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- W618263208 abstract "Almost sure convergence rates for linear algorithms $h_{k+1} = h_k +frac{1}{k^chi} (b_k-A_kh_k)$ are studied, where $chiin(0,1)$, ${A_{k}}_{k=1}^infty$ are symmetric, positive semidefinite random matrices and ${b_{k}}_{k=1}^infty$ are random vectors. It is shown that $n^{gamma}|h_n- A^{-1}b|rightarrow 0 ,$ a.s. for the $gammain[0,chi)$, positive definite $A$ and vector $b$ such that $frac{1}{n^{chi-gamma}}sum_{k=1}^n (A_{k}- A)to 0$ and $frac{1}{n^{chi-gamma}}sum_{k=1}^n (b_k-b)to 0$ a.s. When $chi-gammainleft(frac12,1right)$, these assumptions are implied by the Marcinkiewicz strong law of large numbers, which allows the ${A_k}$ and ${b_k}$ to have heavy tails, long-range dependence, or both. Finally, corroborating experimental outcomes and decreasing-gain design considerations are provided." @default.
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- W618263208 date "2015-01-01" @default.
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- W618263208 title "Convergence Rates and Decoupling in Linear Stochastic Approximation Algorithms" @default.
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- W618263208 doi "https://doi.org/10.1137/14095707x" @default.
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