index.xml

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  <channel>
    <title>Kishor</title>
    <link>https://keyshor.github.io/</link>
      <atom:link href="https://keyshor.github.io/index.xml" rel="self" type="application/rss+xml" />
    <description>Kishor</description>
    <generator>Wowchemy (https://wowchemy.com)</generator><language>en-us</language><lastBuildDate>Sat, 01 Jun 2030 13:00:00 +0000</lastBuildDate>
    <image>
      <url>https://keyshor.github.io/media/icon_hua548646eb0ef2068e315ad4f7b192ca6_20428_512x512_fill_lanczos_center_3.png</url>
      <title>Kishor</title>
      <link>https://keyshor.github.io/</link>
    </image>
    
    <item>
      <title>Example Talk</title>
      <link>https://keyshor.github.io/talk/example-talk/</link>
      <pubDate>Sat, 01 Jun 2030 13:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/talk/example-talk/</guid>
      <description>&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Click on the &lt;strong&gt;Slides&lt;/strong&gt; button above to view the built-in slides feature.
  &lt;/div&gt;
&lt;/div&gt;
&lt;p&gt;Slides can be added in a few ways:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;strong&gt;Create&lt;/strong&gt; slides using Wowchemy&amp;rsquo;s &lt;a href=&#34;https://wowchemy.com/docs/managing-content/#create-slides&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;em&gt;Slides&lt;/em&gt;&lt;/a&gt; feature and link using &lt;code&gt;slides&lt;/code&gt; parameter in the front matter of the talk file&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Upload&lt;/strong&gt; an existing slide deck to &lt;code&gt;static/&lt;/code&gt; and link using &lt;code&gt;url_slides&lt;/code&gt; parameter in the front matter of the talk file&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Embed&lt;/strong&gt; your slides (e.g. Google Slides) or presentation video on this page using &lt;a href=&#34;https://wowchemy.com/docs/writing-markdown-latex/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;shortcodes&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;Further event details, including &lt;a href=&#34;https://wowchemy.com/docs/writing-markdown-latex/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;page elements&lt;/a&gt; such as image galleries, can be added to the body of this page.&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>Robust Subtask Leaning for Compositional Generalization</title>
      <link>https://keyshor.github.io/publication/jothimurugan-robust-2023/</link>
      <pubDate>Thu, 01 Jun 2023 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/publication/jothimurugan-robust-2023/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Policy Synthesis and Reinforcement Learning for Discounted LTL</title>
      <link>https://keyshor.github.io/publication/alur-policy-2023/</link>
      <pubDate>Mon, 15 May 2023 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/publication/alur-policy-2023/</guid>
      <description></description>
    </item>
    
