{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:34:41Z","timestamp":1772120081150,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,1,19]],"date-time":"2024-01-19T00:00:00Z","timestamp":1705622400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,1,19]],"date-time":"2024-01-19T00:00:00Z","timestamp":1705622400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002954","name":"Universit\u00e0 degli Studi di Milano - Bicocca","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100002954","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Data Sci Anal"],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This paper deals with the problem of optimising bids and budgets of a set of digital advertising campaigns. We improve on the current state of the art by introducing support for multi-ad group marketing campaigns and developing a highly data efficient parametric contextual bandit. The bandit, which exploits domain knowledge to reduce the exploration space, is shown to be effective under the following settings; few clicks and\/or small conversion rate, short horizon scenarios, rapidly changing markets and low budget. Furthermore, a bootstrapped Thompson sampling algorithm is adapted to fit the parametric bandit. Extensive numerical experiments, performed on synthetic and real-world data, show that, on average, the parametric bandit gains more conversions than state-of-the-art bandits. Gains in performance are particularly high when an optimisation algorithm is needed the most, i.e. with tight budget or many ad groups, though gains are present also in the case of a single-ad group.<\/jats:p>","DOI":"10.1007\/s41060-023-00493-7","type":"journal-article","created":{"date-parts":[[2024,1,19]],"date-time":"2024-01-19T11:02:17Z","timestamp":1705662137000},"page":"151-165","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Multi-armed bandits for performance marketing"],"prefix":"10.1007","volume":"20","author":[{"given":"Marco","family":"Gigli","sequence":"first","affiliation":[]},{"given":"Fabio","family":"Stella","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,1,19]]},"reference":[{"key":"493_CR1","doi-asserted-by":"publisher","DOI":"10.1287\/educ.2019.0204","author":"S Agrawal","year":"2019","unstructured":"Agrawal, S.: Recent advances in Multiarmed Bandits for sequential decision making. Oper. Res. Manag. Sci. Age Anal. (2019). https:\/\/doi.org\/10.1287\/educ.2019.0204","journal-title":"Oper. Res. Manag. Sci. Age Anal."},{"key":"493_CR2","unstructured":"Agrawal, S., Goyal, N.: Thompson sampling for contextual bandits with linear payoffs. In: ICML. pp. 127\u2013135. PMLR (2013)"},{"issue":"4","key":"493_CR3","doi-asserted-by":"publisher","first-page":"864","DOI":"10.1287\/mnsc.2014.2022","volume":"61","author":"SR Balseiro","year":"2015","unstructured":"Balseiro, S.R., Besbes, O., Weintraub, G.Y.: Repeated auctions with budgets in ad exchanges: approximations and design. Manag. Sci. 61(4), 864\u2013884 (2015)","journal-title":"Manag. Sci."},{"key":"493_CR4","unstructured":"Bubeck, S., Slivkins, A.: The best of both worlds: Stochastic and adversarial bandits. In: Proceedings of the 25th annual conference on learning theory. vol.\u00a023, pp. 42.1\u201342.23. PMLR (2012)"},{"issue":"3","key":"493_CR5","doi-asserted-by":"publisher","first-page":"380","DOI":"10.3390\/e23030380","volume":"23","author":"E Cavenaghi","year":"2021","unstructured":"Cavenaghi, E., Sottocornola, G., Stella, F., Zanker, M.: Non stationary multi-armed bandit: empirical evaluation of a new concept drift-aware algorithm. Entropy 23(3), 380 (2021)","journal-title":"Entropy"},{"key":"493_CR6","doi-asserted-by":"crossref","unstructured":"Cesa-Bianchi, N., Cesari, T., Colomboni, R., Fusco, F., Leonardi, S.: The role of transparency in repeated first-price auctions with unknown valuations. arXiv:2307.09478 (2023)","DOI":"10.1145\/3618260.3649658"},{"key":"493_CR7","doi-asserted-by":"crossref","unstructured":"Chapelle, O.: Offline evaluation of response prediction in online advertising auctions. In: Proceedings of the 24th international conference on world wide web. pp. 919\u2013922 (2015)","DOI":"10.1145\/2740908.2742566"},{"key":"493_CR8","first-page":"2249","volume":"24","author":"O