Excess risk of SGD and ridge regression on GNNs is characterized through graph spectra, showing graph shape decides which algorithm generalizes better and deeper networks amplify the difference.
A Markov Chain Theory Approach to Characterizing the Minimax Optimality of Stochastic Gradient Descent (for Least Squares)
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abstract
This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and by sharply characterizing the stationary covariance matrix of this process. The finite rate optimality characterization captures the constant factors and addresses model mis-specification.
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cs.LG 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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On the Interplay between Graph Structure and Learning Algorithms in Graph Neural Networks
Excess risk of SGD and ridge regression on GNNs is characterized through graph spectra, showing graph shape decides which algorithm generalizes better and deeper networks amplify the difference.