algorithms-optimization / Stochastic optimization

Bounded Oracle Error in Nonconvex Stochastic Optimization

Arjevani et al. asked whether almost-surely bounded oracle error permits a better rate than bounded variance for smooth nonconvex stochastic optimization. It does not: every randomized adaptive algorithm still needs Omega(dL/eps^2 + dL sigma^2/eps^4) queries, matching the standard upper bound.

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algorithms-optimizationAug 10, 2026Significance 12/100Registry: unreviewed

Bounded Oracle Error in Nonconvex Stochastic Optimization

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Arjevani et al. asked whether almost-surely bounded oracle error permits a better rate than bounded variance for smooth nonconvex stochastic optimization. It does not: every randomized adaptive algorithm still needs Omega(dL/eps^2 + dL sigma^2/eps^4) queries, matching the standard upper bound.

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Arjevani et al. asked whether almost-surely bounded oracle error permits a better rate than bounded variance for smooth nonconvex stochastic optimization. It does not: every randomized adaptive algorithm still needs Omega(dL/eps^2 + dL sigma^2/eps^4) queries, matching the standard upper bound.

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Bounded Oracle Error in Nonconvex Stochastic Optimization — Mathematical Frontier Network