This work demonstrates linear dimension dependence for one-point feedback ZO optimization algorithms, highlighting improvements over traditional approaches.
We revisit the one-point feedback zeroth-order (ZO) optimization problem, a classical setting in derivative-free optimization where only a single noisy function evaluation is available per query. Compared to their two-point counterparts, existing one-point feedback ZO algorithms typically suffer from poor dimension dependence in their sample complexities -- often quadratic or worse -- even for convex problems. This gap has led to the open question of whether one-point feedback ZO algorithms can match the optimal linear dimension dependence achieved by two-point methods. In this work, we answer this question affirmatively.
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Ye et al. (2025) studied this question.
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