{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,12,24]],"date-time":"2024-12-24T05:04:13Z","timestamp":1735016653797,"version":"3.32.0"},"reference-count":53,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2023,3,16]],"date-time":"2023-03-16T00:00:00Z","timestamp":1678924800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:p>We consider a sequential treatment problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision-maker targets the treatment which maximizes a general <jats:italic>functional<\/jats:italic> of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socioeconomic functional such as an inequality, welfare, or poverty measure. We develop expected regret lower bounds for this problem and construct a near minimax optimal sequential assignment policy.<\/jats:p>","DOI":"10.1017\/s0266466623000051","type":"journal-article","created":{"date-parts":[[2023,3,16]],"date-time":"2023-03-16T05:54:34Z","timestamp":1678946074000},"page":"1211-1252","source":"Crossref","is-referenced-by-count":0,"title":["FUNCTIONAL SEQUENTIAL TREATMENT ALLOCATION WITH COVARIATES"],"prefix":"10.1017","volume":"40","author":[{"given":"Anders Bredahl","family":"Kock","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Preinerstorfer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bezirgen","family":"Veliyev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2023,3,16]]},"reference":[{"key":"S0266466623000051_r48","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1109\/JSTSP.2016.2592622","article-title":"Risk-averse multi-armed bandit problems under mean-variance measure","volume":"10","author":"Vakili","year":"2016","journal-title":"IEEE Journal of Selected Topics in Signal Processing"},{"key":"S0266466623000051_r53","unstructured":"Zimin, A. , Ibsen-Jensen, R. , & Chatterjee, K. (2014) Generalized risk-aversion in stochastic multi-armed bandits. Preprint, arXiv:1405.0833."},{"key":"S0266466623000051_r5","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1257\/aer.96.4.988","article-title":"What mean impacts miss: Distributional effects of welfare reform experiments","volume":"96","author":"Bitler","year":"2006","journal-title":"American Economic Review"},{"key":"S0266466623000051_r23","unstructured":"Ma, X. , Zhang, Q. , Xia, L. , Zhou, Z. , Yang, J. , & Zhao, Q. (2020) Distributional soft actor critic for risk sensitive learning. Preprint, arXiv:2004.14547."},{"key":"S0266466623000051_r20","unstructured":"Kock, A.B. & Thyrsgaard, M. (2018) Optimal sequential treatment allocation. Preprint, arXiv:1705.09952."},{"key":"S0266466623000051_r19","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1080\/01621459.2020.1851236","article-title":"Functional sequential treatment allocation","volume":"117","author":"Kock","year":"2022","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466623000051_r29","doi-asserted-by":"crossref","first-page":"647","DOI":"10.2307\/1913469","article-title":"Some generalized functions for the size distribution of income","volume":"52","author":"McDonald","year":"1984","journal-title":"Econometrica"},{"key":"S0266466623000051_r6","unstructured":"Cassel, A. , Mannor, S. , & Zeevi, A. (2018) A general approach to multi-armed bandits under risk criteria. In S. Bubeck, V. Perchet, & P. Rigollet (eds.), Proceedings of the 31st Conference on Learning Theory, vol. 75, pp. 1295\u20131306. PMLR."},{"key":"S0266466623000051_r26","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1111\/j.1468-0262.2004.00530.x","article-title":"Statistical treatment rules for heterogeneous populations","volume":"72","author":"Manski","year":"2004","journal-title":"Econometrica"},{"key":"S0266466623000051_r28","doi-asserted-by":"crossref","first-page":"10518","DOI":"10.1073\/pnas.1612174113","article-title":"Sufficient trial size to inform clinical practice","volume":"113","author":"Manski","year":"2016","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"S0266466623000051_r47","doi-asserted-by":"crossref","unstructured":"Vakili, S. , Boukouvalas, A. , & Zhao, Q. (2019) Decision variance in online learning. Preprint, arXiv:1807.09089.","DOI":"10.1109\/CDC40024.2019.9029461"},{"key":"S0266466623000051_r13","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.3982\/ECTA6630","article-title":"Asymptotics for statistical treatment rules","volume":"77","author":"Hirano","year":"2009","journal-title":"Econometrica"},{"key":"S0266466623000051_r2","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1214\/009053606000001217","article-title":"Fast learning rates for plug-in classifiers","volume":"35","author":"Audibert","year":"2007","journal-title":"Annals of Statistics"},{"key":"S0266466623000051_r49","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1080\/01621459.1979.10481033","article-title":"A one-armed bandit problem with