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On the convergence of linear stochastic approximation procedures

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1 Author(s)
M. A. Kouritzin ; Inst. for Math. & Applications, Minnesota Univ., Minneapolis, MN, USA

Many stochastic approximation procedures result in a stochastic algorithm of the form hk+1=hk+1/k(bk-A khk), for all k=1,2,3,... . Here, {bk,k=1,2,3...} is a Rd-valued process, {Ak,k=1,2,3,...} is a symmetric, positive semidefinite R ed×d-valued process, and {hk,k=1,2,3,...} is a sequence of stochastic estimates which hopefully converges to hΔ=[limN→∞/1 k=1NEAk]-1 {limN→∞/1k=1NEb k} (assuming everything here is well defined). We give an elementary proof which relates the almost sure convergence of {hk ,k=1,2,3,...} to strong laws of large numbers for {bk,k=1,2,3,...} and {Ak,k=1,2,3,...}

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IEEE Transactions on Information Theory  (Volume:42 ,  Issue: 4 )