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\title{Fast Interactive Search under a
Scale-Free Comparison Oracle}



\usepackage{authblk}

\author[1]{Daniyar Chumbalov\thanks{Authors contributed equally and are listed in alphabetical order.} \thanks{Work done while at EPFL.}}
\author[1]{Lars Klein\protect\footnotemark[1]}
\author[2]{Lucas Maystre}
\author[1]{Matthias Grossglauser}
\affil[1]{INDY Lab, EPFL, Lausanne, Switzerland}
\affil[2]{Spotify, London, UK}
\begin{document}


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\maketitle




\begin{abstract}
    A comparison-based search algorithm lets a user find a target item $t$ in a database by answering queries of the form, ``Which of items $i$ and $j$ is closer to $t$?''
    Instead of formulating an explicit query (such as one or several keywords), the user navigates towards the target via a sequence of such (typically noisy) queries.
    We propose a scale-free probabilistic oracle model called $\gamma$-CKL for such similarity triplets $(i,j;t)$, which generalizes the CKL triplet model proposed in the literature. %
    The generalization affords independent control over the discriminating power of the oracle and the dimension of the feature space containing the items.
    We develop a search algorithm with provably exponential rate of convergence under the $\gamma$-CKL oracle, thanks to a backtracking strategy that deals with the unavoidable errors in updating the belief region around the target.
    We evaluate the performance of the algorithm both over the posited oracle and over several real-world triplet datasets.
    We also report on a comprehensive user study, where human subjects navigate a database of face portraits.
\end{abstract}


\input{notations.tex}




\input{1_introduction_camera_ready}
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\bibliography{scale_free_search}

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\title{Fast Interactive Search under a
Scale-Free Comparison Oracle\\(Supplementary Material)}
\maketitle

\appendix

\input{appendix_search_camera_ready}

\end{document}
