Unverified50% confidenceOpinionExact time
In 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.
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10/15/2026
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Related Claims
UnverifiedSince the joint lower bound shows that the dependence on (d, δ, ε) cannot be optimized in a decomposed manner, the trade-offs in algorithm design should be placed on improving constants and practical sample reuse efficiency, rather than attempting to break through the product structure of the three in worst-case guarantees.69% similarUnverifiedIn zeroth-order optimization, converting function values into gradient estimates via finite differences or Gaussian smoothing and then applying first-order methods usually incurs a cost linear in the dimension d.69% similarUnverified能用确定性工具解决的解析任务不应交给概率性的LLM，因为确定性工具速度快、结果确定、零幻觉69% similarUnverifiedInformation-theoretic lower bounds characterize the best performance achievable by any algorithm (even exponential-time) without computational resource constraints, corresponding in this problem to Õ(md+k); computational lower bounds, by contrast, assume the algorithm must run in polynomial time, and the resulting bounds are usually larger.67% similarUnverifiedFor practical algorithm design, when the dimension d is large and the number of switches k is non-negligible, accepting Õ(dk)-level regret or seeking additional structural assumptions may be a more pragmatic direction than relying on discretization or exact optimization.67% similar
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