a concomitant variable","volume":"74","author":"Woodroofe","year":"1979","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466623000051_r50","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1214\/aos\/1015362186","article-title":"Randomized allocation with nonparametric estimation for a multi-armed bandit problem with covariates","volume":"30","author":"Yang","year":"2002","journal-title":"Annals of Statistics"},{"key":"S0266466623000051_r10","doi-asserted-by":"crossref","first-page":"847","DOI":"10.3982\/ECTA16591","article-title":"Understanding doctor decision making: The case of depression treatment","volume":"88","author":"Currie","year":"2020","journal-title":"Econometrica"},{"key":"S0266466623000051_r32","unstructured":"Rigollet, P. & Zeevi, A. (2010) Nonparametric bandits with covariates. In: In A.T. Kalai & M. Mohri (eds.), Proceedings title: 23rd Annual Conference on Learning Theory, pp. 54\u201366. Omnipress."},{"volume-title":"Real Analysis: Modern Techniques and Their Applications","year":"1999","author":"Folland","key":"S0266466623000051_r12"},{"key":"S0266466623000051_r25","doi-asserted-by":"crossref","first-page":"1808","DOI":"10.1214\/aos\/1017939240","article-title":"Smooth discrimination analysis","volume":"27","author":"Mammen","year":"1999","journal-title":"Annals of Statistics"},{"key":"S0266466623000051_r52","first-page":"3331","volume-title":"International Conference on Artificial Intelligence and Statistics","author":"Zhou","year":"2021b"},{"key":"S0266466623000051_r9","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:osobl\/9780199594030.001.0001","volume-title":"Measuring Inequality","author":"Cowell","year":"2011"},{"key":"S0266466623000051_r4","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.jeconom.2011.11.007","article-title":"Inferring welfare maximizing treatment assignment under budget constraints","volume":"167","author":"Bhattacharya","year":"2012","journal-title":"Journal of Econometrics"},{"key":"S0266466623000051_r35","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/0047-2727(74)90006-1","article-title":"Informational bases of alternative welfare approaches: Aggregation and income distribution","volume":"3","author":"Sen","year":"1974","journal-title":"Journal of Public Economics"},{"key":"S0266466623000051_r51","doi-asserted-by":"crossref","unstructured":"Zhou, Z. , Athey, S. , & Wager, S. (2022) Offline multi-action policy learning: Generalization and optimization. Operations Research 71, 148\u2013183.","DOI":"10.1287\/opre.2022.2271"},{"key":"S0266466623000051_r17","doi-asserted-by":"crossref","first-page":"591","DOI":"10.3982\/ECTA13288","article-title":"Who should be treated? Empirical welfare maximization methods for treatment choice","volume":"86","author":"Kitagawa","year":"2018","journal-title":"Econometrica"},{"key":"S0266466623000051_r24","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1007\/978-3-642-40935-6_16","volume-title":"Algorithmic Learning Theory","author":"Maillard","year":"2013"},{"key":"S0266466623000051_r1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.3982\/ECTA15732","article-title":"Policy learning with observational data","volume":"89","author":"Athey","year":"2021","journal-title":"Econometrica"},{"key":"S0266466623000051_r37","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1561\/2200000018","article-title":"Online learning and online convex optimization","volume":"4","author":"Shalev-Shwartz","year":"2012","journal-title":"Foundations and Trends\u00ae in Machine Learning"},{"key":"S0266466623000051_r16","doi-asserted-by":"crossref","first-page":"113","DOI":"10.3982\/ECTA17527","article-title":"Adaptive treatment assignment in experiments for policy choice","volume":"89","author":"Kasy","year":"2021","journal-title":"Econometrica"},{"key":"S0266466623000051_r34","first-page":"3275","volume-title":"Advances in Neural Information Processing Systems 25","author":"Sani","year":"2012"},{"key":"S0266466623000051_r45","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1214\/aos\/1079120131","article-title":"Optimal aggregation of classifiers in statistical learning","volume":"32","author":"Tsybakov","year":"2004","journal-title":"Annals of Statistics"},{"key":"S0266466623000051_r46","doi-asserted-by":"crossref","DOI":"10.1007\/b13794","volume-title":"Introduction to Nonparametric Estimation","author":"Tsybakov","year":"2009"},{"key":"S0266466623000051_r41","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.jeconom.2011.06.012","article-title":"Minimax regret treatment choice with covariates or with limited validity of experiments","volume":"166","author":"Stoye","year":"2012","journal-title":"Journal of Econometrics"},{"key":"S0266466623000051_r7","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-79253-8","volume-title":"Inequality, Polarization and Poverty","author":"Chakravarty","year":"2009"},{"key":"S0266466623000051_r30","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/978-0-387-72796-7_8","volume-title":"Modeling Income Distributions and Lorenz Curves","author":"McDonald","year":"2008"},{"key":"S0266466623000051_r8","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/S0304-4076(99)00039-1","article-title":"Econometrics and decision theory","volume":"95","author":"Chamberlain","year":"2000","journal-title":"Journal of Econometrics"},{"key":"S0266466623000051_r3","unstructured":"Besson, L. & Kaufmann, E. (2018) What doubling tricks can and can\u2019t do for multi-armed bandits. Preprint, arXiv:1803.06971."