Github user thvasilo commented on a diff in the pull request:
https://github.com/apache/flink/pull/1985#discussion_r63519390
--- Diff:
flink-libraries/flink-ml/src/main/scala/org/apache/flink/ml/optimization/RegularizationPenalty.scala
---
@@ -0,0 +1,215 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements. See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership. The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.flink.ml.optimization
+
+import org.apache.flink.ml.math.{Vector, BLAS}
+import org.apache.flink.ml.math.Breeze._
+import breeze.linalg.{norm => BreezeNorm}
+
+/** Represents a type of regularization penalty
+ *
+ * Regularization penalties are used to restrict the optimization problem
to solutions with
+ * certain desirable characteristics, such as sparsity for the L1
penalty, or penalizing large
+ * weights for the L2 penalty.
+ *
+ * The regularization term, `R(w)` is added to the objective function,
`f(w) = L(w) + lambda*R(w)`
+ * where lambda is the regularization parameter used to tune the amount
of regularization applied.
+ */
+trait RegularizationPenalty extends Serializable {
+
+ /** Calculates the new weights based on the gradient and regularization
penalty
+ *
+ * @param weightVector The weights to be updated
+ * @param gradient The gradient used to update the weights
+ * @param regularizationConstant The regularization parameter to be
applied
+ * @param learningRate The effective step size for this iteration
+ * @return Updated weights
+ */
+ def takeStep(
+ weightVector: Vector,
+ gradient: Vector,
+ regularizationConstant: Double,
+ learningRate: Double)
+ : Vector
+
+ /** Adds regularization to the loss value
+ *
+ * @param oldLoss The loss to be updated
+ * @param weightVector The gradient used to update the loss
+ * @param regularizationConstant The regularization parameter to be
applied
+ * @return Updated loss
+ */
+ def regLoss(oldLoss: Double, weightVector: Vector,
regularizationConstant: Double): Double
+
+}
+
+
+/** `L_2` regularization penalty.
+ *
+ * The regularization function is the square of the L2 norm
`1/2*||w||_2^2`
+ * with `w` being the weight vector. The function penalizes large weights,
+ * favoring solutions with more small weights rather than few large ones.
+ */
+object L2Regularization extends RegularizationPenalty {
+
+ /** Calculates the new weights based on the gradient and L2
regularization penalty
+ *
+ * The updated weight is `w - learningRate *(gradient + lambda * w)`
where
+ * `w` is the weight vector, and `lambda` is the regularization
parameter.
+ *
+ * @param weightVector The weights to be updated
+ * @param gradient The gradient according to which we will update the
weights
+ * @param regularizationConstant The regularization parameter to be
applied
+ * @param learningRate The effective step size for this iteration
+ * @return Updated weights
+ */
+ override def takeStep(
+ weightVector: Vector,
+ gradient: Vector,
+ regularizationConstant: Double,
+ learningRate: Double)
+ : Vector = {
+ // add the gradient of the L2 regularization
+ BLAS.axpy(regularizationConstant, weightVector, gradient)
+
+ // update the weights according to the learning rate
+ BLAS.axpy(-learningRate, gradient, weightVector)
+
+ weightVector
+ }
+
+ /** Adds regularization to the loss value
+ *
+ * The updated loss is `l + lambda * 1/2*||w||_2^2` where `l` is the
old loss,
--- End diff --
I would recommend spelling out `loss` here, as in some fonts it's hard tell
the letter "l" apart from the number 1,
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