Youming Tao , Xiuzhen Cheng , Falko Dressler , Zhipeng Cai , Dongxiao Yu
{"title":"鲁棒阵强盗优化:对抗性污染下的接近最优率","authors":"Youming Tao , Xiuzhen Cheng , Falko Dressler , Zhipeng Cai , Dongxiao Yu","doi":"10.1016/j.tcs.2025.115416","DOIUrl":null,"url":null,"abstract":"<div><div>We study the matroid bandit optimization problem, a fundamental and broadly applicable framework for combinatorial multi-armed bandits where the action space is constrained by a matroid. In particular, we address the challenge of designing algorithms that remain effective under adversarial contamination of feedback rewards, which may severely degrade performance or even mislead existing methods. Our main contribution is an efficient and robust algorithm named <span>ROMM</span>, which builds upon the principle of optimistic matroid maximization and leverages robust statistical estimators to assess base arm quality in polynomial time. Under the <em>ϵ</em>-contamination model, we establish lower bounds and prove that <span>ROMM</span> achieves near-optimal regret guarantees up to polylogarithmic factors. Our analysis further reveals a sharp phase transition between the low and high contamination regimes. Notably, <span>ROMM</span> can tolerate up to a universal constant fraction of corrupted feedback, which is optimal under mild conditions. Finally, we validate our theoretical findings with numerical experiments that demonstrate the effectiveness of the proposed method.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1051 ","pages":"Article 115416"},"PeriodicalIF":1.0000,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Robust matroid bandit optimization: Near-optimal rates under adversarial contamination\",\"authors\":\"Youming Tao , Xiuzhen Cheng , Falko Dressler , Zhipeng Cai , Dongxiao Yu\",\"doi\":\"10.1016/j.tcs.2025.115416\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We study the matroid bandit optimization problem, a fundamental and broadly applicable framework for combinatorial multi-armed bandits where the action space is constrained by a matroid. In particular, we address the challenge of designing algorithms that remain effective under adversarial contamination of feedback rewards, which may severely degrade performance or even mislead existing methods. Our main contribution is an efficient and robust algorithm named <span>ROMM</span>, which builds upon the principle of optimistic matroid maximization and leverages robust statistical estimators to assess base arm quality in polynomial time. Under the <em>ϵ</em>-contamination model, we establish lower bounds and prove that <span>ROMM</span> achieves near-optimal regret guarantees up to polylogarithmic factors. Our analysis further reveals a sharp phase transition between the low and high contamination regimes. Notably, <span>ROMM</span> can tolerate up to a universal constant fraction of corrupted feedback, which is optimal under mild conditions. Finally, we validate our theoretical findings with numerical experiments that demonstrate the effectiveness of the proposed method.</div></div>\",\"PeriodicalId\":49438,\"journal\":{\"name\":\"Theoretical Computer Science\",\"volume\":\"1051 \",\"pages\":\"Article 115416\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-06-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical Computer Science\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0304397525003548\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Computer Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304397525003548","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Robust matroid bandit optimization: Near-optimal rates under adversarial contamination
We study the matroid bandit optimization problem, a fundamental and broadly applicable framework for combinatorial multi-armed bandits where the action space is constrained by a matroid. In particular, we address the challenge of designing algorithms that remain effective under adversarial contamination of feedback rewards, which may severely degrade performance or even mislead existing methods. Our main contribution is an efficient and robust algorithm named ROMM, which builds upon the principle of optimistic matroid maximization and leverages robust statistical estimators to assess base arm quality in polynomial time. Under the ϵ-contamination model, we establish lower bounds and prove that ROMM achieves near-optimal regret guarantees up to polylogarithmic factors. Our analysis further reveals a sharp phase transition between the low and high contamination regimes. Notably, ROMM can tolerate up to a universal constant fraction of corrupted feedback, which is optimal under mild conditions. Finally, we validate our theoretical findings with numerical experiments that demonstrate the effectiveness of the proposed method.
期刊介绍:
Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.