{"id":976014,"date":"2023-10-12T04:15:03","date_gmt":"2023-10-12T11:15:03","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=976014"},"modified":"2023-10-12T04:15:03","modified_gmt":"2023-10-12T11:15:03","slug":"robust-dynamic-assortment-optimization-in-the-presence-of-outlier-customers","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/robust-dynamic-assortment-optimization-in-the-presence-of-outlier-customers\/","title":{"rendered":"Robust dynamic assortment optimization in the presence of outlier customers"},"content":{"rendered":"<p>We consider the dynamic assortment optimization problem under the multinomial logit model with unknown utility parameters. The main question investigated in this paper is model mis-specification under the\u00a0<i>\u03b5<\/i>-contamination model, which is a fundamental model in robust statistics and machine learning. In particular, throughout a selling horizon of length\u00a0<i>T<\/i>, we assume that customers make purchases according to a well-specified underlying multinomial logit choice model in a <span class=\"equationTd inline-formula\"><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" style=\"font-style: normal;font-weight: normal;line-height: normal;font-size: 16px;text-indent: 0px;text-align: left;text-transform: none;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;padding: 0px;margin: 0px;position: relative\" role=\"presentation\" data-mathml=\"<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" id=\"i02\" overflow=\"scroll\" altimg=\"eq-00002.gif\"><mrow><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>&#x2212;<\/mo><mi>&#x3B5;<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/math>\"><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math id=\"i02\" display=\"inline\" overflow=\"scroll\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mn>(1-eps)-fra<\/mn><\/mrow><\/math><\/span><\/span><\/span>ction of the time periods and make arbitrary purchasing decisions instead in the remaining <i>\u03b5<\/i>-fraction of the time periods. In this model, we develop a new robust online assortment optimization policy via an active-elimination strategy. We establish both upper and lower bounds on the regret, and we show that our policy is optimal up to a logarithmic factor in\u00a0<i>T<\/i>\u00a0when the assortment capacity is constant. We further develop a fully adaptive policy that does not require any prior knowledge of the contamination parameter\u00a0<i>\u03b5<\/i>. In the case of the existence of a suboptimality gap between optimal and suboptimal products, we also established gap-dependent logarithmic regret upper bounds and lower bounds in both the known-<i>\u03b5<\/i>\u00a0and unknown-<i>\u03b5<\/i>\u00a0cases. Our simulation study shows that our policy outperforms the existing policies based on upper confidence bounds and Thompson sampling.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We consider the dynamic assortment optimization problem under the multinomial logit model with unknown utility parameters. The main question investigated in this paper is model mis-specification under the\u00a0\u03b5-contamination model, which is a fundamental model in robust statistics and machine learning. In particular, throughout a selling horizon of length\u00a0T, we assume that customers make purchases according [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Operations 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