% \documentclass{uai2022} % for initial submission
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\myexternaldocument{maiti_414-supp}

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\title{A Causal Bandit Approach to Learning Good Atomic Interventions in Presence of Unobserved Confounders}

% The standard author block has changed for UAI 2022 to provide
% more space for long author lists and allow for complex affiliations
%
% All author information is automatically removed by the class for the
% anonymous submission version of your paper, so you can already add your
% information below.
% 
% Important: in case of equal contributions, we strongly recommend to NOT show it in this part of the paper, but rather describe it in the appropriate section at the end of the paper "Author Contribution", where you have more space to describe how each author contributed.
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% Add authors
% Remember to use the order convention "First/Given name" "Last/Family name", e.g. John Smith, Hanako Yamada, Marco Rossi, Wei Zhang
\author[1]{\href{mailto:aurghya.kgp@gmail.com?Subject=Your UAI 2022 paper}{Aurghya Maiti}{}}
\author[2]{\href{mailto:vineetn90@gmail.com?Subject=Your UAI 2022 paper}{Vineet Nair}{}}
\author[1]{\href{mailto:sinhagaur88@gmail.com?Subject=Your UAI 2022 paper}{Gaurav Sinha}{}}

\affil[1]{%
    Adobe Research,
    Bangalore, India
}
\affil[2]{%
    Technion Israel Institute of Technology,
    Haifa, Israel
}

\begin{document}
\maketitle
\begin{abstract}
We study the problem of determining the best atomic intervention in a Causal Bayesian Network (CBN) specified only by its causal graph. We model this as a stochastic multi-armed bandit (MAB) problem with side-information, where interventions on CBN correspond to arms of the bandit instance. First, we propose a simple regret minimization algorithm that takes as input a causal graph with observable and unobservable nodes and in $T$ exploration rounds achieves $\tilde{O}(\sqrt{m(\mathcal{C})/T})$ expected simple regret. Here $m(\mathcal{C})$ is a parameter dependent on the input CBN $\mathcal{C}$ and could be much smaller than the number of arms. We also show that this is almost optimal for CBNs whose causal graphs have an $n$-ary tree structure. 
Next, we propose a cumulative regret minimization algorithm that takes as input a causal graph with observable nodes and performs better than the optimal MAB algorithms that do not use causal side-information. We experimentally compare both our algorithms with the best known algorithms in the literature. 
\end{abstract}

\input{sections/sec_introduction}
\input{sections/sec_model_and_preliminaries}
\input{sections/sec_simple_regret_for_general_graphs}
\input{sections/sec_lower_bound_for_simple_regret}
\input{sections/sec_cumulative_regret_general_graph}
\input{sections/sec_experiments}
\input{sections/sec_conclusion}
\input{sections/sec_author_contributions}

\bibliography{maiti_414}
\end{document}
