Unverified50% confidenceFactExact time
In the adversarial environment, the regret of the paper's algorithm is \tilde{\mathcal{O}}(δ_*^{1/3} T^{2/3}), where δ_* is the fractional weak domination number.
1
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50%
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Long-term
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11/4/2026
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Related Claims
UnverifiedIn the stochastic environment, the regret of the paper's algorithm is \tilde{\mathcal{O}}(δ_* \log T / Δ_{\min}^2), where Δ_{\min} is the minimum suboptimality gap.78% similarUnverifiedFor nonsmooth nonconvex problems, the known optimal first-order complexity is O(ε^{-3}) and the zeroth-order complexity is O(d ε^{-3}).65% similarUnverifiedThree methods are commonly used in scaling-law fitting practice—least squares with fixed E, fitting with E as a free parameter, and linear regression in log space—and the optimal ratios they yield may differ.64% similarUnverifiedIn the non-convex, high-dimensional, small-accuracy regime, the reasonable goal for zeroth-order algorithms is linear in d and close to ε^{-4} in accuracy, rather than pursuing sublinear dimension.64% similarUnverifiedUnder the premises of smooth stochastic nonconvexity, a global lower bound for the population objective, and a second-moment bound on the sample Lipschitz constant, the paper gives a scalar oracle lower bound of Ω(d L_0^2 min{ΔH, L_0^2} / ε^4), which is linear in d and ε^{-4} in accuracy.63% similar
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