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This work provides a simplified proof of the statistical minimax optimalityof (iterate averaged) stochastic gradient descent (SGD), for the special caseof least squares. This result is obtained by analyzing SGD as a stochasticprocess and by sharply characterizing the stationary covariance matrix of thisprocess. The finite rate optimality characterization captures the constantfactors and addresses model mis-specification.

A Markov Chain Theory Approach to Characterizing the Minimax Optimality of Stochastic Gradient Descent (for Least Squares)