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While resilience and black-box offline-to-online reductions have been studied in single-objective settings, extending these ideas to bi-criteria problems introduces new challenges due to the coupled degradation of approximation guarantees for objectives and constraints. We introduce a notion of $(\\alpha,\\beta,\\delta,\\texttt{N})$-resilience for bi-criteria approximation algorithms, capturing how joint approximation guarantees degrade under bounded (possibly worst-case) oracle noise, and develop a general black-box framework that converts any resilient offline algorithm into an online algorithm for bi-criteria combinatorial multi-armed bandits with bandit feedback. The resulting online guarantees achieve sublinear regret and cumulative constraint violation of order $\\tilde{O}(\\delta^{2/3}\\texttt{N}^{1/3}T^{2/3})$ without requiring structural assumpt","title":"A Resilience Framework for Bi-Criteria Combinatorial Optimization with Bandit Feedback","url":"https://arxiv.org/abs/2503.12285","vendor":"arxiv_cs_ai"},"summary":"arXiv:2503.12285v2 Announce Type: replace-cross \nAbstract: We study bi-criteria combinatorial optimization under noisy function evaluations. While resilience and black-box offline-to-online reductions have been studied in single-objective settings, extending these ideas to bi-criteria problems introduces new challenges due to the coupled degradation of approximation guarantees for objectives and constraints. We introduce a notion of $(\\alpha,\\beta,\\delta,\\texttt{N})$-resilience for bi-criteria approximation algorithms, capturing how joint approximation guarantees degrade under bounded (possibly worst-case) oracle noise, and develop a general black-box framework that converts any resilient offline algorithm into an online algorithm for bi-criteria combinatorial multi-armed bandits with bandit feedback. 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