AI RESEARCH
Central Limit Theorems for Stochastic Gradient Descent Quantile Estimators
arXiv CS.LG
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ArXi:2503.02178v2 Announce Type: replace-cross This paper develops asymptotic theory for quantile estimation via stochastic gradient descent (SGD) with a constant learning rate. The quantile loss function is neither smooth nor strongly convex. Beyond conventional perspectives and techniques, we view quantile SGD iteration as an irreducible, periodic, and positive recurrent Marko chain, which cyclically converges to its unique stationary distribution regardless of the arbitrarily fixed initialization.