Abstract-This paper presents a theoretical and empirical analysis of linear programming relaxations to ad network optimization. The underlying problem is to select a sequence of ads to send to websites; while an optimal policy can be produced using a Markov Decision Process, in practice one must resort to relaxations to bypass the curse of dimensionality. We focus on a state-of-art relaxation scheme based on linear programming. We build a Markov Decision Process that captures the worst-case behavior of such a linear programming relaxation, and derive theoretical guarantees concerning linear relaxations. We then report on extensive empirical evaluation of linear relaxations; our results suggest that for large problems (similar to ones found in practice), the loss of performance introduced by linear relaxations is rather small.
Primeiramente, gostaria de agradecer a minha orientadora, Prof. Dra. Anna Helena Reali Costa, por ter confiado na minha capacidade, me aceitando como orientado durante as minhas duas iniciações científicas e durante este trabalho de mestrado, exigindo sempre o máximo de seus alunos e me inspirando sempre a ser um melhor pesquisador e pessoa. Gostaria de agradecer ao Prof. Dr. Fábio Gagliardi Cozman, que me apresentou este problema, me ajudando a definir o escopo deste trabalho, participando em minhas publicações, sempre com conselhos extremamente pertinentes. Agradeço ao Prof. Dr. Valdinei Freire da Silva, por sua paciência e contribuição para esta pesquisa, sendo que sem ele ela não seria possível. Agradeço a todos os membros do Laboratório de Técnicas Inteligêntes da USP, pelas discussões construtivas e um ambiente amigável durante todo este trabalho de pesquisa. Agradeço a empresa Yahoo, por ceder uma base de dados extremamente rica que foi utilizada para a avaliação e comparação de um dos algoritmos propostos neste trabalho. Agradeço a minha namorada Mariana, pelo carinho, amizade, paciência, apoio e pelas revisões que eu a forcei fazer. Expresso minha gratição especial a minha família, minha mãe, Vera Lucia Sales Truzzi, meu pai, Claudio Roberto Truzzi, meus irmãos Vitor Sales Truzzi e Rafael Sales Truzzi, pelo apoio quando tomei a decisão de fazer o mestrado, e sua contribuição emocional e financeira. Por fim, agradeço a CAPES pela bolsa de mestrado que foi fundamental para a execução deste trabalho de mestrado.
Background: Ad Networks connect advertisers to websites that want to host advertisements. When users request websites, the Ad Network decides which ad to send so as to maximize the number of ads that are clicked by users. Due to the difficulty in solving such maximization problems, there are solutions in the literature that are based on linear programming (LP) relaxations. Methods: We contribute with a formulation for the Ad Network optimization problem, where it is cast as a Markov decision process (MDP). We analyze theoretically the relative performance of MDP and LP solutions. We report on an empirical evaluation of solutions for LP relaxations, in which we analyze the effect of problem size in performance loss compared to the MDP solution. Results: We show that in some configurations, the LP relaxations incur in approximately 58 % revenue loss when compared to MDP solutions. However, such relative loss decreases as problem size increases. We also propose new heuristics to improve the use of solutions achieved by LP relaxation. Conclusions: We show that solutions obtained by LP relaxations are suitable for Ad Networks, as the performance loss introduced by such solutions are small in large problems observed in practice.
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