Toward Optimal Adversarial Policies in the Multiplicative Learning System with a Malicious Expert
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by
S. Rasoul Etesami, Negar Kiyavash, Vincent Leon, H. Vincent Poor
2020
Abstract
We consider a learning system based on the conventional multiplicative weight
(MW) rule that combines experts' advice to predict a sequence of true outcomes.
It is assumed that one of the experts is malicious and aims to impose the
maximum loss on the system. The loss of the system is naturally defined to be
the aggregate absolute difference between the sequence of predicted outcomes
and the true outcomes. We consider this problem under both offline and online
settings. In the offline setting where the malicious expert must choose its
entire sequence of decisions a priori, we show somewhat surprisingly that a
simple greedy policy of always reporting false prediction is asymptotically
optimal with an approximation ratio of 1+O(√(ln N/N)), where N
is the total number of prediction stages. In particular, we describe a policy
that closely resembles the structure of the optimal offline policy. For the
online setting where the malicious expert can adaptively make its decisions, we
show that the optimal online policy can be efficiently computed by solving a
dynamic program in O(N^3). Our results provide a new direction for
vulnerability assessment of commonly used learning algorithms to adversarial
attacks where the threat is an integral part of the system.
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