作者：
Qu, ZhihaiLi, XiuxianLi, LiYi, XinleiTongji Univ
Shanghai Res Inst Intelligent Autonomous Syst Coll Elect & Informat Engn Dept Control Sci & Engn Shanghai 201804 Peoples R China Tongji Univ
Shanghai Inst Intelligent Sci & Technol Shanghai 201804 Peoples R China MIT
Lab Informat & Decis Syst Cambridge MA USA
Existing algorithms in onlineoptimization usually rely on trustful information, e.g., reliable knowledge of gradients, which makes them vulnerable to attacks. To take into account the security issue in online optimiz...
详细信息
Existing algorithms in onlineoptimization usually rely on trustful information, e.g., reliable knowledge of gradients, which makes them vulnerable to attacks. To take into account the security issue in onlineoptimization, this paper investigates the effect of randomly corrupted attacks, which can corrupt gradient information arbitrarily. To conquer the randomly corrupted attack, an online muLtiple normaLized Gradient Descent (L3GD) algorithm is proposed. Under mild conditions, the algorithm is proven to achieve satisfactory expected dynamic regret, i.e,O({P-T*+T-3/4,S-T*+Sigma(T )(t=1)||( )del( )f(t)(xt*)||(2)}) and O(F-T+T-3/4), without convex assumption, where P-T*, S-T*, and F-T denote the path-length, squared path-length, and the functional variation, respectively. The results are comparable to state-of-the-art algorithms in the absence of randomly corrupted attacks. To our best knowledge, this paper is the first to consider randomly corrupted attacks in onlineoptimization. Simulations conducted on both synthetic examples and real-world datasets, namely MNIST and CIFAR-10, corroborate the resilience of L3GD.
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