Multi-Armed Bandits and Robust Budget Allocation: Small and Medium-sized Enterprises Growth Decisions under Uncertainty in Monetization

Wenwen Liu

doi:10.71222/g1pdz259

Authors

Wenwen Liu University of Washington, Seattle, USA Author

DOI:

https://doi.org/10.71222/g1pdz259

Keywords:

multi-armed bandits, robust budget allocation, small and medium-sized enterprises (SMEs), monetization decision, uncertainty, business growth

Abstract

Small and medium-sized enterprises (SMEs) often face significant uncertainty when allocating limited advertising budgets across multiple channels, as the return on investment (ROI) of each channel is typically unknown and volatile. This paper proposes a robust budget allocation framework based on the multi-armed bandit (MAB) model to address this challenge, specifically tailored to the advertising decisions of SMEs. By integrating robustness principles into traditional MAB algorithms, the framework balances "exploration" (testing new advertising channels) and "exploitation" (scaling effective channels) while mitigating the impact of ROI uncertainty. An empirical simulation is conducted using realistic advertising scenarios (including social media ads, search engine marketing, influencer collaborations, and offline promotions) to validate the model. Results show that the proposed robust MAB framework outperforms traditional budget allocation methods (e.g., equal distribution, heuristic allocation) in terms of cumulative ROI, budget efficiency, and risk resistance. This study provides SMEs with a practical, data-driven tool for advertising budget optimization under uncertainty, contributing to sustainable business growth. The findings also enrich the application of MAB models in the advertising domain, particularly for resource-constrained enterprises.

References

1. P. Auer, N. Cesa-Bianchi, and P. Fischer, "Finite-time analysis of the multiarmed bandit problem," Machine learning, vol. 47, no. 2, pp. 235-256, 2002.

2. A. Ben-Tal, A. Nemirovski, and L. El Ghaoui, "Robust optimization," 2009. doi: 10.1515/9781400831050

3. S. Bubeck, and N. Cesa-Bianchi, "Regret analysis of stochastic and nonstochastic multi-armed bandit problems," Foundations and Trends® in Machine Learning, vol. 5, no. 1, pp. 1-122, 2012.

4. A. Ekaputra, R. D. Sari, Y. Yuniarsih, and M. Algunadi, "Are digital marketing trends and challenges aligned with SDGs?: A review of Indonesian SMEs," Sinergi International Journal of Economics, vol. 2, no. 2, pp. 98-109, 2024.

5. L. A. Mitchell, "An examination of methods of setting advertising budgets: practice and the literature," European Journal of Marketing, vol. 27, no. 5, pp. 5-21, 1993. doi: 10.1108/03090569310039697

6. J. Hurstinen, "Data-driven marketing-Impacting a Revolution in the Marketing Industry: Using data-driven marketing to improve profitability," 2020.

7. L. Li, W. Chu, J. Langford, and R. E. Schapire, "A contextual-bandit approach to personalized news article recommendation," In Proceedings of the 19th international conference on World wide web, April, 2010, pp. 661-670. doi: 10.1145/1772690.1772758

8. D. G. Luenberger, and Y. Ye, "Linear and nonlinear programming," Reading, MA: Addison-wesley, vol. 2, 1984.

9. A. Nogaj, "An investigation of the factors that influence marketing decision makers in their budget allocation process (Doctoral dissertation, Dublin Business School)," 2014.

10. B. Kádár, and E. Jáki, "COVID-19 and SMEs: An umbrella review of systematic literature (2020-2024) and future directions for entrepreneurship: Introduction to the "The Entrepreneurial Landscape in the Post-COVID Era: Insights, Challenges, and Future Perspectives" special issue," Society and Economy, vol. 46, no. 4, pp. 323-341, 2024.

11. H. Robbins, "Some aspects of the sequential design of experiments," 1952. doi: 10.1090/s0002-9904-1952-09620-8

12. R. Almestarihi, A. Y. Ahmad, R. H. Frangieh, I. A. Abualsondos, K. K. Nser, and A. Ziani, "Measuring the ROI of paid advertising campaigns in digital marketing and its effect on business profitability," 2024.

13. I. A. Botosan, and P. Bilokon, "Optimal Resource Allocation Using Multi-Armed Bandits," 2024.

14. B. Han, and C. Arndt, "Budget allocation as a multi-agent system of contextual & continuous bandits," In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, August, 2021, pp. 2937-2945.