Chapelle","year":"2011","unstructured":"Chapelle, O., Li, L.: An empirical evaluation of Thompson sampling. Adv. Neural. Inf. Process. Syst. 24, 2249\u20132257 (2011)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"issue":"50","key":"493_CR9","first-page":"1","volume":"17","author":"W Chen","year":"2016","unstructured":"Chen, W., Wang, Y., Yuan, Y., Wang, Q.: Combinatorial multi-armed bandit and its extension to probabilistically triggered arms. JMLR 17(50), 1\u201333 (2016)","journal-title":"JMLR"},{"key":"493_CR10","unstructured":"Chu, W., Li, L., Reyzin, L., Schapire, R.: Contextual bandits with linear payoff functions. In: AISTATS 2011. pp. 208\u2013214. PLMR (2011)"},{"issue":"5","key":"493_CR11","doi-asserted-by":"publisher","first-page":"888","DOI":"10.1177\/00222437211030201","volume":"58","author":"S Despotakis","year":"2021","unstructured":"Despotakis, S., Ravi, R., Sayedi, A.: First-price auctions in online display advertising. J. Mark. Res. 58(5), 888\u2013907 (2021)","journal-title":"J. Mark. Res."},{"key":"493_CR12","doi-asserted-by":"crossref","unstructured":"Diemert Eustache, Meynet Julien, Galland, P., Lefortier, D.: Attribution modeling increases efficiency of bidding in display advertising. In: Proceedings of the ADKDD\u201917. pp.\u00a01\u20136. ACM (2017)","DOI":"10.1145\/3124749.3124752"},{"key":"493_CR13","unstructured":"Filippi, S., Cappe, O., Garivier, A., Szepesv\u00e1ri, C.: Parametric bandits: the generalized linear case. In: NIPS. vol.\u00a023, pp. 586\u2013594 (2010)"},{"key":"493_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.trc.2020.102775","volume":"120","author":"D Gammelli","year":"2020","unstructured":"Gammelli, D., Peled, I., Rodrigues, F., Pacino, D., Kurtaran, H.A., Pereira, F.C.: Estimating latent demand of shared mobility through censored Gaussian processes. Transp. Res. Part C Emerg. Technol. 120, 102775 (2020)","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"493_CR15","doi-asserted-by":"crossref","unstructured":"Geyik, S.C., Saxena, A., Dasdan, A.: Multi-touch attribution based budget allocation in online advertising. In: Proceedings of the eighth international workshop on data mining for online advertising. pp.\u00a01\u20139 (2014)","DOI":"10.1145\/2648584.2648586"},{"key":"493_CR16","doi-asserted-by":"crossref","unstructured":"Gigli, M., Stella, F.: Parametric bandits for search engine marketing optimisation. In: Advances in knowledge discovery and data mining. PAKDD 2022. pp. 326\u2013337. Springer (2022)","DOI":"10.1007\/978-3-031-05981-0_26"},{"key":"493_CR17","unstructured":"Google Ads: Google Ads Help (2021), https:\/\/support.google.com\/google-ads, see: answer\/1704396, answer\/1722122, answer\/2616012"},{"key":"493_CR18","unstructured":"Han, Y., Zhou, Z., Flores, A., Ordentlich, E., Weissman, T.: Learning to bid optimally and efficiently in adversarial first-price auctions. arXiv:2007.04568 (2020)"},{"key":"493_CR19","doi-asserted-by":"crossref","unstructured":"Harrell, F.E.: Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis, vol. 608. Springer (2001)","DOI":"10.1007\/978-1-4757-3462-1"},{"issue":"12","key":"493_CR20","doi-asserted-by":"publisher","first-page":"2949","DOI":"10.1287\/mnsc.2014.2018","volume":"60","author":"K Iyer","year":"2014","unstructured":"Iyer, K., Johari, R., Sundararajan, M.: Mean field equilibria of dynamic auctions with learning. Manage. Sci. 60(12), 2949\u20132970 (2014)","journal-title":"Manage. Sci."},{"key":"493_CR21","doi-asserted-by":"crossref","unstructured":"Nuara, A., Trov\u00f2, F., Gatti, N., Restelli, M.: A combinatorial-bandit algorithm for the online joint bid\/budget optimization of pay-per-click advertising campaigns. In: Thirty-second AAAI conference on artificial intelligence (2018)","DOI":"10.1609\/aaai.v32i1.11888"},{"key":"493_CR22","unstructured":"Nuara, A., Trov\u00f2, F., Gatti, N., Restelli, M.: Online joint bid\/daily budget optimization of internet advertising campaigns. arXiv:2003.01452 (2020)"},{"key":"493_CR23","unstructured":"Osband, I., Van\u00a0Roy, B.: Bootstrapped Thompson sampling and deep exploration. arXiv:1507.00300 (2015)"},{"issue":"3","key":"493_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3628603","volume":"18","author":"W