发表机构
Samsung Electronics; Korea Advanced Institute of Science and Technology（三星电子; 韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对固定查询次数的随机单调包含问题，提出VRAF和RRSEG两种加速算法，分别实现最优方差依赖和近乎最优复杂度，并证明确定性项下界不可达。
AI 中文摘要
我们研究了单调Lipschitz包含问题的随机一阶方法的加速，其中每次迭代使用固定数量的预言机查询，性能以期望平方残差衡量。现有方法要么具有次优的预言机复杂度，要么需要每次迭代增加预言机查询次数，或两者兼有。在同样本预言机访问和均方Lipschitz随机噪声条件下，我们提出了方差缩减锚定前向-后向算法（VRAF），这是一种任意时间复合方法，每次迭代进行两次预言机查询。VRAF在这些预言机假设下首次实现了无对数因子的$O(1/\epsilon)$复杂度，从而获得了最优的$O(\sigma^2/\epsilon)$方差依赖性。然而，这留下了最优的$O(1/\sqrt{\epsilon})$确定性项是否也能实现的问题。我们通过将Foster等人（2019）的下界扩展到允许对采样随机算子进行重复查询的随机预言机，建立了一个不可能性结果，表明$O(LD/\sqrt{\epsilon}+\sigma^2/\epsilon)$预言机复杂度在一般情况下是无法达到的。因此，我们开发了重中心正则化随机外梯度算法（RRSEG），该算法在每次迭代使用固定查询次数的情况下，实现了先前仅通过每次迭代增加查询次数才能达到的近乎最优预言机复杂度。
英文摘要
We study acceleration of stochastic first-order methods for monotone Lipschitz inclusions with a fixed number of oracle queries per iteration, measured by the expected squared residual. Existing methods either have suboptimal oracle complexity, require an increasing number of oracle queries per iteration, or both. Under same-sample oracle access and mean-square Lipschitz stochastic noise, we develop variance-reduced anchored forward-backward (VRAF), an anytime composite method that makes two oracle queries per iteration. VRAF attains the first log-free $O(1/ε)$ complexity under these oracle assumptions and hence the optimal $O(σ^2/ε)$ variance dependence. This, however, leaves open whether the optimal $O(1/\sqrtε)$ deterministic term can also be attained. We establish an impossibility result by extending the lower bound of Foster et al. (2019) to stochastic oracles permitting repeated queries to sampled stochastic operators, showing that $O(LD/\sqrtε+σ^2/ε)$ oracle complexity is unattainable in general. We therefore develop recentered regularized stochastic extragradient (RRSEG), which attains the near-optimal oracle complexity previously achievable only with an increasing number of queries per iteration, while using a fixed number of queries.
