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% Title
\title{Stein Variational Evolution Strategies}

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% Authors
\author[1]{Cornelius V.\ Braun}
\author[2]{Robert T.\ Lange}
\author[1]{Marc Toussaint}
\affil[1]{%
    TU Berlin
}
\affil[2]{%
    Sakana AI
}

  
\begin{document}
\maketitle

\begin{abstract}
Efficient global optimization and sampling are fundamental challenges, particularly in fields such as robotics and reinforcement learning, where gradients may be unavailable or unreliable.
In this context, jointly optimizing multiple solutions is a promising approach to avoid local optima.
While Stein Variational Gradient Descent (SVGD) provides a powerful framework for sampling diverse solutions, its reliance on first-order information limits its applicability to differentiable objectives. 
Existing gradient-free SVGD variants often suffer from slow convergence and poor scalability.
To improve gradient-free sampling and optimization, we propose Stein Variational CMA-ES, a novel gradient-free SVGD-like method that combines the efficiency of evolution strategies with SVGD-based repulsion forces.
We perform an extensive empirical evaluation across several domains, which shows that the integration of the ES update in SVGD significantly improves the performance on multiple challenging benchmark problems.
Our findings establish SV-CMA-ES as a scalable method for zero-order sampling and blackbox optimization, bridging the gap between SVGD and evolution strategies.
\end{abstract}


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% Figure
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% Intro
\section{Introduction}\label{secIntro}
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% Background
\section{Preliminaries}\label{secPrelim}
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% Main
\section{A Stein Variational Evolution Strategy}\label{secMain}
\input{contents/sv-cma-es}

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% Related
\section{Related Work}\label{secRelated}
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% Experiments
\section{Experiments}\label{secExp}
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% Conclusion
\section{Conclusion}\label{secConc}
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% Acknowledgements
\begin{acknowledgements}
This research was funded by the Amazon Development Center Germany GmbH.
The authors want to thank anonymous reviewers for constructive feedback which helped improve the paper.
\end{acknowledgements}

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\title{Supplementary Material}\label{secAppendix}
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\appendix
\input{contents/appendix}

\end{document}
