A Resilience Framework for Bi-Criteria Combinatorial Optimization with Bandit Feedback
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915990097362944 |
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| author | Aggarwal, Vaneet Jain, Shweta Pokhriyal, Subham Quinn, Christopher John |
| author_facet | Aggarwal, Vaneet Jain, Shweta Pokhriyal, Subham Quinn, Christopher John |
| contents | 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 $(α,β,δ,\texttt{N})$-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 $\tilde{O}(δ^{2/3}\texttt{N}^{1/3}T^{2/3})$ without requiring structural assumptions such as linearity, submodularity, or semi-bandit feedback on the noisy functions. We demonstrate the applicability of the framework by establishing resilience for several classical greedy algorithms in submodular optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Resilience Framework for Bi-Criteria Combinatorial Optimization with Bandit Feedback Aggarwal, Vaneet Jain, Shweta Pokhriyal, Subham Quinn, Christopher John Machine Learning Artificial Intelligence Computer Science and Game Theory Systems and Control 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 $(α,β,δ,\texttt{N})$-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 $\tilde{O}(δ^{2/3}\texttt{N}^{1/3}T^{2/3})$ without requiring structural assumptions such as linearity, submodularity, or semi-bandit feedback on the noisy functions. We demonstrate the applicability of the framework by establishing resilience for several classical greedy algorithms in submodular optimization. |
| title | A Resilience Framework for Bi-Criteria Combinatorial Optimization with Bandit Feedback |
| topic | Machine Learning Artificial Intelligence Computer Science and Game Theory Systems and Control |
| url | https://arxiv.org/abs/2503.12285 |