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

Kemal Kilic; Menekse G. Saygi; Semih O. Sezer

doi:10.3934/jimo.2018073

Article Contents

2019, Volume 15, Issue 2: 833-854. Doi: 10.3934/jimo.2018073

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

Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, 34956, Turkey

* Corresponding author: Kemal Kilic
* Corresponding author: Kemal Kilic

Received: October 2016

Revised: December 2017

Early access: June 2018

Published: January 2019

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Abstract

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.

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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

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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

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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

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

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

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

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

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Table 1. Parameters for numerical experiments

Problem Specific Parameters	Algorithm Specific Parameters
Problem Size	$h$ value
Initial States	Iteration Number
Transition Rates	Resolution (i.e., Step Length in Time)
$\beta$-probabilities
Exposure Payment Matrix
Min./Max. Display Constraint
Min./Max. Payment Constraint

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Table 2. Experimental Conditions

Experiment #	Maximum Display	Minimum Payment	Maximum Payment
111	5	10	40
112	5	10	70
121	5	30	40
122	5	30	70
211	8	10	40
212	8	10	70
221	8	30	40
222	8	30	70

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

	Heuristics				Finite Difference		Value Iteration
Exp.#	A	B	C	Random	SMR	ER	SMR	ER
111	32.25	45.46	42.24	28.83	45.93	45.57	45.90	44.57
112	32.69	45.99	42.24	28.99	46.47	46.01	46.49	45.01
121	13.28	14.86	9.54	9.70	30.75	30.46	30.79	29.61
122	13.82	15.40	9.54	9.86	33.71	33.38	33.64	32.35
211	33.81	49.55	49.13	29.71	49.63	49.27	49.62	48.16
212	35.28	49.85	49.34	30.11	49.89	49.55	49.91	48.46
221	15.66	31.44	30.75	11.52	34.80	34.36	34.85	33.17
222	17.00	31.75	30.96	11.92	39.94	39.90	39.90	38.55

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References

[1]	S. M. Bae, S. C. Park and S. H. Ha, Fuzzy web ad selector based on web usage mining, Intelligent Systems, IEEE, 18 (2003), 62-69.
[2]	M. C. Campbell and K. L. Keller, Brand familiarity and advertising repetition effects, Journal of Consumer Research, 30 (2003), 292-304. doi: 10.1086/376800.
[3]	S. A. Freedman, E. Dayan, Y. B. Kimelman, H. Weissman and R. Eitan, Early intervention for preventing posttraumatic stress disorder: An internet-based virtual reality treatment European Journal of Psychotraumatology, 6 (2015), 25608. doi: 10.3402/ejpt.v6.25608.
[4]	S. H. Ha, An intelligent system for personalized advertising on the internet, in E-Commerce and Web Technologies, Springer, 2004, 21–30. doi: 10.1007/978-3-540-30077-9_3.
[5]	P. Kazienko and M. Adamski, Adrosa adaptive personalization of web advertising, Information Sciences, 177 (2007), 2269-2295. doi: 10.1016/j.ins.2007.01.002.
[6]	K. Kilic and O. Bozkurt, Computational intelligence based decision support tool for personalized advertisement assignment system, International Journal of Computational Intelligence Systems, 6 (2013), 396-410. doi: 10.1080/18756891.2013.780725.
[7]	K. Kilic, M. G. Saygi and S. O. Sezer, A mathematical model for personalized advertisement in virtual reality environments, Mathematical Methods of Operations Research, 85 (2017), 241-264. doi: 10.1007/s00186-016-0567-8.
[8]	M. Langheinrich, A. Nakamura, N. Abe, T. Kamba and Y. Koseki, Unintrusive customization techniques for web advertising, Computer Networks, 31 (1999), 1259-1272. doi: 10.1016/S1389-1286(99)00033-X.
[9]	A. Marchand and T. Hennig-Thurau, Value creation in the video game industry: Industry economics, consumer benefits, and research opportunities, Journal of Interactive Marketing, 27 (2013), 141-157.
[10]	J. J. Pan, J. Chang, X. Yang, H. Liang, J. J. Zhang, T. Qureshi, R. Howell and T. Hickish, Virtual reality training and assessment in laparoscopic rectum surgery, The International Journal of Medical Robotics and Computer Assisted Surgery, 11 (2015), 194-209. doi: 10.1002/rcs.1582.
[11]	J. E. Phelps, R. Lewis, L. Mobilio, D. Perry and N. Raman, Viral marketing or electronic word-of-mouth advertising: Examining consumer responses and motivations to pass along email, Journal of Advertising Research, 44 (2004), 333-348. doi: 10.1017/S0021849904040371.
[12]	S. Schmidt and M. Eisend, Advertising repetition: A meta-analysis on effective frequency in advertising, Journal of Advertising, 44 (2015), 415-428. doi: 10.1080/00913367.2015.1018460.
[13]	J. A. Tomlin, An entropy approach to unintrusive targeted advertising on the web, Computer Networks, 33 (2000), 767-774. doi: 10.1016/S1389-1286(00)00062-1.
[14]	W. W. Tsang and A. S. Fu, Virtual reality exercise to improve balance control in older adults at risk of falling, Hong Kong Medical Journal, 22 (2016), 19-22.
[15]	J. Turner, The planning of guaranteed targeted display advertising, Operations Research, 60 (2012), 18-33. doi: 10.1287/opre.1110.0996.
[16]	J. Turner, A. Scheller-Wolf and S. Tayur, Or practice-scheduling of dynamic in-game advertising, Operations Research, 59 (2011), 1-16. doi: 10.1287/opre.1100.0852.
[17]	I. Yaveroglu and N. Donthu, Advertising repetition and placement issues in on-line environments, Journal of Advertising, 37 (2008), 31-44. doi: 10.2753/JOA0091-3367370203.
[18]	ZenithOptimedia, Advertising expenditure forecasts march 2016, https://www.performics.com/executive-summary-advertising-expenditure-forecasts-march-2016/, 2016, Accessed March 28, 2018.
[19]	N. Zhou, Y. Chen and H. Zhang, Study on personalized recommendation model of internet advertisement, in Integration and Innovation Orient to E-Society Volume 2, Springer, 2007, 176–183. doi: 10.1007/978-0-387-75494-9_22.