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From dbtsai <...@git.apache.org>
Subject [GitHub] spark pull request: L-BFGS Documentation
Date Fri, 09 May 2014 22:55:19 GMT
Github user dbtsai commented on a diff in the pull request:

https://github.com/apache/spark/pull/702#discussion_r12499273

--- Diff: docs/mllib-optimization.md ---
@@ -128,10 +128,24 @@ is sampled, i.e. $|S|=$ miniBatchFraction $\cdot n = 1$, then
the algorithm is
standard SGD. In that case, the step direction depends from the uniformly random sampling
of the
point.

+### Limited-memory BFGS
+[Limited-memory BFGS (L-BFGS)](http://en.wikipedia.org/wiki/Limited-memory_BFGS) is an
optimization
+algorithm in the family of quasi-Newton methods to solve the optimization problems of
the form
+$\min_{\wv \in\R^d} \; f(\wv)$. The L-BFGS approximates the objective function locally
+without evaluating the second partial derivatives of the objective function to construct
the
+Hessian matrix. The Hessian matrix is approximated by previous gradient evaluations,
so there is no
+vertical scalability issue (the number of training features) when computing the Hessian
matrix
+explicitly in Newton method. As a result, L-BFGS often achieves rapider convergence compared
with
+other first-order optimization.

+Since the Hessian is constructed approximately from previous gradient evaluations, the
objective
+function can not be changed during the optimization process. As a result, Stochastic
L-BFGS will
+not work naively by just using miniBatch; therefore, we don't provide this until we have
better
+understanding.
--- End diff --

I decided to move those message to the code.

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