    <item>
      <title>AAAI Tutorial on Specification-Guided Reinforcement Learning</title>
      <link>https://keyshor.github.io/teaching/aaai_tutorial/</link>
      <pubDate>Tue, 07 Feb 2023 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/teaching/aaai_tutorial/</guid>
      <description>&lt;p&gt;The unprecedented proliferation of data-driven approaches, especially machine learning, has put the spotlight on building trustworthy AI through the combination of logical reasoning and machine learning. &lt;em&gt;Reinforcement Learning from Logical Specifications&lt;/em&gt; is one such topic where formal logical constructs are utilized to overcome challenges faced by modern RL algorithms. Research on this topic is scattered across venues targeting subareas of AI. Foundational work has appeared at formal methods and AI venues. Algorithmic development and applications have appeared at machine learning, robotics, and cyber-physical systems venues. This tutorial consolidates recent progress in one capsule for a typical AI researcher. The tutorial is designed to explain the importance of using formal specifications in RL and encourage researchers to apply existing techniques for RL from logical specifications as well as contribute to the growing body of work on this topic.&lt;/p&gt;
&lt;p&gt;In this tutorial, we introduce reinforcement learning as a tool for automated synthesis of control policies and discuss the challenge of encoding long-horizon tasks using rewards. We then formulate the problem of reinforcement learning from logical specifications and present recent progress in developing scalable algorithms as well as theoretical results demonstrating the hardness of learning in this context.&lt;/p&gt;
&lt;p&gt;The syllabus of this tutorial can be found in the &lt;a href=&#34;proposal.pdf&#34;&gt;AAAI proposal&lt;/a&gt;.&lt;/p&gt;
&lt;h4 id=&#34;presenters&#34;&gt;Presenters&lt;/h4&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;https://www.cis.upenn.edu/~alur/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Rajeev Alur&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://suguman.github.io/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Suguman Bansal&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://obastani.github.io/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Osbert Bastani&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;http://keyshor.github.io/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Kishor Jothimurugan&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;h3 id=&#34;reading-material&#34;&gt;Reading Material&lt;/h3&gt;
&lt;p&gt;The tutorial is organized into three modules. Reading material corresponding to these modules as well as additional resources are provided below.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Introduction&lt;/strong&gt;. We introduce reinforcement learning and motivation behind the use of logical specifications. We discuss two specification languages: &lt;em&gt;LTL&lt;/em&gt; and &lt;em&gt;SpectRL&lt;/em&gt;.&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;First three sections of the &lt;a href=&#34;https://arxiv.org/pdf/2111.00272.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;paper&lt;/a&gt; on specifications in reinforcement learning&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://www.cmi.ac.in/~madhavan/papers/pdf/isical97.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Notes&lt;/a&gt; on Linear Temporal Logic (LTL)&lt;/li&gt;
&lt;li&gt;First two sections of the &lt;a href=&#34;https://arxiv.org/pdf/2008.09293.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;paper&lt;/a&gt; on SpectRL
&lt;/br&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;&lt;strong&gt;Practical Algorithms&lt;/strong&gt;. We discuss two learning algorithms: one for LTL specs that is based on reward machines and a compositional algorithm for SpectRL specifications.&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;https://arxiv.org/pdf/2010.03950.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Paper&lt;/a&gt; on reward machines&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://www.ijcai.org/proceedings/2019/0840.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Paper&lt;/a&gt; on generating reward machines from LTL specs&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://arxiv.org/pdf/2106.13906.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Paper&lt;/a&gt; on a compositional RL algorithm for SpectRL specs
&lt;/br&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;&lt;strong&gt;Theoretical Results&lt;/strong&gt;. We discuss hardness results regarding learning from logical specifications as well as a reward generation procedure for LTL specifications that has a weak optimality preservation guarantee.&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Sections 4, 5 and 6 of the &lt;a href=&#34;https://arxiv.org/pdf/2111.00272.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;paper&lt;/a&gt; on specifications in reinforcement learning&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://arxiv.org/pdf/1810.00950.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Paper&lt;/a&gt; on faithful reward generation from LTL specs&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://arxiv.org/pdf/1909.05081.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Paper&lt;/a&gt; on good-for-MDP automata
&lt;/br&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;&lt;strong&gt;Additional Resources&lt;/strong&gt;. Though not presented in the tutorial, the following material is provided for those interested in exploring further.&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;https://arxiv.org/pdf/2111.12679.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Paper&lt;/a&gt; characterizing the exact class of LTL specs for which PAC learning is possible&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://arxiv.org/pdf/1909.07299.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Paper&lt;/a&gt; providing an alternate approach for generating optimality preserving rewards from LTL specs&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://arxiv.org/pdf/2206.03348.pdf&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Paper&lt;/a&gt; on multi-agent reinforcement learning from SpectRL specifications&lt;/li&gt;
&lt;/ul&gt;
</description>
    </item>
    
