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Exact and heuristic methods for personalized display advertising in virtual reality platforms

  • * Corresponding author: Kemal Kilic

    * Corresponding author: Kemal Kilic 
Abstract / Introduction Full Text(HTML) Figure(7) / Table(3) Related Papers Cited by
  • In this paper, motivated from a real problem faced by an online Virtual Reality (VR) platform provider, we study a personalized advertisement assignment problem. In this platform users log in/out and change their virtual locations. A number of advertisers are willing to pay for ad locations to reach these users. Every time a user visits a new location, the company displays one of the ads. At the end of a fixed time horizon, a reward is collected which depends on the number of ads of each advertiser displayed to different users. The objective is to assign ads dynamically to maximize the expected reward. The problem is studied in a framework where the behaviors of users are modeled with two-state continuous-time Markov processes. We describe two exact and four heuristic algorithms. We compare these algorithms and conduct a sensitivity analysis over problem and algorithm specific parameters. These are the main contributions of the current paper. Exact algorithms suffer from the curse of dimensionality, hence, heuristic methods might be considered instead in some cases. However, exact methods can also be used as part of heuristics since the experimental analysis demonstrates that they are robust for parameters that influence the computational requirements.

    Mathematics Subject Classification: Primary: 90C40; Secondary: 90C39.

    Citation:

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  • Figure 1.  The sample mean revenues of the six algorithms for varying number of replications in Experiment 111

    Figure 2.  Computed expected revenues (ER) and the sample mean revenues (SMR) obtained for various L = 1/h values for the finite difference algorithm in Experiment #111

    Figure 3.  Computed expected revenues determined at each iteration (that is, $n \mapsto U_n$) for the value iteration algorithms with different resolution parameter values in Experiment # 111

    Figure 4.  Computed expected revenues determined by the value iteration algorithm after 40 iterations for different resolution parameter values in Experiment #111

    Figure 5.  The computational time in days for the value iteration algorithm with iteration number = 40, for different resolution parameter values in Experiment 111

    Figure 6.  The expected revenues determined by the value iteration algorithm with iteration number = 40, for different resolution parameter values in Experiment 111

    Figure 7.  The sample mean revenues (SMRs) determined by the finite difference algorithm for different h-value in Experiment 111

    Table 1.  Parameters for numerical experiments

    Problem Specific Parameters Algorithm Specific Parameters
    Problem Size $h$ value
    Initial StatesIteration Number
    Transition RatesResolution (i.e., Step Length in Time)
    $\beta$-probabilities
    Exposure Payment Matrix
    Min./Max. Display Constraint
    Min./Max. Payment Constraint
     | Show Table
    DownLoad: CSV

    Table 2.  Experimental Conditions

    Experiment #Maximum DisplayMinimum PaymentMaximum Payment
    11151040
    11251070
    12153040
    12253070
    21181040
    21281070
    22183040
    22283070
     | Show Table
    DownLoad: CSV

    Table 3.  Revenue performance of the algorithms for different experimental conditions

    HeuristicsFinite DifferenceValue Iteration
    Exp.#ABCRandomSMRERSMRER
    11132.2545.4642.2428.8345.9345.5745.9044.57
    11232.6945.9942.2428.9946.4746.0146.4945.01
    12113.2814.869.549.7030.7530.4630.7929.61
    12213.8215.409.549.8633.7133.3833.6432.35
    21133.8149.5549.1329.7149.6349.2749.6248.16
    21235.2849.8549.3430.1149.8949.5549.9148.46
    22115.6631.4430.7511.5234.8034.3634.8533.17
    22217.0031.7530.9611.9239.9439.9039.9038.55
     | Show Table
    DownLoad: CSV
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