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\title{Online Generalized Magician's Problem with Multiple Workers}

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% All author information is authomatically removed by the class for the
% anonymous submission version of your paper, so you can already add your
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% Add authors
\author[1]{\href{mailto:<ruoyu.wu@sydney.edu.au>?Subject=Your UAI 2025 paper}{Ruoyu~Wu}{}}
\author[1]{\href{mailto:<wei.bao@sydney.edu.au>?Subject=Your UAI 2025 paper}{Wei~Bao}{}}
\author[2]{\href{mailto:<liang@ece.utoronto.ca>?Subject=Your UAI 2025 paper}{Ben~Liang}{}}
\author[1]{\href{mailto:<liming.ge@sydney.edu.au>?Subject=Your UAI 2025 paper}{Liming~Ge}{}}
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\affil[1]{%
    School of Computer Science\\
    The University of Sydney\\
    Sydney, NSW, Australia
}
\affil[2]{%
    Department of Electrical and Computer Engineering\\
    University of Toronto\\
    Toronto, Ontario, Canada
} 
  \begin{document}
\maketitle

\begin{abstract}
We study the online Generalized Magician's Problem with Multiple Workers (GMPMW), where tasks arrive sequentially and must be assigned to one of several workers for processing, with each worker consuming a stochastic amount of resources and generating an unknown reward. 
The system must decide on the acceptance of each task and its assignment to a worker, in order to maximize the accumulated reward within the budget. To address this problem, we propose the Online Worker Assignment (OWA) Algorithm. 
It optimally solves an optimization problem to balance resource allocation across workers and maintains virtual resource utilization according to the joint evolution of different workers. The competitive ratio of OWA is lower bounded by the closed-form expression $\max\{{1}/{L},c\}\cdot(1-K^{-\frac{1}{2}})$, where $L$ is the number of workers, $K$ is the resource budget, and $c$ is a constant derived from the problem instance. 
We perform trace-driven experiments with real-time video analytics, demonstrating the excellent capability of OWA to accommodate multiple workers in GMPMW.
\end{abstract}

\input{Sections/Introduction}
\input{Sections/RelatedWork}
\input{Sections/ProblemFormulation}
\input{Sections/AlgorithmDesign}
\input{Sections/CompetitiveRatio}
\input{Sections/Experiment}
\input{Sections/Conclusion}



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\include{Sections/Appendix/Appendix}

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