% \documentclass{uai2025} % for initial submission
\documentclass[accepted]{uai2025} % after acceptance, for a revised version; 
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%\documentclass[mathfont=newtx]{uai2025} % newtx fonts (improves upon
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%% Choose your variant of English; be consistent
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\usepackage{tikz} % nice language for creating drawings and diagrams

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\title{Efficient Algorithms for Logistic Contextual Slate Bandits with Bandit Feedback}

% The standard author block has changed for UAI 2025 to provide
% more space for long author lists and allow for complex affiliations
%
% All author information is authomatically removed by the class for the
% anonymous submission version of your paper, so you can already add your
% information below.
%
% Add authors
\author[1]{\href{mailto:t-tangoyal@microsoft.com}{Tanmay Goyal}{}}
\author[1]{\href{mailto:gauravsinha@microsoft.com}{Gaurav Sinha}{}}
% Add affiliations after the authors
\affil[1]{%
   Microsoft Research India
}

\input{preamble}
  
\begin{document}
\maketitle

\begin{abstract}
We study the Logistic Contextual Slate Bandit problem, where, at each round, an agent selects a slate of $N$ items from an exponentially large set (of size $2^{\Omega(N)}$) of candidate slates provided by the environment. A single binary reward, determined by a logistic model, is observed for the chosen slate. Our objective is to develop algorithms that maximize cumulative reward over $T$ rounds while maintaining low per-round computational costs. We propose two algorithms, \texttt{Slate-GLM-OFU}\ and \texttt{Slate-GLM-TS}, that accomplish this goal. These algorithms achieve $N^{O(1)}$ per-round time complexity via ``local planning'' (independent slot selections), and low regret through ``global learning'' (joint parameter estimation). We provide theoretical and empirical evidence supporting these claims. Under a well-studied diversity assumption, we prove that \texttt{Slate-GLM-OFU}\ incurs only $\tilde{O}(\sqrt{T})$ regret. Extensive experiments across a wide range of synthetic settings demonstrate that our algorithms consistently outperform state-of-the-art baselines, achieving both the lowest regret and the fastest runtime. Furthermore, we apply our algorithm to select in-context examples in prompts of Language Models for solving binary classification tasks such as sentiment analysis. Our approach achieves competitive test accuracy, making it a viable alternative in practical scenarios.
\end{abstract}

\input{Sections/Paper_Sections/introduction}
\input{Sections/Paper_Sections/notations}
\input{Sections/Paper_Sections/main-algorithm}
\input{Sections/Paper_Sections/other-experiments}
\input{Sections/Paper_Sections/conclusions}
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% You can include footnotes in your text.\footnote{
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% }
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%     A footnote is material put at the foot of a page.
% }
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%   See the \textsf{amsmath} documentation at \url{https://ctan.org/pkg/amsmath} for further details.
% }.
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%   See the \textsf{mathtools} documentation at \url{https://ctan.org/pkg/mathtools} for further details.
% }
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% So, specifically, use the \texttt{equation} environment instead of \verb|$$...$$| and the \texttt{align} environment instead of \texttt{eqnarray}.\footnote{For reasons why you should not use the obsolete \texttt{eqnarray} environment, see Lars Madsen, \textit{Avoid eqnarray!} TUGboat 33(1):21--25, 2012.}
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% For an example, see Figure~\ref{fig:tikz}.
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%     \caption{A Nice Filled Ellipse with a Pair of Coordinate Axes.}\label{fig:tikz}
% \end{figure*}

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% \begin{figure}[!htb]
%   \centering
%   \includegraphics[width=\linewidth]{rio.jpg}
%   \caption{A View of a Nice City.}\label{fig:city}
% \end{figure}

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% For an example, see Table~\ref{tab:data}.
% \begin{table}
%     \centering
%     \caption{An Interesting Table.}\label{tab:data}
%     \begin{tabular}{rl}
%       \toprule % from booktabs package
%       \bfseries Dataset & \bfseries Result\\
%       \midrule % from booktabs package
%       Data1 & 0.12345\\
%       Data2 & 0.67890\\
%       Data3 & 0.54321\\
%       Data4 & 0.09876\\
%       \bottomrule % from booktabs package
%     \end{tabular}
% \end{table}

% \subsection{Algorithms}\label{sec:algorithms}
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% \section{Back Matter}
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% \begin{itemize}
%   \item Author Contributions (optional)
%   \item Acknowledgements (optional)
%   \item References
% \end{itemize}
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% (These Sections/Paper_Sections are automatically removed for the anonymous submission version of your paper.)
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% (See below.)

% (This ‘Back Matter’ section itself should not be included in your paper.)


% \begin{contributions} % will be removed in pdf for initial submission 
% 					  % (without ‘accepted’ option in \documentclass)
%                       % so you can already fill it to test with the
%                       % ‘accepted’ class option
%     Briefly list author contributions. 
%     This is a nice way of making clear who did what and to give proper credit.
%     This section is optional.

%     H.~Q.~Bovik conceived the idea and wrote the paper.
%     Coauthor One created the code.
%     Coauthor Two created the figures.
% \end{contributions}

% \begin{acknowledgements} % will be removed in pdf for initial submission,
% 						 % (without ‘accepted’ option in \documentclass)
%                          % so you can already fill it to test with the
%                          % ‘accepted’ class option
%     Briefly acknowledge people and organizations here.

%     \emph{All} acknowledgements go in this section.
% \end{acknowledgements}

% References
\bibliography{main}

\newpage

\onecolumn


\title{Efficient Algorithms for Logistic Slate Contextual Bandits with Bandit Feedback\\(Supplementary Material)}
\maketitle

\appendix
\input{Sections/Paper_Sections/appendix}

% This Supplementary Material should be submitted together with the main paper.

% \appendix
% \section{Additional simulation results}
% Table~\ref{tab:supp-data} lists additional simulation results; see also \citet{einstein} for a comparison. 

% \begin{table}[!h]
%     \centering
%     \caption{An Interesting Table.} \label{tab:supp-data}
%     \begin{tabular}{rl}
%         \toprule % from booktabs package
%         \bfseries Dataset & \bfseries Result\\
%         \midrule % from booktabs package
%         Data1 & 0.12345\\
%         Data2 & 0.67890\\
%         Data3 & 0.54321\\
%         Data4 & 0.09876\\
%         \bottomrule % from booktabs package
%     \end{tabular}
% \end{table}

% \section{Math font exposition}
% % NOTE: necessary when ptmx or no mathfont class option is given
% \providecommand{\upGamma}{\Gamma}
% \providecommand{\uppi}{\pi}
% How math looks in equations is important:
% \begin{equation*}
%     F_{\alpha,\beta}^\eta(z) = \upGamma(\tfrac{3}{2}) \prod_{\ell=1}^\infty\eta \frac{z^\ell}{\ell} + \frac{1}{2\uppi}\int_{-\infty}^z\alpha \sum_{k=1}^\infty x^{\beta k}\mathrm{d}x.
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% It is a polynomial \(f(z)=\alpha z + \beta z^2\), where \(-n<\alpha<\beta/n\leq\gamma\), with \(\gamma\) a positive real number.


\end{document}