    <item>
      <title>How to Wrtie Wowchemy Posts</title>
      <link>https://keyshor.github.io/random/wowchemy_syntax/</link>
      <pubDate>Thu, 10 Nov 2022 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/random/wowchemy_syntax/</guid>
      <description>&lt;p&gt;Wowchemy is designed to give technical content creators a seamless experience. You can focus on the content and Wowchemy handles the rest.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Highlight your code snippets, take notes on math classes, and draw diagrams from textual representation.&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;On this page, you&amp;rsquo;ll find some examples of the types of technical content that can be rendered with Wowchemy.&lt;/p&gt;
&lt;h2 id=&#34;examples&#34;&gt;Examples&lt;/h2&gt;
&lt;h3 id=&#34;code&#34;&gt;Code&lt;/h3&gt;
&lt;p&gt;Wowchemy supports a Markdown extension for highlighting code syntax. You can customize the styles under the &lt;code&gt;syntax_highlighter&lt;/code&gt; option in your &lt;code&gt;config/_default/params.yaml&lt;/code&gt; file.&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```python
import pandas as pd
data = pd.read_csv(&amp;quot;data.csv&amp;quot;)
data.head()
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-python&#34; data-lang=&#34;python&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;kn&#34;&gt;import&lt;/span&gt; &lt;span class=&#34;nn&#34;&gt;pandas&lt;/span&gt; &lt;span class=&#34;k&#34;&gt;as&lt;/span&gt; &lt;span class=&#34;nn&#34;&gt;pd&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;data&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;pd&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;.&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;read_csv&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s2&#34;&gt;&amp;#34;data.csv&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;data&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;.&lt;/span&gt;&lt;span class=&#34;n&#34;&gt;head&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;h3 id=&#34;mindmaps&#34;&gt;Mindmaps&lt;/h3&gt;
&lt;p&gt;Wowchemy supports a Markdown extension for mindmaps.&lt;/p&gt;
&lt;p&gt;Simply insert a Markdown &lt;code&gt;markmap&lt;/code&gt; code block and optionally set the height of the mindmap as shown in the example below.&lt;/p&gt;
&lt;p&gt;A simple mindmap defined as a Markdown list:&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;
&lt;pre class=&#34;chroma&#34;&gt;
&lt;code&gt;
```markmap {height=&#34;200px&#34;}
- Hugo Modules
  - wowchemy
  - wowchemy-plugins-netlify
  - wowchemy-plugins-netlify-cms
  - wowchemy-plugins-reveal
```
&lt;/code&gt;
&lt;/pre&gt;
&lt;/div&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;div class=&#34;markmap&#34; style=&#34;height: 200px;&#34;&gt;

&lt;pre&gt;- Hugo Modules
  - wowchemy
  - wowchemy-plugins-netlify
  - wowchemy-plugins-netlify-cms
  - wowchemy-plugins-reveal&lt;/pre&gt;
&lt;/div&gt;

&lt;p&gt;A more advanced mindmap with formatting, code blocks, and math:&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;
&lt;pre class=&#34;chroma&#34;&gt;
&lt;code&gt;
```markmap
- Mindmaps
  - Links
    - [Wowchemy Docs](https://wowchemy.com/docs/)
    - [Discord Community](https://discord.gg/z8wNYzb)
    - [GitHub](https://github.com/wowchemy/wowchemy-hugo-themes)
  - Features
    - Markdown formatting
    - **inline** ~~text~~ *styles*
    - multiline
      text
    - `inline code`
    -
      ```js
      console.log(&#39;hello&#39;);
      console.log(&#39;code block&#39;);
      ```
    - Math: $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$
```
&lt;/code&gt;
&lt;/pre&gt;
&lt;/div&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;div class=&#34;markmap&#34; style=&#34;height: 500px;&#34;&gt;

&lt;pre&gt;- Mindmaps
  - Links
    - [Wowchemy Docs](https://wowchemy.com/docs/)
    - [Discord Community](https://discord.gg/z8wNYzb)
    - [GitHub](https://github.com/wowchemy/wowchemy-hugo-themes)
  - Features
    - Markdown formatting
    - **inline** ~~text~~ *styles*
    - multiline
      text
    - `inline code`
    -
      ```js
      console.log(&#39;hello&#39;);
      console.log(&#39;code block&#39;);
      ```
    - Math: $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$&lt;/pre&gt;
&lt;/div&gt;

