EW with Gaussian prior matches the optimal O(d log(Bn)) regret for online logistic regression at O(B^3 n^5) cost and converges geometrically to a truncated Gaussian vote in the large-B separable regime.
and Telgarsky, M
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abstract
Gradient descent, when applied to the task of logistic regression, outputs iterates which are biased to follow a unique ray defined by the data. The direction of this ray is the maximum margin predictor of a maximal linearly separable subset of the data; the gradient descent iterates converge to this ray in direction at the rate $\mathcal{O}(\ln\ln t / \ln t)$. The ray does not pass through the origin in general, and its offset is the bounded global optimum of the risk over the remaining data; gradient descent recovers this offset at a rate $\mathcal{O}((\ln t)^2 / \sqrt{t})$.
fields
cs.LG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Mini-batch noise reverses how Adam's β2 controls anti-regularization, making default momentum values suitable for small batches but requiring β1 closer to β2 for large batches to favor flatter minima.
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Efficient Logistic Regression with Mixture of Sigmoids
EW with Gaussian prior matches the optimal O(d log(Bn)) regret for online logistic regression at O(B^3 n^5) cost and converges geometrically to a truncated Gaussian vote in the large-B separable regime.
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The Effect of Mini-Batch Noise on the Implicit Bias of Adam
Mini-batch noise reverses how Adam's β2 controls anti-regularization, making default momentum values suitable for small batches but requiring β1 closer to β2 for large batches to favor flatter minima.