Heuristic learning for co-design scheme of optimal sequential attack

Abstract

This paper considers a novel co-design problem of the optimal sequential attack, whose attack strategy changes with the time series, and in which the sequential attack selection strategy and sequential attack signal are simultaneously designed. Different from the existing attack design works that separately focus on attack subsets or attack signals, the joint design of the attack strategy poses a huge challenge due to the deep coupling relation between the sequential attack selection strategy and sequential attack signal. In this manuscript, we decompose the sequential co-design problem into two equivalent sub-problems. Specifically, we first derive an analytical closed-form expression between the optimal attack signal and the sequential attack selection strategy. Furthermore, we prove the finite-time inverse convergence of the critical parameters in the injected optimal attack signal by discrete-time Lyapunov analysis, which enables the efficient off-line design of the attack signal and saves computing resources. Finally, we exploit its relationship to design a heuristic two-stage learning-based joint attack algorithm (HTL-JA), which can accelerate the realization of the attack target compared to the one-stage proximal-policy-optimization-based (PPO) algorithm. Extensive simulations are conducted to show the effectiveness of the injected optimal sequential attack.