[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83508-en":3,"doc-seo-83508-105":29,"detail-sidebar-cat-0-en-105":83},{"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},83508,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Decision-focused Sparse Tangent Portfolio Optimization","Sparse tangent portfolio optimization targets an interpretable low-cardinality portfolio aligned with the tangency direction of the mean-variance frontier, but the cardinality-constrained formulation is NP-hard and common predict-then-optimize methods can misalign forecasting quality with realized portfolio performance. The work introduces an end-to-end decision-focused learning framework using a DPP-compliant convex programming layer and a smooth top-k operator to enforce exact cardinality k. Experiments across four equity markets show competitive, often superior out-of-sample Sharpe ratios versus baseline approaches, with stronger gains for larger universes.","Decision-focused Sparse Tangent Portfolio Optimization  \nHaeun Jeon * 1 Seunghoon Choi * 1 Hyunglip Bae 2 Yongjae Lee 3 Woo Chang Kim 1  \narXiv :2607 .0058 1v 1 [ cs .LG] 1 Jul 2026  \nAbstract  \nSparse tangent portfolio optimization aims to learn an interpretable, low-cardinality portfolio in the tangency direction of the mean-variance frontier. However, the associated cardinalityconstrained formulation is NP-hard, and standard predict-then-optimize pipelines often misalign forecasting accuracy with downstream portfolio quality. We propose an end-to-end decisionfocused learning framework that reformulates Sharpe ratio maximization as a Disciplined Parametrized Programming (DPP)-compliant convex programming layer and replaces discrete selection with a smooth top-k operator enforcing an exact cardinality k. This enables gradient flow through prediction, asset selection, and re-optimization, allowing the predictive model to directly optimize portfolio performance.  \nAcross four major equity markets, our method achieves competitive and often superior out-ofsample Sharpe ratios compared with historical and prediction-focused baselines, with particularly strong gains in larger asset universes. Our code is publicly available.  \n1. Introduction  \nOriginating from Markowitz’s mean-variance model (Markowitz, 1952), modern portfolio theory views investment decisions through the lens of balancing risk and return at the portfolio level, rather than evaluating assets in isolation (Kim et al., 2021) . By combining assets with heterogeneous  risk-return characteristics, investors can con-  \n*Equal contribution 1Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea 2Department of Big Data Convergence, and Bigdata Research Lab, Chonnam National University, Gwangju, Republic of Korea 3Department of Industrial Engineering, Ulsan National Institute of Science and Technology, Ulsan, Republic of Korea. Correspondence to: Yongjae Lee \u003Cyong[jaelee@unist.ac.kr](jaelee@unist.ac.kr) >, Woo Chang Kim \u003C[wkim@kaist.ac.kr](wkim@kaist.ac.kr) >.  \nProceedings of the 43 rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026 . Copyright 2026 by the author(s) .  \nstruct diversified portfolios that deliver lower variance fora given level of expected return. This principle is formalized through the efficient frontier and performance measures such as the Sharpe ratio, which captures the trade-off between excess return and portfolio volatility (Sharpe, 1966) . Although diversification is appealing in theory, holding too many assets is often impractical, as it raises monitoring and transaction costs and makes the portfolio harder to interpret (Woodside-Oriakhi, 2011) .  \nFor these practical reasons, portfolio managers often favor sparse allocations that concentrate exposure on a limited number of assets. A standard way to formalize this preference is through a cardinality constraint, which limits the number of nonzero positions. Enforcing such sparsity, however, introduces a fundamental tension: while restricting the number of holdings improves interpretability and reduces transaction costs, it turns portfolio construction into a challenging combinatorial problem. As a result, existing approaches must balance solution quality, computational efficiency, and flexibility under varying cardinality levels. Recently, heuristic pipelines that decouple asset selection from re-optimization have shown promise as practical tools for constructing sparse tangent portfolios, offering a favorable balance between solution quality and scalability. However, these pipelines still rely on upstream forecasts produced by a separate predictive model, and their effectiveness ultimately depends on the end-to-end interaction between prediction, discrete selection, and continuous re-optimization.  \nEven with strong heuristics for sparse optimization, a persistent disconnect remains between pr","cbCaiqCYFDujZiTR","https://ap.wps.com/l/cbCaiqCYFDujZiTR","pdf",4523108,1,18,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"How does the method perform on real markets?\",\"answer\":\"Across four major equity markets, it achieves competitive and often superior out-of-sample Sharpe ratios compared with historical and prediction-focused baselines, with larger improvements when the asset universe is bigger.\"}]",1784188523,45,{"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":78,"head_meta":80,"extra_data":82,"updated_unix":27},"decision-focused-sparse-tangent-portfolio-optimization","",{"@graph":35,"@context":77},[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/decision-focused-sparse-tangent-portfolio-optimization/83508/",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],{"name":72,"@type":73,"acceptedAnswer":74},"How does the method perform on real markets?","Question",{"text":75,"@type":76},"Across four major equity markets, it achieves competitive and often superior out-of-sample Sharpe ratios compared with historical and prediction-focused baselines, with larger improvements when the asset universe is bigger.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":45,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":45,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":45,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":45,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]