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Non-Asymptotic SGD Inference via Rates of Martingale CLT

GGAM Colloquium

Speaker: Krishna Balasubramanian, UC Davis, Dept. of Statistics, GGAM
Location: 1147 MSB
Start time: Thu, Feb 28 2019, 3:35PM

We provide non-asymptotic convergence rates of the Polyak-Ruppert averaged Stochastic Gradient Descent (SGD) to a normal random vector for a class of twice-differentiable test functions. A crucial intermediate step is proving a non-asymptotic martingale Central Limit Theorem (CLT), i.e., establishing the rates of convergence of a multivariate martingale difference sequence to a normal random vector, which might be of independent interest. The results have potentially interesting consequences for computing confidence intervals for parameter estimation with SGD and constructing hypothesis tests with SGD that are valid in a non-asymptotic sense.