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--- papers:bordes-bottou-gallinari-2009 [2010/12/28 10:56]
leonb
+++ papers:bordes-bottou-gallinari-2009 [2017/11/29 10:27] (current)
leonb [Errata]
@@ Line 12: / Line 12: @@
 PASCAL Large Scale Learning Challenge.
-//Note//:
+<html><font color=blue></html>
-The appendix contains a derivation of upper and lower bounds
+//Errata//:
-on the asymptotic convergence speed of stochastic gradient algorithm.
+Please see section [[#Errata]] below.
-This result is exact in the case of second order stochastic gradient.
+<html></font></html>
 <box 99% orange>
@@ Line 22: / Line 21: @@
 [[http://jmlr.csail.mit.edu/papers/v10/bordes09a.html|JMLR Link]]
+[[http://jmlr.csail.mit.edu/papers/v11/bordes10a.html|JMLR Erratum]]
+<html>&nbsp;&nbsp;</html>
 [[http://leon.bottou.org/publications/djvu/jmlr-2009.djvu|jmlr-2009.djvu]]
 [[http://leon.bottou.org/publications/pdf/jmlr-2009.pdf|jmlr-2009.pdf]]
@@ Line 46: / Line 47: @@
 This source code comes with a script that replicates the
 experiments discussed in this paper.
+==== Appendix ====
+The appendix contains a derivation of upper and lower bounds
+on the asymptotic convergence speed of stochastic gradient algorithm.
+The constants are exact in the case of second order stochastic gradient.
+==== Errata ====
+The SGDQN algorithm as described in this paper contains a subtle flaw
+described in a subsequent [[:papers:bordes-2010|erratum]].
+There is a missing 1/2 factor in the bounds of theorem 1.
+\[
+ \def\w{\mathbf{w}}
+ {\frac{1}{2}} \frac{{\mathrm tr}(\mathbf{HBGB})}{2\lambda_{\max}-1}\,t^{-1} + {\mathrm o}(t^{-1})
+  ~\leq~ \mathbb{E}_{\sigma}\big[\:{\cal P}_n(\w_t)-{\cal P}_n(\w^*_n)\:\big] ~\leq~
+  {\frac{1}{2}} \frac{{\mathrm tr}(\mathbf{HBGB})}{2\lambda_{\min}-1}\,t^{-1} + {\mathrm o}(t^{-1})
+\]
+The version of the paper found on this site contains the correct theorem and proof.

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