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\title{No-regret Learning of Nash Equilibria for Black-Box Games via Gaussian Processes}%A Bayesian Optimization Approach to Compute Nash Equilibria for Black-Box Games}

% PAC-learning for Nash Equilibria for Black-Box Games

%No-regret Learning of Nash Equilibria for Black-Box Games via Gaussian Processes


\author{\name Minbiao Han \email minbiaohan@cs.uchicago.edu \\
       \addr Department of Computer Science\\
       The University of Chicago \\
       Chicago, IL 60637-1468, USA}

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In this project, we study the equilibrium for black-box games, i.e. games in which the underlying utility function is unknown for every player. There is extensive literature related to the theoretical analysis of algorithms for computing the Nash Equilibrium (NE) with complete information about the game, while a few studies on the computation of NE for black-box games. Bayesian Optimization (BO) is an approach that is widely adopted to tackle black-box optimization problems. In this project, we develop a new efficient algorithm for finding the NE based on \textit{efficient BO with region-of-interest identification}. Our algorithm balances between exploration and exploitation and improves over the best existing result of \citep{al2018approximating, picheny2019bayesian}.
\end{abstract}

\begin{keywords}
  Bayesian Optimization, Nash Equilibria, Black-Box Games
\end{keywords}


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\input{C7-conclusion.tex}



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