Slides (#554)

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* [WIP] minor fixes

* minor edit

* working on slides and drive-by update of loose agnostic documentation

* full draft of slides is done.

* bug fix

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Author: DLWoodruff

doc/slides/ICS2025/dlw_slides.pdf

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+\documentclass[9pt,usenames,dvipsnames]{beamer}
+
+\usetheme[progressbar=frametitle,numbering=fraction]{metropolis}
+\usepackage{appendixnumberbeamer}
+\usepackage{booktabs}
+\usepackage[scale=2]{ccicons}
+\usepackage{pgfplots}
+\usepgfplotslibrary{dateplot}
+\usepackage{xspace}
+\usepackage{algorithm2e}
+
+%\usepackage[utf8]{inputenc}
+%\usepackage{amsfonts} % For AMS Beautification
+%\usepackage{fullpage} % For More Realistic Page Usage
+%\usepackage{algpseudocode} % For algorithm layout
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+\usepackage{mathabx} % \widecheck - inverse Fourier transform
+\usepackage{mathtools}
+\usepackage{graphicx} %includegraphics[scale=#]{filename}
+\usepackage{float}
+ \usepackage{relsize}
+%\usepackage{pdfsync}
+%\usepackage{hyperref}  
+%\usepackage{upgreek}
+%\usepackage[round]{natbib}
+% \usepackage[backend=biber,style=numeric, citestyle=ieee]{biblatex}
+\usepackage[style=apa]{biblatex}
+\addbibresource{reference.bib} %Imports bibliography file
+
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+
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+\renewcommand\cite[1]{\hyperlink{#1}{\textcolor{blue}{\small{(\oldcite{#1})}}}}
+
+
+\renewcommand{\footnotesize}{\scriptsize}
+
+\newcommand{\themename}{\textbf{\textsc{metropolis}}\xspace}
+
+\title{Agnostic MPI-SPPY and Consensus ADMM Under Uncertainty}
+% \subtitle{A Bootstrap Approach}
+\date{}
+\author{David L Woodruff \inst{1}\\
+(with coauthors noted as we go along)}
+
+
+\institute{\inst{1} Graduate School of Management, \\ University of California, Davis}
+% \titlegraphic{\hfill\includegraphics[height=1.5cm]{logo.pdf}}
+\date{INFORMS 2024}
+
+\begin{document}
+
+\maketitle
+
+
+\metroset{sectionpage=none}
+
+\begin{frame}{Optimization Under Uncertainty}
+
+Today we will work with abstract problems such as:
+\alert{
+\Large
+$$
+\min_x h(x,\boldmath\Xi)
+$$}
+\begin{itemize}
+\item $\boldmath\Xi$ is a random variable
+\item The function $h$ captures constraints as well as any data modeled as known with certainty.
+\end{itemize}
+But the random variable necessitates some additional specification such as
+requiring a form of robustness or perhaps...
+\pause
+\alert{
+\Large
+\begin{equation}
+        \min_x E_{\xi\sim F}h(x,\xi)  \label{eq:TheProblem}
+\end{equation}
+}
+Where the distribution $F$ is unknown and, of course, unknownable (exactly). 
+\end{frame}
+
+
+\section{MPI-sppy}
+\begin{frame}{MPI-sppy: The paper and the software}
+\begin{itemize}
+\item B. Knueven, D Mildebrath, C. Muir, JD Siirola, J-P Watson, DL Woodruff, ``A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty,'' {\em MPC}
+\item Find $\hat{x}$ with bounds and/or confidence intervals on the objective function for a scenario-based $T$-stage expected value problem with scenario set $\Xi$.
+\end{itemize}
+  
+\end{frame}
+
+\begin{frame}{MPI-sppy: The paper and the software}
+\begin{itemize}
+\item B. Knueven, D Mildebrath, C. Muir, JD Siirola, J-P Watson, DL Woodruff, ``A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty,'' {\em MPC}
+\item Find $\hat{x}$ with bounds on the objective function (and confidence intervals) for the problem solved to do that; generally scenario-based, e.g.:
+  $$
+   \min_x \frac{1}{N} \sum_{i=1}^N h(x, D_i).
+   $$
+   for some sample $D$ of size $N$.
+\item I want to talk mainly about the architecture, but first a few words about the software 
+  \begin{itemize}
+  \item Available at \url{https://github.com/Pyomo/mpi-sppy}
+  \item It is a library, but we also have a generic program (coming back toward PySP)
+    \item It is designed for HPC, but does run on a laptop.
