[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83982-en":3,"doc-seo-83982-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},83982,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Safe Bayesian Optimization with Counterfactual Policies","Safe decision-making often requires that new actions not reduce outcomes below an established threshold relative to a baseline standard of care. Safe Bayesian optimization maximizes an objective under safety constraints, but baseline safety depends on counterfactual outcomes that are unobserved and must be estimated. This work uses conformal prediction to build valid uncertainty intervals for counterfactual baseline outcomes and integrates them into safe Bayesian optimization to enforce constraint violations at a user-specified rate. It also adapts to covariate shift, with a safety proof, experiments, and sensitivity analysis.","Safe Bayesian Optimization with Counterfactual Policies  \nKatherine Avery  \nCollege of Computer Science University of Massachusetts Amherst Amherst, MA 01002 [kavery@cs.umass.edu](kavery@cs.umass.edu)  \nBruno Castro da Silva  \nCollege of Computer Science University of Massachusetts Amherst Amherst, MA 01002 [bsilva@cs.umass.edu](bsilva@cs.umass.edu)  \narXiv :2607 .05620v 1 [ cs .LG] 6 Jul 2026  \nDavid Jensen  \nCollege of Computer Science  \nUniversity of Massachusetts Amherst  \nAmherst, MA 01002  \n[jensen@cs.umass.edu](jensen@cs.umass.edu)  \nAbstract  \nIn many decision-making settings, new interventions are acceptable only if they do not reduce outcomes below some established threshold. For example, in clinical medicine, new treatments are often acceptable only if they do not worsen outcomes relative to an established standard of care. Safe Bayesian optimization maximizesan objective subject to safety constraints. In the setting that we consider here, safety is defined relative to a known baseline policy whose outcomes are counterfactual and therefore unobserved. Thus, the counterfactual outcomes of the baseline policy must be estimated and those (uncertain) estimates must be used to safely optimize the objective. We address this estimation problem by using conformal prediction to construct valid uncertainty intervals for counterfactual baseline outcomes, and we show how these intervals can be integrated into safe Bayesian optimization to ensure that constraint violations occur at or below a user-specified rate. We also show how to adapt these conformal estimates to different kinds of covariate shift.  \nWe provide a safety proof, experimental evidence, and a sensitivity analysis.  \n1 Introduction  \nIn many sequential decision-making problems, we seek to improve performance while ensuring that each action is safe. We may define safety in absolute terms, such as keeping blood pressure below a threshold, but we may instead define it relative to an established baseline. For example, when determining the effectiveness of a new drug for cancer treatment, we may not want patients’ quality of life to be substantially worse than it would have been under the pre-existing standard of care. This type of safety constraint is challenging since the patients’ quality of life when taking the standard drug is not observed and can only be estimated.  \nWe frame this problem using the framework of safe Bayesian optimization (SafeOpt), 1 which optimizes some objective function f(x), such as information gain, with respect to some constraint:  \nmax f(x) s.t. q (x) ≥ 0. (1)  \nx∈X  \n1 SafeOpt sometimes refers to the specific method proposed in Sui et al. [2015] and sometimes refers to safe Bayesian optimization in general. In this work, it refers to the latter.  \nPreprint.  \nSafeOpt optimizes the objective within a set of safe states S (where X ⊆ S) and expands S as more information is gathered. We focus specifically on SafeOpt with online conformal prediction [Zhang et al., 2024], which provides distribution-free safety guarantees. Conformal SafeOpt ensures that the rate that q(x) ≥ 0 is violated over T optimization steps is at or below α, where α is user-specified. See Sec. 3.1.  \nPotential safe x values are typically determined based on the values of q that have been seen so far. However, we are interested in safety constraints that contain counterfactuals. For example, we may want the value of a variable Y under a treatment minus the counterfactual Y under a standard-of-care treatment to be at least some value −ω . Because q depends on a counterfactual that is not observed, it is difficult to provide typical SafeOpt-style safety guarantees. Simply making a point estimate of the counterfactual can result in a violate rate above α .  \nTherefore, we use split conformal prediction to estimate the outcome of the counterfactual x under a standard of care [Lei and Candès, 2021] . Split conformal prediction creates interval estimates, rather than point esti","cbCaigyOWrsdiBEn","https://ap.wps.com/l/cbCaigyOWrsdiBEn","pdf",1271998,1,20,"English","en",105,"# Abstract\n# Introduction\n## Motivating example","[{\"question\":\"What problem does Safe Bayesian Optimization with counterfactual policies address?\",\"answer\":\"It addresses safe sequential decision-making when safety must be measured relative to a baseline policy, but the baseline counterfactual outcomes are unobserved and must be estimated.\"},{\"question\":\"How does the method estimate uncertain counterfactual baseline outcomes?\",\"answer\":\"It uses conformal prediction to construct distribution-free uncertainty intervals for the counterfactual outcomes rather than relying on point estimates.\"},{\"question\":\"How are safety guarantees enforced during optimization?\",\"answer\":\"The conformal uncertainty intervals are integrated into safe Bayesian optimization so that constraint violation rates occur at or below a user-specified level. The paper also provides a safety proof, experimental evidence, and sensitivity analysis.\"}]",1784191843,50,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"safe-bayesian-optimization-with-counterfactual-policies","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/safe-bayesian-optimization-with-counterfactual-policies/83982/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does Safe Bayesian Optimization with counterfactual policies address?","Question",{"text":75,"@type":76},"It addresses safe sequential decision-making when safety must be measured relative to a baseline policy, but the baseline counterfactual outcomes are unobserved and must be estimated.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the method estimate uncertain counterfactual baseline outcomes?",{"text":80,"@type":76},"It uses conformal prediction to construct distribution-free uncertainty intervals for the counterfactual outcomes rather than relying on point estimates.",{"name":82,"@type":73,"acceptedAnswer":83},"How are safety guarantees enforced during optimization?",{"text":84,"@type":76},"The conformal uncertainty intervals are integrated into safe Bayesian optimization so that constraint violation rates occur at or below a user-specified level. 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