&lt;h3 id=&#34;charts&#34;&gt;Charts&lt;/h3&gt;
&lt;p&gt;Wowchemy supports the popular &lt;a href=&#34;https://plot.ly/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Plotly&lt;/a&gt; format for interactive charts.&lt;/p&gt;
&lt;p&gt;Save your Plotly JSON in your page folder, for example &lt;code&gt;line-chart.json&lt;/code&gt;, and then add the &lt;code&gt;{{&amp;lt; chart data=&amp;quot;line-chart&amp;quot; &amp;gt;}}&lt;/code&gt; shortcode where you would like the chart to appear.&lt;/p&gt;
&lt;p&gt;Demo:&lt;/p&gt;




&lt;div id=&#34;chart-748123659&#34; class=&#34;chart&#34;&gt;&lt;/div&gt;
&lt;script&gt;
  (function() {
    let a = setInterval( function() {
      if ( typeof window.Plotly === &#39;undefined&#39; ) {
        return;
      }
      clearInterval( a );

      Plotly.d3.json(&#34;./line-chart.json&#34;, function(chart) {
        Plotly.plot(&#39;chart-748123659&#39;, chart.data, chart.layout, {responsive: true});
      });
    }, 500 );
  })();
&lt;/script&gt;

&lt;p&gt;You might also find the &lt;a href=&#34;http://plotly-json-editor.getforge.io/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Plotly JSON Editor&lt;/a&gt; useful.&lt;/p&gt;
&lt;h3 id=&#34;math&#34;&gt;Math&lt;/h3&gt;
&lt;p&gt;Wowchemy supports a Markdown extension for $\LaTeX$ math. You can enable this feature by toggling the &lt;code&gt;math&lt;/code&gt; option in your &lt;code&gt;config/_default/params.yaml&lt;/code&gt; file.&lt;/p&gt;
&lt;p&gt;To render &lt;em&gt;inline&lt;/em&gt; or &lt;em&gt;block&lt;/em&gt; math, wrap your LaTeX math with &lt;code&gt;{{&amp;lt; math &amp;gt;}}$...${{&amp;lt; /math &amp;gt;}}&lt;/code&gt; or &lt;code&gt;{{&amp;lt; math &amp;gt;}}$$...$${{&amp;lt; /math &amp;gt;}}&lt;/code&gt;, respectively. (We wrap the LaTeX math in the Wowchemy &lt;em&gt;math&lt;/em&gt; shortcode to prevent Hugo rendering our math as Markdown. The &lt;em&gt;math&lt;/em&gt; shortcode is new in v5.5-dev.)&lt;/p&gt;
&lt;p&gt;Example &lt;strong&gt;math block&lt;/strong&gt;:&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-latex&#34; data-lang=&#34;latex&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nb&#34;&gt;{{&lt;/span&gt;&amp;lt; math &amp;gt;&lt;span class=&#34;nb&#34;&gt;}}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;sb&#34;&gt;$$&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nb&#34;&gt;&lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\gamma&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;_{n} &lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\frac&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;{ &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\left&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; | &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\left&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;o&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\mathbf&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; x_{n} &lt;/span&gt;&lt;span class=&#34;o&#34;&gt;-&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\mathbf&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; x_{n&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;-&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;} &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\right&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;o&#34;&gt;)&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;^T &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\left&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;o&#34;&gt;[&lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\nabla&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; F &lt;/span&gt;&lt;span class=&#34;o&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\mathbf&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; x_{n}&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;)&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;o&#34;&gt;-&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\nabla&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; F &lt;/span&gt;&lt;span class=&#34;o&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\mathbf&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; x_{n&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;-&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;}&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;)&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\right&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;o&#34;&gt;]&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\right&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; |}{&lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\left&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\|\nabla&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; F&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\mathbf&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;{x}_{n}&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;)&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;o&#34;&gt;-&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\nabla&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; F&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\mathbf&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;{x}_{n&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;-&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;}&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;)&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\right&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\|&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;^&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;2&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;}
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nb&#34;&gt;&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;$$&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nb&#34;&gt;{{&lt;/span&gt;&amp;lt; /math &amp;gt;&lt;span class=&#34;nb&#34;&gt;}}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;renders as&lt;/p&gt;



