2 problems
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Improved logarithmic factors for high-probability stochastic minimization
Logarithmic-factor improvement conjecture. Adjusting the proof technique from Nguyen et al. should improve the logarithmic factors in the authors' results as well.
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The high-probability logarithmic-factor necessity conjecture
Consider high-probability statistical bounds for estimators, including the total-variation estimator in Gaussian denoising, where logarithmic factors may appear in the rate. Bounds…