Byzantine-Resilient Distributed Optimization of Multi-Dimensional Functions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913252145889280 |
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| author | Kuwaranancharoen, Kananart Xin, Lei Sundaram, Shreyas |
| author_facet | Kuwaranancharoen, Kananart Xin, Lei Sundaram, Shreyas |
| contents | The problem of distributed optimization requires a group of agents to reach agreement on a parameter that minimizes the average of their local cost functions using information received from their neighbors. While there are a variety of distributed optimization algorithms that can solve this problem, they are typically vulnerable to malicious (or ``Byzantine'') agents that do not follow the algorithm. Recent attempts to address this issue focus on single dimensional functions, or provide analysis under certain assumptions on the statistical properties of the functions at the agents. In this paper, we propose a resilient distributed optimization algorithm for multi-dimensional convex functions. Our scheme involves two filtering steps at each iteration of the algorithm: (1) distance-based and (2) component-wise removal of extreme states. We show that this algorithm can mitigate the impact of up to $F$ Byzantine agents in the neighborhood of each regular node, without knowing the identities of the Byzantine agents in advance. In particular, we show that if the network topology satisfies certain conditions, all of the regular states are guaranteed to asymptotically converge to a bounded region that contains the global minimizer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_09038 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Byzantine-Resilient Distributed Optimization of Multi-Dimensional Functions Kuwaranancharoen, Kananart Xin, Lei Sundaram, Shreyas Optimization and Control Multiagent Systems 93A16 (Primary), 90C25, 68M15 (Secondary) C.2.4; G.1.6; B.4.5 The problem of distributed optimization requires a group of agents to reach agreement on a parameter that minimizes the average of their local cost functions using information received from their neighbors. While there are a variety of distributed optimization algorithms that can solve this problem, they are typically vulnerable to malicious (or ``Byzantine'') agents that do not follow the algorithm. Recent attempts to address this issue focus on single dimensional functions, or provide analysis under certain assumptions on the statistical properties of the functions at the agents. In this paper, we propose a resilient distributed optimization algorithm for multi-dimensional convex functions. Our scheme involves two filtering steps at each iteration of the algorithm: (1) distance-based and (2) component-wise removal of extreme states. We show that this algorithm can mitigate the impact of up to $F$ Byzantine agents in the neighborhood of each regular node, without knowing the identities of the Byzantine agents in advance. In particular, we show that if the network topology satisfies certain conditions, all of the regular states are guaranteed to asymptotically converge to a bounded region that contains the global minimizer. |
| title | Byzantine-Resilient Distributed Optimization of Multi-Dimensional Functions |
| topic | Optimization and Control Multiagent Systems 93A16 (Primary), 90C25, 68M15 (Secondary) C.2.4; G.1.6; B.4.5 |
| url | https://arxiv.org/abs/2003.09038 |