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Across prediction, generation, and decision-making, models with similar accuracy may diverge in transparency, interpretability, robustness, fairness, privacy, and certifiability. This survey explains how optimization- and certification-oriented reasoning creates a unified framework spanning training, auditing, and post-training certification tasks, synthesizing results at the CO–trustworthy ML intersection and highlighting global guarantees, formal certificates, and explicit trade-offs.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/trustworthy-machine-learning-through-the-lens-of-combinatorial-optimization-survey-and-research-perspectives/272518/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/trustworthy-machine-learning-through-the-lens-of-combinatorial-optimization-survey-and-research-perspectives/272518.png","ImageObject",300,407,{"name":92,"@type":93},"Stanley","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-23","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"Why is predictive accuracy insufficient for trustworthy machine learning?","Question",{"text":113,"@type":114},"Many real-world incidents show failures in transparency, fairness, security, and reliability, even when accuracy is comparable. Trustworthiness requires methods that address these dimensions directly.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the Rashomon effect influence trustworthy model choice?",{"text":118,"@type":114},"It indicates that multiple models can achieve near-identical performance while relying on different features or inductive biases. This enables selecting models that satisfy trustworthiness goals without sacrificing accuracy.",{"name":120,"@type":111,"acceptedAnswer":121},"What role does combinatorial optimization play in trustworthy ML?",{"text":122,"@type":114},"Combinatorial optimization provides a framework to cast trustworthiness questions with explicit objectives and constraints. It supports training and post-training tasks, offering global guarantees, formal certificates, and clearer trade-offs than purely heuristic approaches.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},272518,1790426949,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146,"preview_page_count":4},2336477405376,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","arXiv :2607 .07762v 1 [ cs .LG] 8 Jul 2026  \nTrustworthy Machine Learning through the Lens of Combinatorial Optimization: Survey and Research Perspectives  \nThibaut Vidal, Julien Ferry  \nCIRRELT & SCALE-AI Chair in Data-Driven Supply Chains, Department of Mathematics and Industrial Engineering, Polytechnique Montreal, Montreal, Canada [thibaut.vidal@polymtl.ca](thibaut.vidal@polymtl.ca)  \nAbstract. Modern machine learning (ML) increasingly relies on complex models whose behavior is difficult to characterize beyond empirical performance metrics. Across a wide range of tasks, including prediction, generation, and decision-making, models with similar empirical performance can exhibit markedly different properties in terms of their transparency, interpretability, robustness, fairness, privacy, and certifiability. This survey highlights how optimization- and certificationoriented reasoning can provide a useful framework for reasoning about such differences, supporting tasks ranging from model training and selection to auditing and certification. We review and synthesize recent advances at the intersection of combinatorial optimization (CO) and trustworthy ML, covering both training and post-training tasks, including interpretable model learning, explanation generation, robustness analysis, fairness auditing, model compression, and privacy attacks and protections. Across these domains, CO formulations offer additional capabilities over purely heuristic approaches, e.g., gradient-based ones, notably global guarantees, formal certificates, and explicit treatment of trade-offs. While scalability remains an important challenge, continued progress in solvers and hybrid algorithms suggests a growing role for CO in the design and deployment of trustworthy ML systems.  \nKeywords. Trustworthy machine learning; Combinatorial optimization; Explainability and interpretability; Robustness; Fairness; Privacy; Certification and auditing  \n1 Introduction  \nMachine learning (ML) has witnessed unprecedented progress over the past decade, rapidly becoming ubiquitous across domains where prediction, pattern recognition, content generation, and automated decision-making increasingly match or surpass human performance. Modern ML systems now underpin applications ranging from computer vision and natural language processing to credit scoring, medical diagnosis, recommender systems, supply chain optimization, transportation, and autonomous systems. In many of these settings, ML models no longer merely assist human judgment but directly inform or automate high-stakes decisions.  \nAt the same time, the deployment of ML in consequential contexts has made it increasingly clear that predictive accuracy alone is insufficient. A growing number of incidents have revealed systematic shortcomings in the design, evaluation, and deployment of ML systems. These include biased or arbitrary decisions (e.g., recidivism prediction tools that are opaque and no more accurate or fair than non-expert human judgment; Dressel and Farid 2018; or recruitment tools found to discriminate on the basis of age; EEOC 2022), security and reliability failures (e.g., coding assistants causing catastrophic data loss; Nolan 2025), and, in extreme cases, harmful interactions with users (language models assisting suicide or encouraging delusional behavior; Hill 2025a,b) . These risks are further amplified as decision and action capabilities are increasingly delegated to autonomous agents operating with limited human oversight.  \nAll these examples point in the same direction: the responsible use of ML requires methodological tools that go well beyond training or fine-tuning models on available data. Ensuring that ML systems are trustworthy (transparent, explainable, robust, fair, and privacy-preserving) has therefore emerged as a formidable challenge for the coming decades. Importantly, technical approaches to trustworthiness are not optional refinements or post hoc fixes; they fundamentally sh","cbCaifwFSbRaiI7v","https://ap.wps.com/l/cbCaifwFSbRaiI7v","pdf",538589,67,"English","# Introduction\n## Trustworthiness as more than accuracy\n## The Rashomon effect and model selection\n## Why combinatorial optimization matters\n## Scope of training and post-training tasks","[{\"question\":\"Why is predictive accuracy insufficient for trustworthy machine learning?\",\"answer\":\"Many real-world incidents show failures in transparency, fairness, security, and reliability, even when accuracy is comparable. Trustworthiness requires methods that address these dimensions directly.\"},{\"question\":\"How does the Rashomon effect influence trustworthy model choice?\",\"answer\":\"It indicates that multiple models can achieve near-identical performance while relying on different features or inductive biases. This enables selecting models that satisfy trustworthiness goals without sacrificing accuracy.\"},{\"question\":\"What role does combinatorial optimization play in trustworthy ML?\",\"answer\":\"Combinatorial optimization provides a framework to cast trustworthiness questions with explicit objectives and constraints. It supports training and post-training tasks, offering global guarantees, formal certificates, and clearer trade-offs than purely heuristic approaches.\"}]","Trustworthy Machine Learning through the Lens of Combinatorial Optimization - Survey and Research Perspectives | PDF",1789465719,169]