[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86443-en":3,"doc-seo-86443-105":30,"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86443,5909877438554,"Maeve","https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272",8,"Research & Report","Learning Predictive Ambiguity Sets for Decision-Focused Distributionally Robust Optimization","Predict-then-optimize pipelines often compress uncertainty into a point forecast and then solve a downstream optimization problem as if the forecast were reliable. Distributionally robust optimization (DRO) guards against misspecification, yet its ambiguity set is commonly tied to historical samples with a fixed Wasserstein radius. This work introduces learned predictive ambiguity sets (LPAS), where a deep contextual model produces a nominal scenario distribution and a state-dependent Wasserstein radius, optionally with an anisotropic metric, enabling adaptive robustness.","Learning Predictive Ambiguity Sets for Decision-Focused Distributionally Robust  \nOptimization  \nJunjie Guo  \nRutgers University  \n[jg1806@scarletmail.rutgers.edu](jg1806@scarletmail.rutgers.edu)  \narXiv :2607 .09820v 1 [ cs .LG] 10 Jul 2026  \nAbstract  \nPredict-then-optimize systems usually compress uncertainty into a point forecast and then solve a downstream optimization problem as if the forecast were reliable. Distributionally robust optimization (DRO) offers protection against misspecification, but the ambiguity set is often centered at historical samples and uses a fixed radius. We propose learned predictive ambiguity sets (LPAS): a deep contextual model outputs a finite nominal scenario distribution, a state-dependent Wasserstein radius, and optionally an anisotropic ground metric. These outputs define a contextual ambiguity set that feedsa DRO decision layer. The radius is trained by a combination of conditional quantile calibration, size regularization, and downstream decision loss, so that robustness is adaptive rather than globally fixed. We derive the finite dual form used by the decision layer, present a staged training algorithm, and evaluate the method on distributionally robust portfolio optimization with 20 S&P 500 constituents from 2018–2026 . The proposed method substantially improves over equal-weight, predict-then-optimize, and historical Wasserstein DRO baselines, achieving 26.28% annualized return, Sharpe ratio 1.30, final wealth 1.61, and lower tail loss than a deep fixed-radius DRO baseline while using a smaller average radius. The results show that learned ambiguity radii can recover most of the performance of strong fixed-radius DRO while reducing unnecessary conservatism and improving regime adaptivity.  \n1 Introduction  \nMany machine-learning decision systems are built around the pipeline  \nwhfutlioeuorereptzquimtianizstatiatyion,c,,ie1iswttcr,asdettecuofisrniso;annin uIninncpveertortntao(f1inory)-control, it represents demand; in network optimization, it may represent edge costs. This architecture is simple, but it over-trusts the predictive model. Errors that are small in prediction space can be large in decision space, especially when the optimizer amplifies mistakes along active constraints or high-sensitivity directions.  \nDRO replaces a single predictive distribution by an ambiguity set and optimizes against the worst plausible distribution. A common formulation is  \nmin  \nx∈X  \nsup EQ [ℓ(x,ξ)],  \nQ∈P  \n(2)  \nwhere ℓ is a downstream loss and P is an ambiguity set. Wasserstein DRO is attractive because it provides a geometry-aware way to perturb an empirical or nominal distribution and often admits tractable convex reformulations (Mohajerin Esfahani and Kuhn 2018; Gao and Kleywegt 2023; Blanchet and Murthy 2019; Kuhn et al. 2019) . However, the ambiguity set is commonly hand-designed: the center is a historical empirical distribution and the radius is a fixed scalar tuned by validation or statistical concentration. This can be mismatched in contextual environments. A radius that is safe in volatile periods can be too conservative in stable periods, while a radius tuned for average validation loss can fail under regime shift.  \nThis paper asks whether the ambiguity set itself can be predicted. Given context zt , a deep model outputs a finite nominal distribution  \nN  \nθ (· | zt ) = Xi=1 pθ,i (zt)δθ, i (zt) , (3)  \nplus a nonnegative radius ρϕ (zt) . These define the contextual Wasserstein ambiguity set  \nThe Pdθe,ϕciztio Qhen: WcocQpu,(b· y| )􀀁D≤ROρϕla(ztyer).oT. he k(4ey) modeling principle is that uncertainty should be both statistically calibrated and decision relevant: the radius should be large when the forecast is unreliable or the decision is sensitive to errors, and small when robustness mainly induces conservatism.  \nContributions. This work makes four contributions. First, it introduces learned predictive ambiguity sets, a contextual bridge between probabilistic deep forecasting and ","cbCaiogTmhK6TDPa","https://ap.wps.com/l/cbCaiogTmhK6TDPa","pdf",779683,3,1,7,"English","en",105,"# Abstract\n# Introduction\n# Related Work\n## Robust optimization and DRO\n## Decision-focused learning","[{\"question\":\"Why do predict-then-optimize systems struggle with uncertainty modeling?\",\"answer\":\"They usually rely on point forecasts and treat them as reliable, so small prediction errors can become large decision errors, especially along active constraints or sensitive directions.\"},{\"question\":\"What are learned predictive ambiguity sets (LPAS) in this paper?\",\"answer\":\"LPAS uses a deep contextual model to output a finite nominal scenario distribution plus a nonnegative, state-dependent Wasserstein radius (and optionally an anisotropic ground metric), forming a contextual ambiguity set for a DRO decision layer.\"},{\"question\":\"How is the ambiguity radius trained to balance robustness and conservatism?\",\"answer\":\"The radius is trained using a combination of conditional quantile calibration, size regularization, and downstream decision loss, so robustness adapts to forecast reliability and decision sensitivity rather than using a globally fixed radius.\"}]",1784211772,18,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"learning-predictive-ambiguity-sets-for-decision-focused-distributionally-robust-optimization","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/learning-predictive-ambiguity-sets-for-decision-focused-distributionally-robust-optimization/86443/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","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},"Why do predict-then-optimize systems struggle with uncertainty modeling?","Question",{"text":75,"@type":76},"They usually rely on point forecasts and treat them as reliable, so small prediction errors can become large decision errors, especially along active constraints or sensitive directions.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What are learned predictive ambiguity sets (LPAS) in this paper?",{"text":80,"@type":76},"LPAS uses a deep contextual model to output a finite nominal scenario distribution plus a nonnegative, state-dependent Wasserstein radius (and optionally an anisotropic ground metric), forming a contextual ambiguity set for a DRO decision layer.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the ambiguity radius trained to balance robustness and conservatism?",{"text":84,"@type":76},"The radius is trained using a combination of conditional quantile calibration, size regularization, and downstream decision loss, so robustness adapts to forecast 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