Merge pull request #459 from srowen/UpdaterL2Regularization

Correct L2 regularized weight update with canonical form

Per thread on the user@ mailing list, and comments from Ameet, I believe the weight update for L2 regularization needs to be corrected. See http://mail-archives.apache.org/mod_mbox/spark-user/201401.mbox/%3CCAH3_EVMetuQuhj3__NdUniDLc4P-FMmmrmxw9TS14or8nT4BNQ%40mail.gmail.com%3E

mllib/src/main/scala/org/apache/spark/mllib/optimization/Updater.scala

@@ -86,13 +86,17 @@ class L1Updater extends Updater {
 
 /**
  * Updater that adjusts the learning rate and performs L2 regularization
+ *
+ * See, for example, explanation of gradient and loss with L2 regularization on slide 21-22
+ * of <a href="http://people.cs.umass.edu/~sheldon/teaching/2012fa/ml/files/lec7-annotated.pdf">
+ * these slides</a>.
  */
 class SquaredL2Updater extends Updater {
   override def compute(weightsOld: DoubleMatrix, gradient: DoubleMatrix,
       stepSize: Double, iter: Int, regParam: Double): (DoubleMatrix, Double) = {
     val thisIterStepSize = stepSize / math.sqrt(iter)
     val normGradient = gradient.mul(thisIterStepSize)
-    val newWeights = weightsOld.sub(normGradient).div(2.0 * thisIterStepSize * regParam + 1.0)
+    val newWeights = weightsOld.mul(1.0 - 2.0 * thisIterStepSize * regParam).sub(normGradient)
     (newWeights, pow(newWeights.norm2, 2.0) * regParam)
   }
 }