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However, existing methods often require heuristic adjustments based on domain knowledge and are primarily developed for binary treatments. This paper presents Gaussianized Design Optimization, a novel framework for optimally balancing covariates in experimental design. The core idea is to Gaussianize the treatment assignments: we model treatments as transformations of random variables drawn from a multivariate Gaussian distribution and convert the design problem into a nonlinear continuous optimization over Gaussian covariance matrices. Compared to existing methods, our approach offers significant flexibility in optimizing covariate balance across a diverse range of designs and covariate types. Adapting the Burer\u2013Monteiro approach for solving semidefinite programmes, we introduce first-order local algorithms for optimizing covariate balance, improving upon several widely used designs. Furthermore, we develop inferential procedures for constructing design-based confidence intervals under Gaussianization and extend the framework to accommodate continuous treatments. Simulations demonstrate the effectiveness of Gaussianization in multiple practical scenarios.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkag067","type":"journal-article","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T11:54:40Z","timestamp":1775649280000},"source":"Crossref","is-referenced-by-count":0,"title":["Gaussianized design optimization for covariate balance in randomized experiments"],"prefix":"10.1093","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-0038-2272","authenticated-orcid":false,"given":"Wenxuan","family":"Guo","sequence":"first","affiliation":[{"name":"Booth School of Business, The University of Chicago , Chicago, IL 60637 ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6202-9605","authenticated-orcid":false,"given":"Tengyuan","family":"Liang","sequence":"additional","affiliation":[{"name":"Booth School of Business, The University of Chicago , Chicago, IL 60637 ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0061-9984","authenticated-orcid":false,"given":"Panos","family":"Toulis","sequence":"additional","affiliation":[{"name":"Booth School of Business, The University of Chicago , Chicago, IL 60637 ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2026,4,22]]},"reference":[{"key":"2026042218310501600_qkag067-B1","first-page":"90","volume-title":"Essays in the theory of risk-bearing","author":"Arrow","year":"1971"},{"issue":"1","key":"2026042218310501600_qkag067-B2","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1093\/biomet\/69.1.61","article-title":"Optimum biased coin designs for sequential clinical trials with prognostic factors","volume":"69","author":"Atkinson","year":"1982","journal-title":"Biometrika"},{"issue":"12","key":"2026042218310501600_qkag067-B3","doi-asserted-by":"publisher","first-page":"3911","DOI":"10.1257\/aer.20201856","article-title":"Optimality of matched-pair designs in randomized controlled trials","volume":"112","author":"Bai","year":"2022","journal-title":"American Economic Review"},{"issue":"2","key":"2026042218310501600_qkag067-B4","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1016\/j.jeconom.2021.10.009","article-title":"Why randomize? 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