Byzantine Fault-Tolerant Min-Max Optimization
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866914680478367744 |
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| author | Liu, Shuo Vaidya, Nitin |
| author_facet | Liu, Shuo Vaidya, Nitin |
| contents | In this paper, we consider a min-max optimization problem under adversarial manipulation, where there are $n$ cost functions, up to $f$ of which may be replaced by arbitrary faulty functions by an adversary. The goal is to minimize the maximum cost over $x$ among the $n$ functions despite the faulty functions. The problem formulation could naturally extend to Byzantine fault-tolerant distributed min-max optimization.
We present a simple algorithm for Byzantine min-max optimization, and provide bounds on the output of the algorithm. We also present an approximate algorithm for this problem. We then extend the problem to a distributed setting and present a distributed algorithm. To the best of our knowledge, we are the first to consider this problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_14881 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Byzantine Fault-Tolerant Min-Max Optimization Liu, Shuo Vaidya, Nitin Distributed, Parallel, and Cluster Computing In this paper, we consider a min-max optimization problem under adversarial manipulation, where there are $n$ cost functions, up to $f$ of which may be replaced by arbitrary faulty functions by an adversary. The goal is to minimize the maximum cost over $x$ among the $n$ functions despite the faulty functions. The problem formulation could naturally extend to Byzantine fault-tolerant distributed min-max optimization. We present a simple algorithm for Byzantine min-max optimization, and provide bounds on the output of the algorithm. We also present an approximate algorithm for this problem. We then extend the problem to a distributed setting and present a distributed algorithm. To the best of our knowledge, we are the first to consider this problem. |
| title | Byzantine Fault-Tolerant Min-Max Optimization |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2205.14881 |