$$\gamma_{n} = \frac{ \left | \left (\mathbf x_{n} - \mathbf x_{n-1} \right )^T \left [\nabla F (\mathbf x_{n}) - \nabla F (\mathbf x_{n-1}) \right ] \right |}{\left \|\nabla F(\mathbf{x}_{n}) - \nabla F(\mathbf{x}_{n-1}) \right \|^2}$$

&lt;p&gt;Example &lt;strong&gt;inline math&lt;/strong&gt; &lt;code&gt;{{&amp;lt; math &amp;gt;}}$\nabla F(\mathbf{x}_{n})${{&amp;lt; /math &amp;gt;}}&lt;/code&gt; renders as 

$\nabla F(\mathbf{x}_{n})$.&lt;/p&gt;
&lt;p&gt;Example &lt;strong&gt;multi-line math&lt;/strong&gt; using the math linebreak (&lt;code&gt;\\&lt;/code&gt;):&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-latex&#34; data-lang=&#34;latex&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nb&#34;&gt;{{&lt;/span&gt;&amp;lt; math &amp;gt;&lt;span class=&#34;nb&#34;&gt;}}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;sb&#34;&gt;$$&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;f&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;k;p_{&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;}^{&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;*&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;}&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;)&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\begin&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;{cases}p_{&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;}^{&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;*&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;} &amp;amp; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\text&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;{if }k&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;, &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\\&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nb&#34;&gt;&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;1&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;-&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;p_{&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;}^{&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;*&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;} &amp;amp; &lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\text&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;{if }k&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;m&#34;&gt;0&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;.&lt;/span&gt;&lt;span class=&#34;nv&#34;&gt;\end&lt;/span&gt;&lt;span class=&#34;nb&#34;&gt;{cases}&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;$$&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;nb&#34;&gt;{{&lt;/span&gt;&amp;lt; /math &amp;gt;&lt;span class=&#34;nb&#34;&gt;}}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;renders as&lt;/p&gt;




$$
f(k;p_{0}^{*}) = \begin{cases}p_{0}^{*} &amp; \text{if }k=1, \\
1-p_{0}^{*} &amp; \text{if }k=0.\end{cases}
$$


