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https://issues.apache.org/jira/browse/FLINK-1807?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14519054#comment-14519054
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ASF GitHub Bot commented on FLINK-1807:
---------------------------------------
Github user tillrohrmann commented on a diff in the pull request:
https://github.com/apache/flink/pull/613#discussion_r29322598
--- Diff: docs/libs/ml/optimization.md ---
@@ -0,0 +1,218 @@
+---
+mathjax: include
+title: "ML - Optimization"
+displayTitle: <a href="index.md">ML</a> - Optimization
+---
+<!--
+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.
+-->
+
+* Table of contents
+{:toc}
+
+$$
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\E}{\mathbb{E}}
+\newcommand{\x}{\mathbf{x}}
+\newcommand{\y}{\mathbf{y}}
+\newcommand{\wv}{\mathbf{w}}
+\newcommand{\av}{\mathbf{\alpha}}
+\newcommand{\bv}{\mathbf{b}}
+\newcommand{\N}{\mathbb{N}}
+\newcommand{\id}{\mathbf{I}}
+\newcommand{\ind}{\mathbf{1}}
+\newcommand{\0}{\mathbf{0}}
+\newcommand{\unit}{\mathbf{e}}
+\newcommand{\one}{\mathbf{1}}
+\newcommand{\zero}{\mathbf{0}}
+$$
+
+## Mathematical Formulation
+
+The optimization framework in Flink is a developer-oriented package that
can be used to solve
+[optimization](https://en.wikipedia.org/wiki/Mathematical_optimization)
+problems common in Machine Learning (ML) tasks. In the supervised learning
context, this usually
+involves finding a model, as defined by a set of parameters $w$, that
minimize a function $f(\wv)$
+given a set of $(\x, y)$ examples,
+where $\x$ is a feature vector and $y$ is a real number, which can
represent either a real value in
+the regression case, or a class label in the classification case. In
supervised learning, the
+function to be minimized is usually of the form:
+
+$$
+\begin{equation}
+ f(\wv) :=
+ \frac1n \sum_{i=1}^n L(\wv;\x_i,y_i) +
+ \lambda\, R(\wv)
+ \label{eq:objectiveFunc}
+ \ .
+\end{equation}
+$$
+
+where $L$ is the loss function and $R(\wv)$ the regularization penalty. We
use $L$ to measure how
+well the model fits the observed data, and we use $R$ in order to impose a
complexity cost to the
+model, with $\lambda > 0$ being the regularization parameter.
+
+### Loss Functions
+
+In supervised learning, we use loss functions in order to measure the
model fit, by
+penalizing errors in the predictions $p$ made by the model compared to the
true $y$ for each
+example. Different loss function can be used for regression (e.g. Squared
Loss) and classification
+(e.g. Hinge Loss).
+
+Some common loss functions are:
+
+* Squared Loss: $ \frac{1}{2} (\wv^T \x - y)^2, \quad y \in \R $
+* Hinge Loss: $ \max (0, 1-y \wv^T \x), \quad y \in \{-1, +1\} $
--- End diff --
maybe we can add a small spacing between `y` and `\wv^T\x`
> Stochastic gradient descent optimizer for ML library
> ----------------------------------------------------
>
> Key: FLINK-1807
> URL: https://issues.apache.org/jira/browse/FLINK-1807
> Project: Flink
> Issue Type: Improvement
> Components: Machine Learning Library
> Reporter: Till Rohrmann
> Assignee: Theodore Vasiloudis
> Labels: ML
>
> Stochastic gradient descent (SGD) is a widely used optimization technique in
> different ML algorithms. Thus, it would be helpful to provide a generalized
> SGD implementation which can be instantiated with the respective gradient
> computation. Such a building block would make the development of future
> algorithms easier.
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