Unverified50% confidenceBenchmarkExact time
The complexity given in the paper under zeroth-order access (function value queries) is O(dδ⁻¹ε⁻³), where d is the problem dimension.
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10/12/2026
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UnverifiedFor nonsmooth nonconvex problems, the known optimal first-order complexity is O(ε^{-3}) and the zeroth-order complexity is O(d ε^{-3}).77% similarUnverifiedUnder first-order access, there was previously no known upper bound on the oracle complexity of composite optimization; under zeroth-order access, existing results are not optimal.75% similarUnverifiedThe query complexity given in the paper for finding a Goldstein stationary point under first-order access (stochastic gradient queries) is O(δ⁻¹ε⁻³), where δ is the Goldstein radius and ε is the stationarity tolerance.69% similarUnverifiedWhen using exact rational arithmetic, the bit length of intermediate rational numbers in the classical LLL algorithm can reach O(n·β) in the worst case, with an overall complexity of O(n⁵·β³) or even higher.65% similarUnverified根据率失真理论，若序列包含O(N)比特相关信息而隐状态只有O(d)比特容量，当N远大于d时必然产生信息丢失64% similar
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