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Motivated by broad applications in reinforcement learning and machinelearning, this paper considers the popular stochastic gradient descent (SGD)when the gradients of the underlying objective function are sampled from Markovprocesses. This Markov sampling leads to the gradient samples being biased andnot independent. The existing results for the convergence of SGD under Markovrandomness are often established under the assumptions on the boundedness ofeither the iterates or the gradient samples. Our main focus is to study thefinite-time convergence of SGD for different types of objective functions,without requiring these assumptions. We show that SGD converges nearly at thesame rate with Markovian gradient samples as with independent gradient samples.The only difference is a logarithmic factor that accounts for the mixing timeof the Markov chain.

Finite-Time Analysis of Stochastic Gradient Descent under Markov Randomness