&lt;h3 id=&#34;diagrams&#34;&gt;Diagrams&lt;/h3&gt;
&lt;p&gt;Wowchemy supports a Markdown extension for diagrams. You can enable this feature by toggling the &lt;code&gt;diagram&lt;/code&gt; option in your &lt;code&gt;config/_default/params.toml&lt;/code&gt; file or by adding &lt;code&gt;diagram: true&lt;/code&gt; to your page front matter.&lt;/p&gt;
&lt;p&gt;An example &lt;strong&gt;flowchart&lt;/strong&gt;:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```mermaid
graph TD
A[Hard] --&amp;gt;|Text| B(Round)
B --&amp;gt; C{Decision}
C --&amp;gt;|One| D[Result 1]
C --&amp;gt;|Two| E[Result 2]
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;div class=&#34;mermaid&#34;&gt;graph TD
A[Hard] --&gt;|Text| B(Round)
B --&gt; C{Decision}
C --&gt;|One| D[Result 1]
C --&gt;|Two| E[Result 2]
&lt;/div&gt;
&lt;p&gt;An example &lt;strong&gt;sequence diagram&lt;/strong&gt;:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```mermaid
sequenceDiagram
Alice-&amp;gt;&amp;gt;John: Hello John, how are you?
loop Healthcheck
    John-&amp;gt;&amp;gt;John: Fight against hypochondria
end
Note right of John: Rational thoughts!
John--&amp;gt;&amp;gt;Alice: Great!
John-&amp;gt;&amp;gt;Bob: How about you?
Bob--&amp;gt;&amp;gt;John: Jolly good!
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;div class=&#34;mermaid&#34;&gt;sequenceDiagram
Alice-&gt;&gt;John: Hello John, how are you?
loop Healthcheck
    John-&gt;&gt;John: Fight against hypochondria
end
Note right of John: Rational thoughts!
John--&gt;&gt;Alice: Great!
John-&gt;&gt;Bob: How about you?
Bob--&gt;&gt;John: Jolly good!
&lt;/div&gt;
&lt;p&gt;An example &lt;strong&gt;Gantt diagram&lt;/strong&gt;:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```mermaid
gantt
section Section
Completed :done,    des1, 2014-01-06,2014-01-08
Active        :active,  des2, 2014-01-07, 3d
Parallel 1   :         des3, after des1, 1d
Parallel 2   :         des4, after des1, 1d
Parallel 3   :         des5, after des3, 1d
Parallel 4   :         des6, after des4, 1d
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;div class=&#34;mermaid&#34;&gt;gantt
section Section
Completed :done,    des1, 2014-01-06,2014-01-08
Active        :active,  des2, 2014-01-07, 3d
Parallel 1   :         des3, after des1, 1d
Parallel 2   :         des4, after des1, 1d
Parallel 3   :         des5, after des3, 1d
Parallel 4   :         des6, after des4, 1d
&lt;/div&gt;
&lt;p&gt;An example &lt;strong&gt;class diagram&lt;/strong&gt;:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```mermaid
classDiagram
Class01 &amp;lt;|-- AveryLongClass : Cool
Class03 *-- Class04
Class05 o-- Class06
Class07 .. Class08
Class09 --&amp;gt; C2 : Where am i?
Class09 --* C3
Class09 --|&amp;gt; Class07
Class07 : equals()
Class07 : Object[] elementData
Class01 : size()
Class01 : int chimp
Class01 : int gorilla
Class08 &amp;lt;--&amp;gt; C2: Cool label
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;div class=&#34;mermaid&#34;&gt;classDiagram
Class01 &lt;|-- AveryLongClass : Cool
Class03 *-- Class04
Class05 o-- Class06
Class07 .. Class08
Class09 --&gt; C2 : Where am i?
Class09 --* C3
Class09 --|&gt; Class07
Class07 : equals()
Class07 : Object[] elementData
Class01 : size()
Class01 : int chimp
Class01 : int gorilla
Class08 &lt;--&gt; C2: Cool label
&lt;/div&gt;
&lt;p&gt;An example &lt;strong&gt;state diagram&lt;/strong&gt;:&lt;/p&gt;
&lt;pre&gt;&lt;code&gt;```mermaid
stateDiagram
[*] --&amp;gt; Still
Still --&amp;gt; [*]
Still --&amp;gt; Moving
Moving --&amp;gt; Still
Moving --&amp;gt; Crash
Crash --&amp;gt; [*]
```
&lt;/code&gt;&lt;/pre&gt;
&lt;p&gt;renders as&lt;/p&gt;
&lt;div class=&#34;mermaid&#34;&gt;stateDiagram
[*] --&gt; Still
Still --&gt; [*]
Still --&gt; Moving
Moving --&gt; Still
Moving --&gt; Crash
Crash --&gt; [*]
&lt;/div&gt;
&lt;h3 id=&#34;todo-lists&#34;&gt;Todo lists&lt;/h3&gt;
&lt;p&gt;You can even write your todo lists in Markdown too:&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-markdown&#34; data-lang=&#34;markdown&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;k&#34;&gt;- [x]&lt;/span&gt; Write math example
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;k&#34;&gt;- [x]&lt;/span&gt; Write diagram example
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;k&#34;&gt;- [ ]&lt;/span&gt; Do something else
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;renders as&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Write math example
&lt;ul&gt;