Ou","year":"2023","unstructured":"Ou, W., Chen, B., Dai, X., Zhang, W., Liu, W., Tang, R., Yu, Y.: A survey on bid optimization in real-time bidding display advertising. ACM Trans. Knowl. Discov. Data 18(3), 1\u201331 (2023)","journal-title":"ACM Trans. Knowl. Discov. Data"},{"key":"493_CR25","unstructured":"PwC: IAB Internet advertising revenue report, Full year 2021 results (2022)"},{"key":"493_CR26","unstructured":"PwC: IAB Internet advertising revenue report, Full year 2022 results (2023)"},{"key":"493_CR27","unstructured":"Riquelme, C., Tucker, G., Snoek, J.: Deep Bayesian bandits showdown: an empirical comparison of Bayesian deep networks for Thompson sampling. arXiv:1802.09127 (2018)"},{"key":"493_CR28","doi-asserted-by":"crossref","unstructured":"Russo, D., Van\u00a0Roy, B., Kazerouni, A., Osband, I., Wen, Z.: A tutorial on Thompson sampling. arXiv:1707.02038 (2017)","DOI":"10.1561\/9781680834710"},{"issue":"1\u20132","key":"493_CR29","first-page":"1","volume":"12","author":"A Slivkins","year":"2019","unstructured":"Slivkins, A.: Introduction to multi-armed bandits. Found. Trends\u00ae Mach. Learn. 12(1\u20132), 1\u2013286 (2019)","journal-title":"Found. Trends\u00ae Mach. Learn."},{"key":"493_CR30","unstructured":"Srinivas, N., Krause, A., Kakade, S.M., Seeger, M.: Gaussian process optimization in the bandit setting: no regret and experimental design. arXiv:0912.3995 (2009)"},{"key":"493_CR31","unstructured":"Stan Development Team: Stan modeling language users guide and reference manual (2019), version 2.28"},{"key":"493_CR32","doi-asserted-by":"crossref","unstructured":"Swaminathan, A., Joachims, T.: Counterfactual risk minimization: learning from logged bandit feedback. In: International conference on machine learning. pp. 814\u2013823. PMLR (2015)","DOI":"10.1145\/2740908.2742564"},{"issue":"3\/4","key":"493_CR33","doi-asserted-by":"publisher","first-page":"285","DOI":"10.2307\/2332286","volume":"25","author":"WR Thompson","year":"1933","unstructured":"Thompson, W.R.: On the likelihood that one unknown probability exceeds another in view of the evidence of two samples. Biometrika 25(3\/4), 285\u2013294 (1933)","journal-title":"Biometrika"},{"key":"493_CR34","unstructured":"Valko, M., Korda, N., Munos, R., Flaounas, I., Cristianini, N.: Finite-time analysis of kernelised contextual bandits. arXiv:1309.6869 (2013)"},{"issue":"5","key":"493_CR35","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1257\/aer.104.5.442","volume":"104","author":"Hal R Varian","year":"2014","unstructured":"Varian, Hal R., Harris, Christopher: The VCG auction in theory and practice. Am. Econ. Rev. 104(5), 442\u201345 (2014)","journal-title":"Am. Econ. Rev."},{"key":"493_CR36","unstructured":"Wang, Q., Yang, Z., Deng, X., Kong, Y.: Learning to bid in repeated first-price auctions with budgets. arXiv:2304.13477 (2023)"},{"key":"493_CR37","unstructured":"Weed, J., Perchet, V., Rigollet, P.: Online learning in repeated auctions. In: 29th annual conference on learning theory. vol.\u00a049, pp. 1562\u20131583. PMLR (2016)"},{"key":"493_CR38","doi-asserted-by":"crossref","unstructured":"Williams, C.K., Rasmussen, C.E.: Gaussian processes for machine learning, vol. 2. MIT press Cambridge, MA (2006)","DOI":"10.7551\/mitpress\/3206.001.0001"}],"container-title":["International Journal of Data Science and Analytics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41060-023-00493-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s41060-023-00493-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41060-023-00493-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T03:35:19Z","timestamp":1748403319000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s41060-023-00493-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,19]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["493"],"URL":"https:\/\/doi.org\/10.1007\/s41060-023-00493-7","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-2684616\/v1","asserted-by":"object"}]},"ISSN":["2364-415X","2364-4168"],"issn-type":[{"value":"2364-415X","type":"print"},{"value":"2364-4168","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,19]]},"assertion":[{"value":"12 March 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 December 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}