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        Department of Systems Engineering and Engineering Management

                            The Chinese University of Hong Kong

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Date: 16:30 pm - 17:30 pm on 19 December (Friday)

Venue: ERB 513, The Chinese University of Hong Kong

Title: High-Order Error Bounds for Markovian LSA with Richardson-Romberg Extrapolation

Speaker: Ilya Levin, Faculty of Computer Science, HSE University





Abstract:

We study the bias and high-order error bounds of the Linear Stochastic Approximation (LSA) algorithm with Polyak-Ruppert (PR) averaging under Markovian noise. We focus on the version of the algorithm with constant step size  and propose a novel decomposition of the bias via a linearization technique. We analyze the structure of the bias and show that the leading-order term is linear in  and cannot be eliminated by PR averaging. To address this, we apply the Richardson-Romberg (RR) extrapolation procedure, which effectively cancels the leading bias term. We derive high-order moment bounds for the RR iterates and show that the leading error term aligns with the asymptotically optimal covariance matrix of the vanilla averaged LSA iterates.

Bio:

Ilya Levin a Junior Research Fellow at the International Laboratory of Stochastic Algorithms and High-Dimensional Inference, and a 3rd-year PhD student in Faculty of Computer Science, HSE University, Moscow, Russia. His research interests include stochastic approximation, federated learning and reinforcement learning. Specifically, his work involves probabilistic inference for stochastic approximation and federated stochastic approximation.



Everyone is welcome to attend the talk!