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该论文刻画了在线凸优化中仅能访问线性优化预言机时的紧确遗憾界，给出了维度无关的极小极大期望遗憾 Θ(GD·max{√T, T/(1+min{Q,BT})^{1/4}})，并同时证明了适用于任意随机化学习者的下界与匹配的算法上界。
This paper proves sharp dimension-free first-order lower bounds for finding epsilon-stationary points in higher-order smooth nonconvex optimization, resolving open problems for Hessian-Lipschitz and third-order smooth cases.