Github user mengxr commented on a diff in the pull request: https://github.com/apache/spark/pull/702#discussion_r12460396 --- 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. ## Implementation in MLlib +### Gradient descent and Stochastic gradient descent --- End diff -- `Stochastic` -> `stochastic`.
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