[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84459-en":3,"doc-seo-84459-105":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},84459,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782109480056885918",8,"Research & Report","Self-Creating Random Walks for Decentralized Learning under Pac-Man Attacks","Random walk (RW)-based algorithms are widely used in distributed systems for scalability, and increasingly in decentralized learning where each node relies on local interactions. This paper studies a stealth termination attack called “Pac-Man,” where a malicious node probabilistically terminates any RW that visits it, halting learning without triggering alarms. The CREATE-IF-LATE (CIL) algorithm enables fully decentralized self-creation of RWs to prevent extinction, guaranteeing non-extinction, bounded population, and convergence of RW-based stochastic gradient descent with quantifiable suboptimality. It also bounds learning interruption delay and is validated on synthetic and benchmark data.","Self-Creating Random Walks for Decentralized Learning under Pac-Man Attacks  \nXingran Chen∗ , Member, IEEE, Parimal Parag†, Senior Member, IEEE, Rohit Bhagat‡, Student Member, IEEE, Salim El Rouayheb‡, Senior Member, IEEE  \narXiv :2601 .07674v2 [ cs .MA] 12 Jul 2026  \nAbstract—Random walk (RW)-based algorithms have long been popular in distributed systems due to low overheads and scalability, with recent growing applications in decentralized learning. However, their reliance on local interactions makes them inherently vulnerable to malicious behavior. In this work, we investigate a termination-based attack, termed the “Pac-Man”attack, in which a malicious node probabilistically terminates any RW that visits it. This stealthy behavior gradually eliminates active RWs from the network, effectively halting the learning process without triggering failure alarms. To counter this threat, we propose the CREATE-IF-LATE (CIL) algorithm, which is a fully decentralized mechanism that is resilient to terminationbased Pac-Man attacks by enabling the self-creation of RWs and preventing RW extinction under such attacks. Our theoretical analysis shows that the CIL algorithm guarantees several desirable properties, such as (i) non-extinction of the RW population,(ii) almost sure boundedness of the RW population, and (iii) convergence of RW-based stochastic gradient descent even in the presence of Pac-Man with a quantifiable deviation from the true optimum. Moreover, the learning process experiences at most a linear time delay due to Pac-Man interruptions and RW regeneration. Our extensive empirical results on both synthetic and public benchmark datasets validate our theoretical findings.  \nI. INTRODUCTION  \nDecentralized algorithms are becoming increasingly important in modern large-scale networked applications. These algorithms enable a network of nodes/agents, each with access only to local data and a limited local view of the connection graph, to collaborate in solving global computational tasks without relying on centralized coordination. Among the most widely studied approaches are random-walk (RW)-based algorithms [1], [2] and gossip-based algorithms [3], [4] . RW-based algorithms operate by letting one or more tokens perform RWs over the graph; local updates are carried out only atthe nodes currently holding tokens 1. Gossip-based algorithms, by contrast, rely on frequent broadcast communication in the local neighborhood of the nodes where they exchange model snapshots and update locally based on received messages.  \nXingran Chen is with Engineering Systems and Design Pillar, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372 (E-mail: [xingranc@ieee.org](xingranc@ieee.org)).  \nRohit Bhagat, and Salim El Rouayheb are with Department of Electrical and Computer Engineering, Rutgers University, Piscataway Township, NJ 08854, USA (E-mail: {rb1395, [sye8}@scarletmail.rutgers.edu](sye8}@scarletmail.rutgers.edu)).  \nParimal Parag is with the Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India (E-mail: [parimal@iisc.ac.in](parimal@iisc.ac.in)).  \n1Throughout this paper, we use the terms “random walk” and “token”interchangeably.  \nWhile consensus-based methods are powerful, their repeated local broadcasts can lead to large communication overhead in large-scale systems [3], [4] . This motivates the study of RW-based algorithms, which offer a communication-efficient alternative for large networks due to their simplicity and scalability [1],[2] . By propagating information through tokens that traverse the network, RW-based algorithms require only local updates, no global coordination, and low communication overhead. These features have led to their successful application across a wide range of domains [5]–[9] . A particularly compelling application is decentralized machine learning, where RWs are used to aggregate learning on data distributed across networked","cbCaipfOlf4WBBg0","https://ap.wps.com/l/cbCaipfOlf4WBBg0","pdf",6774399,1,21,"English","en",105,"# Introduction\n## Random-walk and gossip approaches\n## Security vulnerabilities and the Pac-Man attack\n## CREATE-IF-LATE (CIL) and self-creation motivation","[{\"question\":\"What is the “Pac-Man” attack in decentralized learning?\",\"answer\":\"A Pac-Man node probabilistically terminates any random walk that visits it, causing active RWs to disappear and halting the learning process without triggering failure alarms.\"},{\"question\":\"How does the CREATE-IF-LATE (CIL) algorithm mitigate Pac-Man attacks?\",\"answer\":\"CIL is a fully decentralized mechanism that allows random walks to self-create and prevents RW extinction under termination-based attacks.\"},{\"question\":\"What theoretical guarantees does CIL provide?\",\"answer\":\"CIL guarantees non-extinction of the RW population, almost sure boundedness of the population, and convergence of RW-based stochastic gradient descent even with Pac-Man interruptions, with a quantifiable deviation from the true optimum.\"}]",1784195766,53,{"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},"self-creating-random-walks-for-decentralized-learning-under-pac-man-attacks","",{"@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/self-creating-random-walks-for-decentralized-learning-under-pac-man-attacks/84459/",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 is the “Pac-Man” attack in decentralized learning?","Question",{"text":75,"@type":76},"A Pac-Man node probabilistically terminates any random walk that visits it, causing active RWs to disappear and halting the learning process without triggering failure alarms.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the CREATE-IF-LATE (CIL) algorithm mitigate Pac-Man attacks?",{"text":80,"@type":76},"CIL is a fully decentralized mechanism that allows random walks to self-create and prevents RW extinction under termination-based attacks.",{"name":82,"@type":73,"acceptedAnswer":83},"What theoretical guarantees does CIL provide?",{"text":84,"@type":76},"CIL guarantees non-extinction of the RW population, almost sure boundedness of the population, and convergence of RW-based stochastic gradient descent even with Pac-Man interruptions, with a quantifiable deviation from the true 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