&lt;li&gt;&lt;input checked=&#34;&#34; disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Write diagram example&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;&lt;input disabled=&#34;&#34; type=&#34;checkbox&#34;&gt; Do something else&lt;/li&gt;
&lt;/ul&gt;
&lt;h3 id=&#34;callouts&#34;&gt;Callouts&lt;/h3&gt;
&lt;p&gt;Academic supports a &lt;a href=&#34;https://wowchemy.com/docs/content/writing-markdown-latex/#callouts&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;shortcode for callouts&lt;/a&gt;, also referred to as &lt;em&gt;asides&lt;/em&gt;, &lt;em&gt;hints&lt;/em&gt;, or &lt;em&gt;alerts&lt;/em&gt;. By wrapping a paragraph in &lt;code&gt;{{% callout note %}} ... {{% /callout %}}&lt;/code&gt;, it will render as an aside.&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-markdown&#34; data-lang=&#34;markdown&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;{{% callout note %}}
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;A Markdown aside is useful for displaying notices, hints, or definitions to your readers.
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;{{% /callout %}}
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;renders as&lt;/p&gt;
&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    A Markdown aside is useful for displaying notices, hints, or definitions to your readers.
  &lt;/div&gt;
&lt;/div&gt;
&lt;h3 id=&#34;spoilers&#34;&gt;Spoilers&lt;/h3&gt;
&lt;p&gt;Add a spoiler to a page to reveal text, such as an answer to a question, after a button is clicked.&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-markdown&#34; data-lang=&#34;markdown&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;{{&lt;span class=&#34;p&#34;&gt;&amp;lt;&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;spoiler&lt;/span&gt; &lt;span class=&#34;na&#34;&gt;text&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;Click to view the spoiler&amp;#34;&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;&amp;gt;&lt;/span&gt;}}
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;You found me!
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;{{&lt;span class=&#34;p&#34;&gt;&amp;lt;&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;/&lt;/span&gt;&lt;span class=&#34;nt&#34;&gt;spoiler&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;&amp;gt;&lt;/span&gt;}}
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;renders as&lt;/p&gt;
&lt;details class=&#34;spoiler &#34;  id=&#34;spoiler-5&#34;&gt;
  &lt;summary&gt;Click to view the spoiler&lt;/summary&gt;
  &lt;p&gt;You found me!&lt;/p&gt;
&lt;/details&gt;
&lt;h3 id=&#34;icons&#34;&gt;Icons&lt;/h3&gt;
&lt;p&gt;Academic enables you to use a wide range of &lt;a href=&#34;https://wowchemy.com/docs/getting-started/page-builder/#icons&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;icons from &lt;em&gt;Font Awesome&lt;/em&gt; and &lt;em&gt;Academicons&lt;/em&gt;&lt;/a&gt; in addition to &lt;a href=&#34;https://wowchemy.com/docs/content/writing-markdown-latex/#emojis&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;emojis&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;Here are some examples using the &lt;code&gt;icon&lt;/code&gt; shortcode to render icons:&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-markdown&#34; data-lang=&#34;markdown&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;{{&lt;span class=&#34;p&#34;&gt;&amp;lt;&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;icon&lt;/span&gt; &lt;span class=&#34;na&#34;&gt;name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;terminal&amp;#34;&lt;/span&gt; &lt;span class=&#34;na&#34;&gt;pack&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;fas&amp;#34;&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;&amp;gt;&lt;/span&gt;}} Terminal  
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;{{&lt;span class=&#34;p&#34;&gt;&amp;lt;&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;icon&lt;/span&gt; &lt;span class=&#34;na&#34;&gt;name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;python&amp;#34;&lt;/span&gt; &lt;span class=&#34;na&#34;&gt;pack&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;fab&amp;#34;&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;&amp;gt;&lt;/span&gt;}} Python  
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;{{&lt;span class=&#34;p&#34;&gt;&amp;lt;&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;icon&lt;/span&gt; &lt;span class=&#34;na&#34;&gt;name&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;r-project&amp;#34;&lt;/span&gt; &lt;span class=&#34;na&#34;&gt;pack&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;fab&amp;#34;&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;&amp;gt;&lt;/span&gt;}} R