},{"key":"S0266466623000051_r31","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1214\/13-AOS1101","article-title":"The multi-armed bandit problem with covariates","volume":"41","author":"Perchet","year":"2013","journal-title":"Annals of Statistics"},{"key":"S0266466623000051_r36","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1214\/aos\/1176346393","article-title":"Generalized L-, M-, and R-statistics","volume":"12","author":"Serfling","year":"1984","journal-title":"Annals of Statistics"},{"key":"S0266466623000051_r39","unstructured":"Si, N. , Zhang, F. , Zhou, Z. , & Blanchet, J. (2020a) Distributional robust batch contextual bandits. Preprint, arXiv:2006.05630."},{"volume-title":"The Distribution and Redistribution of Income","year":"2001","author":"Lambert","key":"S0266466623000051_r21"},{"key":"S0266466623000051_r11","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.jeconom.2004.04.006","article-title":"Program evaluation as a decision problem","volume":"125","author":"Dehejia","year":"2005","journal-title":"Journal of Econometrics"},{"key":"S0266466623000051_r14","doi-asserted-by":"crossref","unstructured":"Hirano, K. & Porter, J.R. (2020) Asymptotic analysis of statistical decision rules in econometrics. In S.N. Durlauf, L. Peter Hansen, J.J. Heckman, & R.L. Matzkin (eds.), Handbook of Econometrics, vol. 7A, pp. 283\u2013354. Elsevier.","DOI":"10.1016\/bs.hoe.2020.09.001"},{"key":"S0266466623000051_r27","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1080\/00031305.2018.1513377","article-title":"Treatment choice with trial data: Statistical decision theory should supplant hypothesis testing","volume":"73","author":"Manski","year":"2019","journal-title":"American Statistician"},{"key":"S0266466623000051_r38","first-page":"8884","volume-title":"International Conference on Machine Learning","author":"Si","year":"2020b"},{"key":"S0266466623000051_r18","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1080\/07350015.2019.1688664","article-title":"Equality-minded treatment choice","volume":"39","author":"Kitagawa","year":"2019","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466623000051_r40","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.jeconom.2009.02.013","article-title":"Minimax regret treatment choice with finite samples","volume":"151","author":"Stoye","year":"2009","journal-title":"Journal of Econometrics"},{"key":"S0266466623000051_r42","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.jeconom.2011.06.013","article-title":"Statistical treatment choice based on asymmetric minimax regret criteria","volume":"166","author":"Tetenov","year":"2012","journal-title":"Journal of Econometrics"},{"key":"S0266466623000051_r43","first-page":"261","article-title":"Analyzing the American income distribution","volume":"60","author":"Thurow","year":"1970","journal-title":"American Economic Review"},{"volume-title":"Statistical Decision Theory","year":"2008","author":"Liese","key":"S0266466623000051_r22"},{"key":"S0266466623000051_r33","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1111\/j.1467-937X.2009.00564.x","article-title":"Quantile maximization in decision theory","volume":"77","author":"Rostek","year":"2010","journal-title":"Review of Economic Studies"},{"volume-title":"Foundations of Modern Probability","year":"2001","author":"Kallenberg","key":"S0266466623000051_r15"},{"key":"S0266466623000051_r44","unstructured":"Tran-Thanh, L. & Yu, J.Y. (2014) Functional bandits. Preprint, arXiv:1405.2432."}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466623000051","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T06:31:55Z","timestamp":1734935515000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466623000051\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,16]]},"references-count":53,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["S0266466623000051"],"URL":"https:\/\/doi.org\/10.1017\/s0266466623000051","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"type":"print","value":"0266-4666"},{"type":"electronic","value":"1469-4360"}],"subject":[],"published":{"date-parts":[[2023,3,16]]}}}