Quantitative Central Limit Theorems for Discrete Stochastic Processes
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In this paper, we establish a generalization of the classical Central Limit Theorem for a family of stochastic processes that includes stochastic gradient descent and related gradient-based algorithms. Under certain regularity assumptions, we show that the iterates of these stochastic processes converge to an invariant distribution at a rate of O1/√(k) where k is the number of steps; this rate is provably tight.
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