483101a6bc4e6c46a86222eb65fbcb6a-Supplemental.pdf

C.3 Errorpropagation In the next lemma we extend the Lemma 5 to include errors t at computation of the regularized Bellmanoperator. By combining smoothing with regularization, we obtain a smooth regularized Bellman operator. Similar to Lemma 6, the result follows by considering an additional vector of errors in Lemma7. Because the eigenvectors u1,u2,... are pairwise orthogonal, we have kV(t) bk+1k2 O(e λmin(K)t)kV(0) bk+1k2, and so V(t) converges tobk+1 in the limit ast (in any norm, since all norms are equivalent in finite-dimensional spaces) exponentially fast with rate