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keep the description consistent with the formulation #13

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Binary file modified w08_hpo_multicrit/t03_bo.pdf
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6 changes: 3 additions & 3 deletions w08_hpo_multicrit/t03_bo.tex
Original file line number Diff line number Diff line change
Expand Up @@ -152,18 +152,18 @@
$$
c = \max_{i=1,\dots,m}\left(w_i \cost_i(\conf)\right) + \rho \sum_{i=1}^m w_i\cost_i(\conf),
$$
% \begin{scriptsize}
\begin{scriptsize}
\begin{itemize}
\item The norm consists of two components:
\begin{itemize}
\item $\max_{i=1,\dots,m}\left(w_i \cost_i(\conf)\right)$ takes only the cost function with maximum weight into account.
\item $\max_{i=1,\dots,m}\left(w_i \cost_i(\conf)\right)$ takes only the maximum weighted cost into account.
\item $\sum_{i=1}^m w_i\cost_i(\conf)$ is the weighted sum of all cost functions.
\end{itemize}
\item $\rho$ describes the trade-off between these components.
\item By the randomized weights in each iteration and the usually small value of $\rho = 0.05$, this allows exploration of extreme points of single cost functions.
\item One can prove: \textbf{Every solution of the scalarized problem is pareto-optimal!}
\end{itemize}
% \end{scriptsize}
\end{scriptsize}
\end{frame}

\begin{frame}{ParEGO Algorithm}
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