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Generalization Properties and Implicit Regularization for Multiple Passes SGM

ICML 2016 · Optimization › Implicit bias and generalization · approach: Implicit regularization of SGD · 45 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
multiple passes with early stopping (SIGM, fixed step) vs one pass SGM with tuned step-sizeSIGM constant step 1/sqrt(m) · Adult n=32562 / BreastCancer / Ijcnn1 n=49990test error (hinge loss)Mixed
decaying step-size with multiple passes (SIGM, theta=1/2) instead of constant stepSIGM decaying step 1/4, theta=1/2 · Adult / BreastCancer / Ijcnn1 (all n reported)test error (hinge loss)Hurt
multiple passes with early stopping (SIGM, constant step) vs one pass SGM in training timeSIGM constant step · Adult n=32562training time (s)Hurt
SGM and SIGM vs LIBSVM training time on large datasetsSGM/SIGM · Adult n=32562training time (s)Helped
step-size decay exponent theta (fixed step-size theta=0 vs larger theta) as regularizer in one-pass SGM (ablation)SGM with decaying step-size eta_t = 1/4 t^-theta · Adult n=1000test error (hinge loss)Mixed
large fixed step-size (eta=1) in SGM vs small step (1e-3) (ablation)SGM fixed step-size · Adult n=1000test error (hinge loss)Mixed
early stopping (number of passes) as regularizer in SIGM with fixed step 1/sqrt(n) (ablation)SIGM fixed step 1/sqrt(n) · Adult n=1000test error (hinge loss)Helped

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