+    \end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}{The Architecture}
+  \subtitle{MPI: Message Passing Interface}
+
+\includegraphics[width=1.0\linewidth]{hubspoke.pdf}
+But things are changing
+\end{frame}
+
+\begin{frame}{Agnostic to the AML}
+  For scenario based decomposition...
+  \begin{itemize}
+  \item Loose:
+    \begin{itemize}
+    \item You code your AML to write an MPS (or maybe lp) file for each scenario along with a json file for each scenario that lists the nonanticipative variabes for each node in the scenario tree traversed by the scenario.
+    \item You do this once and let mpi-sppy take over.
+      \item No Python programming required (unless, of course, thats how interact with your AML)
+      \end{itemize}
+    \item[]
+    \item Tight: If your ``AML'' is callable in the sense that an outside caller
+      can modify the objective, then
+      \begin{itemize}
+      \item You hope we already have added support for your ``AML'' (we now have support for AMPL, GAMS, and GurobiPy)
+        \item You need to write a thin wrapper in Python for your model
+        \end{itemize}
+  \end{itemize}
+\end{frame}
+
+
+\section{Consensus ADMM Under Uncertainty}
+
+\begin{frame}{Consensus ADMM Under Uncertainty}
+  \begin{itemize}
+  \item There is a paper with Aymeric Legros on OOL, but write to me for a somewhat better version.
+  \item Today, I will give a brief overview, with almost no notation.
+    \begin{itemize}
+    \item You might want to do scenario decomposition for stochastics and you might want to do consensus ADMM decomposition because you have a huge problem (or you might be decomposing just to get parallel speed-up or for security reasons).
+    \item We combine the two. Under the hood, the trick is the tree.
+      \item But the interface is that you tell the software about your scenario tree for stochastics and about your consensus variables and subproblems for ADMM using wrappers for your model.
+      \end{itemize}
+    \item The software is available on github as part of MPI-SPPY.
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{A Simple Example}
+  \begin{itemize}
+  \item Consider a batch production/distribution problem with uncertain production yields
+  \item Batch sizes must be non-anticipative, while shipping quantities, inventory etc. can depend on realized yields.
+  \item Suppose the ADMM subproblems are regions with a few arcs between them.
+    \item So there must be a consensus for flow on the arcs between two regions.
+  \end{itemize}
+
+
+\end{frame}
+
+\begin{frame}{Progressive Hedging and the like}
+\centering
+ \includegraphics[width=1.1\linewidth]{tree1.pdf}
+\end{frame}
+
+\section{Extended Scenarios and Tree}
+\begin{frame}{Under the hood: Extended Scenarios and Tree}
+  \begin{itemize}
+\item The collection of ADMM subproblems, $A$, are considered to emanate from a scenario tree node that is replicated for addition
+  to the original scenario tree at every original leaf node.
+\item So now we have a tree with $T+1$ stages and $|\Xi| |A|$ {\em extended scenarios}.
+\item There's going to need to be some funny business with non-anticipative variables and with probabilities if we are going to use standard stochastic scenario
+  decomposition algorithms.
+\end{itemize}
+\end{frame}
+
+\begin{frame}{Combined ``Scenario'' Tree}
+\centering
+ \includegraphics[width=1.1\linewidth]{tree2.pdf}
+\end{frame}
+
+\begin{frame}{Conclusions about Stochastic consensus ADMM}
+\begin{itemize}
+\item Our paper describes methods and software for using a stochastic programming decomposition algorithm for stochastic consensus ADMM.
+\item You could use similar thinking to adapt an ADMM algorithm for stochastic ADMM.
+\item Aside: decomposition seems to be needed for only a fraction of ``pure'' stochastic problems, so ADMM problems seem like a good place to hawk our wares.
+\end{itemize}
+\end{frame}
+
+\end{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+