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;renders as&lt;/p&gt;
&lt;p&gt;
  &lt;i class=&#34;fas fa-terminal  pr-1 fa-fw&#34;&gt;&lt;/i&gt; Terminal&lt;br&gt;

  &lt;i class=&#34;fab fa-python  pr-1 fa-fw&#34;&gt;&lt;/i&gt; Python&lt;br&gt;

  &lt;i class=&#34;fab fa-r-project  pr-1 fa-fw&#34;&gt;&lt;/i&gt; R&lt;/p&gt;
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</description>
    </item>
    
    <item>
      <title>A Framework for Transforming Specifications in Reinforcement Learning</title>
      <link>https://keyshor.github.io/publication/alur-framework-2021/</link>
      <pubDate>Mon, 01 Aug 2022 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/publication/alur-framework-2021/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Specification-Guided Learning of Nash Equilibria with High Social Welfare</title>
      <link>https://keyshor.github.io/publication/jothimurugan-specification-guided-2022/</link>
      <pubDate>Mon, 01 Aug 2022 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/publication/jothimurugan-specification-guided-2022/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Compositional Reinforcement Learning from Logical Specifications</title>
      <link>https://keyshor.github.io/publication/jothimurugan-compositional-2021/</link>
      <pubDate>Wed, 01 Dec 2021 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/publication/jothimurugan-compositional-2021/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Compositional Learning and Verification of Neural Network Controllers</title>
      <link>https://keyshor.github.io/publication/ivanov-compositional-2021/</link>
      <pubDate>Sun, 01 Aug 2021 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/publication/ivanov-compositional-2021/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Abstract Value Iteration for Hierarchical Reinforcement Learning</title>
      <link>https://keyshor.github.io/publication/jothimurugan-abstract-2021/</link>
      <pubDate>Thu, 01 Apr 2021 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/publication/jothimurugan-abstract-2021/</guid>
      <description></description>
    </item>
    
    <item>
      <title>Learning Algorithms for Regenerative Stopping Problems with Applications to Shipping Consolidation in Logistics</title>
      <link>https://keyshor.github.io/preprints/bell-labs/</link>
      <pubDate>Tue, 01 Sep 2020 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/preprints/bell-labs/</guid>
      <description>&lt;h2 id=&#34;abstract&#34;&gt;Abstract&lt;/h2&gt;
&lt;p&gt;We study regenerative stopping problems in which the system starts anew whenever the
controller decides to stop and the long-term average cost is to be minimized. Traditional model-based solutions involve estimating the underlying process from data and computing strategies for
the estimated model. In this paper, we compare such solutions to deep reinforcement learning
and imitation learning which involve learning a neural network policy from simulations. We
evaluate the different approaches on a real-world problem of shipping consolidation in logistics
and demonstrate that deep learning can be effectively used to solve such problems.&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>Space-efficient Query Evaluation over Probabilistic Event Streams</title>
      <link>https://keyshor.github.io/publication/alur-space-efficient-2020/</link>
      <pubDate>Wed, 01 Jul 2020 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/publication/alur-space-efficient-2020/</guid>
      <description></description>
    </item>
    
    <item>
      <title>A Composable Specification Language for Reinforcement Learning Tasks</title>
      <link>https://keyshor.github.io/publication/jothimurugan-composable-2019/</link>
      <pubDate>Sun, 01 Dec 2019 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/publication/jothimurugan-composable-2019/</guid>
      <description></description>
    </item>
    
    <item>
      <title></title>
      <link>https://keyshor.github.io/admin/config.yml</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      <guid>https://keyshor.github.io/admin/config.yml</guid>
      <description></description>
    </item>
    
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