Lower Bounds for Randomized Linear-Oracle Optimization over Strongly Convex Sets

Name: Lower Bounds for Randomized Linear-Oracle Optimization over Strongly Convex Sets
Uploaded: 2026-10-19T01:09:22.227656+00:00
Duration: 482 s
Description: The authors prove a distributional lower bound of $\Omega(Ldiam(S)^2/T^2)$ for randomized first-order linear minimization oracle methods over strongly convex sets. This demonstrates that randomization cannot improve the order of convergence compared to deterministic methods, establishing a gap between the two bounds.

The authors prove a distributional lower bound of $\Omega(Ldiam(S)^2/T^2)$ for randomized first-order linear minimization oracle methods over strongly convex sets. This demonstrates that randomization cannot improve the order of convergence compared to deterministic methods, establishing a gap between the two bounds.

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