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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
as a quadratic
    +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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