\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\providecommand\babel@aux[2]{}
\@nameuse{bbl@beforestart}
\bibstyle{plainnat}
\citation{owain}
\citation{owain}
\citation{owain}
\citation{owain}
\citation{owain}
\citation{owain}
\citation{activerl}
\citation{ajks}
\providecommand \oddpage@label [2]{}
\babel@aux{american}{}
\@writefile{toc}{\contentsline {section}{\numberline {A}Appendix}{1}{appendix.A}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}Experimental Appendix}{1}{subsection.A.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.1.1}Comparison to BAMCP++}{1}{subsubsection.A.1.1}\protected@file@percent }
\newlabel{appendix:owain}{{A.1.1}{1}{Comparison to BAMCP++}{subsubsection.A.1.1}{}}
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{fig:bamcppp}{{\caption@xref {fig:bamcppp}{ on input line 229}}{1}{Comparison to BAMCP++}{figure.caption.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Replication of Figure 3 of \cite  {owain} with varying settings for the hyperparameter $\delta $. As in \cite  {owain}, mean and standard error are presented over 100 trials.\relax }}{1}{figure.caption.1}\protected@file@percent }
\newlabel{fig:bamcppp}{{6}{1}{Replication of Figure 3 of \cite {owain} with varying settings for the hyperparameter $\delta $. As in \cite {owain}, mean and standard error are presented over 100 trials.\relax }{figure.caption.1}{}}
\citation{activerl}
\citation{mabintro}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Final average per step regret for varying noises $\sigma ^2$, standard error from 20 trials. Note the logarithmic $y$ scale. $T=10000$, $k=5$\relax }}{2}{figure.caption.2}\protected@file@percent }
\newlabel{fig:d}{{7}{2}{Final average per step regret for varying noises $\sigma ^2$, standard error from 20 trials. Note the logarithmic $y$ scale. $T=10000$, $k=5$\relax }{figure.caption.2}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.1.2}Impact of Dimension on Linear Contextual Bandit Results}{2}{subsubsection.A.1.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.1.3}Hyperparameters}{2}{subsubsection.A.1.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.1.4}Impact of Labeling Cost}{2}{subsubsection.A.1.4}\protected@file@percent }
\newlabel{appendix:costexperiments}{{A.1.4}{2}{Impact of Labeling Cost}{subsubsection.A.1.4}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {A.1.5}Worth-it-Width Ablations}{2}{subsubsection.A.1.5}\protected@file@percent }
\newlabel{appendix:wiwablations}{{A.1.5}{2}{Worth-it-Width Ablations}{subsubsection.A.1.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A.2}Proof of Theorem 3}{2}{subsection.A.2}\protected@file@percent }
\@writefile{loe}{\contentsline {lemma}{\ifthmt@listswap Lemma~1\else \numberline {1}Lemma\fi \thmtformatoptarg {KL Bound}}{2}{lemma.1}\protected@file@percent }
\newlabel{lemma:event}{{1}{2}{KL Bound}{lemma.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Final average per step regret for varying values of gaps $\Delta $, across many different horizons $T$ and costs $c$. Standard error from 20 trials. Dashed vertical red line is at the predicted worst-case $\Delta = \sqrt  [3]{c/T}$. Other dashed lines correspond to using the doubling trick.\relax }}{3}{figure.caption.3}\protected@file@percent }
\newlabel{fig:cost}{{8}{3}{Final average per step regret for varying values of gaps $\Delta $, across many different horizons $T$ and costs $c$. Standard error from 20 trials. Dashed vertical red line is at the predicted worst-case $\Delta = \sqrt [3]{c/T}$. Other dashed lines correspond to using the doubling trick.\relax }{figure.caption.3}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Simpler baseline comparisons. Final average per step regret for varying values of gaps $\Delta $, across many different horizons $T$ and costs $c$. Standard error from 20 trials. Dashed red line is at the predicted worst-case $\Delta = \sqrt  [3]{c/T}$. Note the similar performance of the Baseline algorithm to Worth-it-Width for $c<10$, and worse performance in the small arm difference $\Delta $ regime whenever $c\geq 10$.\relax }}{4}{figure.caption.4}\protected@file@percent }
\newlabel{fig:bigbaseline}{{9}{4}{Simpler baseline comparisons. Final average per step regret for varying values of gaps $\Delta $, across many different horizons $T$ and costs $c$. Standard error from 20 trials. Dashed red line is at the predicted worst-case $\Delta = \sqrt [3]{c/T}$. Note the similar performance of the Baseline algorithm to Worth-it-Width for $c<10$, and worse performance in the small arm difference $\Delta $ regime whenever $c\geq 10$.\relax }{figure.caption.4}{}}
\@writefile{toc}{\contentsline {paragraph}{Theorem 3}{5}{paragraph*.5}\protected@file@percent }
\newlabel{proof:lowerbound}{{A.2}{5}{Theorem 3}{paragraph*.5}{}}
\@writefile{toc}{\contentsline {paragraph}{How many times do we play $j^*$ in instance $0$?}{5}{paragraph*.6}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Expected regret in instance $j^*$?}{6}{paragraph*.7}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Conclusion.}{6}{paragraph*.8}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {A.3}Proof of Theorem 2}{7}{subsection.A.3}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Assumption 3.1}{7}{paragraph*.9}\protected@file@percent }
\newlabel{proof:fixednregret}{{A.3}{7}{Assumption 3.1}{paragraph*.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A.4}Proof of Theorem 1}{8}{subsection.A.4}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Theorem 1}{8}{paragraph*.10}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Termination.}{8}{paragraph*.11}\protected@file@percent }
\bibdata{bibliography2}
\bibcite{ajks}{{1}{2023}{{Agarwal et~al.}}{{Agarwal, Jiang, Kakade, and Sun}}}
\@writefile{toc}{\contentsline {paragraph}{Regret.}{9}{paragraph*.12}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Conclusion.}{9}{paragraph*.13}\protected@file@percent }
\bibcite{activerl}{{2}{2016}{{Krueger et~al.}}{{Krueger, Leike, Evans, and Salvatier}}}
\bibcite{owain}{{3}{2018}{{Schulze and Evans}}{{}}}
\bibcite{mabintro}{{4}{2019}{{Slivkins}}{{}}}
\newlabel{LastPage}{{}{10}{}{page.10}{}}
\xdef\lastpage@lastpage{10}
\xdef\lastpage@lastpageHy{10}
\gdef \@abspage@last{10}
