Deep neural networks (DNNs) could be deceived by generating
human-imperceptible perturbations of clean samples. Therefore, enhancing the
robustness of DNNs against adversarial attacks is a crucial task. In this
paper, we aim to train robust DNNs by limiting the set of outputs reachable via
a norm-bounded perturbation added to a clean sample. We refer to this set as
adversarial polytope, and each clean sample has a respective adversarial
polytope. Indeed, if the respective polytopes for all the samples are compact
such that they do not intersect the decision boundaries of the DNN, then the
DNN is robust against adversarial samples. Hence, the inner-working of our
algorithm is based on learning \textbf{c}onfined \textbf{a}dversarial
\textbf{p}olytopes (CAP). By conducting a thorough set of experiments, we
demonstrate the effectiveness of CAP over existing adversarial robustness
methods in improving the robustness of models against state-of-the-art attacks
including AutoAttack.

通过限制对干净样本添加范数约束的微小扰动后得到的输出可达集合，我们旨在训练出对抗攻击具有强鲁棒性的深度神经网络。我们称这个集合为对抗多面体，每个干净样本都对应一个对抗多面体。实际上，如果所有样本对应的多面体都是紧凑的，并且不与深度神经网络的决策边界相交，那么深度神经网络就能对抗攻击具有鲁棒性。因此，我们的算法的内部工作是基于学习受限的对抗多面体（CAP）。通过一系列实验证明了 CAP 相对于现有的对抗鲁棒性方法在提升模型对抗最先进攻击（包括 AutoAttack）的鲁棒性方面的有效性。

通过学习限制性对敌多面体提高对抗攻击鲁棒性

Robustness Against Adversarial Attacks via Learning Confined Adversarial  Polytopes

We consider a general multi-user Mobile Cloud Computing (MCC) system where
each mobile user has multiple independent tasks. These mobile users share the
computation and communication resources while offloading tasks to the cloud. We
study both the conventional MCC where tasks are offloaded to the cloud through
a wireless access point, and MCC with a computing access point (CAP), where the
CAP serves both as the network access gateway and a computation service
provider to the mobile users. We aim to jointly optimize the offloading
decisions of all users as well as the allocation of computation and
communication resources, to minimize the overall cost of energy, computation,
and delay for all users. The optimization problem is formulated as a non-convex
quadratically constrained quadratic program, which is NP-hard in general. For
the case without a CAP, an efficient approximate solution named MUMTO is
proposed by using separable semidefinite relaxation (SDR), followed by recovery
of the binary offloading decision and optimal allocation of the communication
resource. To solve the more complicated problem with a CAP, we further propose
an efficient three-step algorithm named MUMTO-C comprising of generalized MUMTO
SDR with CAP, alternating optimization, and sequential tuning, which always
computes a locally optimal solution. For performance benchmarking, we further
present numerical lower bounds of the minimum system cost with and without the
CAP. By comparison with this lower bound, our simulation results show that the
proposed solutions for both scenarios give nearly optimal performance under
various parameter settings, and the resultant efficient utilization of a CAP
can bring substantial cost benefit.

此研究探讨了一个多用户移动云计算系统中的任务离线决策、资源分配等问题，并且通过提出有效算法使用计算接入点 (CAP) 来优化整个系统的能量、计算和时延成本，从而带来了相当的成本效益。