{"ID":2868563,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.15552","arxiv_id":"2509.15552","title":"The Multi-Query Paradox in Zeroth-Order Optimization","abstract":"Zeroth-order (ZO) optimization provides a powerful framework for problems where explicit gradients are unavailable and have to be approximated using only queries to function value. The prevalent single-query approach is simple, but suffers from high estimation variance, motivating a multi-query paradigm to improve estimation accuracy. This, however, creates a critical trade-off: under a fixed budget of queries (i.e. cost), queries per iteration and the total number of optimization iterations are inversely proportional to one another. How to best allocate this budget is a fundamental, under-explored question. This work systematically resolves this query allocation problem. We analyze two aggregation methods: the de facto simple averaging (ZO-Avg), and a new Projection Alignment method (ZO-Align) we derive from local surrogate minimization. By deriving convergence rates for both methods that make the dependence on the number of queries explicit across strongly convex, convex, non-convex, and stochastic settings, we uncover a stark dichotomy: For ZO-Avg, we prove that using more than one query per iteration is always query-inefficient, rendering the single-query approach optimal. On the contrary, ZO-Align generally performs better with more queries per iteration, resulting in a full-subspace estimation as the optimal approach. Thus, our work clarifies that the multi-query problem boils down to a choice not about an intermediate query size, but between two classic algorithms, a choice dictated entirely by the aggregation method used. These theoretical findings are also consistently validated by extensive experiments.","short_abstract":"Zeroth-order (ZO) optimization provides a powerful framework for problems where explicit gradients are unavailable and have to be approximated using only queries to function value. The prevalent single-query approach is simple, but suffers from high estimation variance, motivating a multi-query paradigm to improve esti...","url_abs":"https://arxiv.org/abs/2509.15552","url_pdf":"https://arxiv.org/pdf/2509.15552v4","authors":"[\"Wei Lin\",\"Qingyu Song\",\"Hong Xu\"]","published":"2025-09-19T03:10:45Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}