switching cost is linear, online algorithms with optimal order-wise competitive ratios are derived for the frugal setting. When the gradient information is noisy, an online algorithm whose competitive ratio grows quadratically with the noise magnitude is derived.","short_abstract":"Online convex optimization with switching cost is considered under the frugal information setting where at time $t$, before action $x_t$ is taken, only a single function evaluation and a single gradient is available at the previously chosen action $x_{t-1}$ for either the current cost function $f_t$ or the most recent...","url_abs":"https://arxiv.org/abs/2507.04133","url_pdf":"https://arxiv.org/pdf/2507.04133v1","authors":"[\"Harsh Shah\",\"Purna Chandrasekhar\",\"Rahul Vaze\"]","published":"2025-07-05T19:08:11Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.DS\",\"cs.LG\"]","methods":"[]","has_code":false}