Large-scale screening for potential threats with limited resources and
capacity for screening is a problem of interest at airports, seaports, and
other ports of entry. Adversaries can observe screening procedures and arrive
at a time when there will be gaps in screening due to limited resource
capacities. To capture this game between ports and adversaries, this problem
has been previously represented as a Stackelberg game, referred to as a Threat
Screening Game (TSG). Given the significant complexity associated with solving
TSGs and uncertainty in arrivals of customers, existing work has assumed that
screenees arrive and are allocated security resources at the beginning of the
time window. In practice, screenees such as airport passengers arrive in bursts
correlated with flight time and are not bound by fixed time windows. To address
this, we propose an online threat screening model in which screening strategy
is determined adaptively as a passenger arrives while satisfying a hard bound
on acceptable risk of not screening a threat. To solve the online problem with
a hard bound on risk, we formulate it as a Reinforcement Learning (RL) problem
with constraints on the action space (hard bound on risk). We provide a novel
way to efficiently enforce linear inequality constraints on the action output
in Deep Reinforcement Learning. We show that our solution allows us to
significantly reduce screenee wait time while guaranteeing a bound on risk.

本研究提出了一种旅客安全检查的在线威胁筛查模型，其中检查策略是当旅客到达时自适应确定的，同时满足不检查威胁的可接受风险硬性约束，解决了传统模型中固定时间窗口的限制，并采用基于线性不等式约束的强化学习算法，有效平衡了较少的安检资源和威胁较高的检查风险。

使用约束动作空间强化学习解决在线威胁筛查游戏

Solving Online Threat Screening Games using Constrained Action Space  Reinforcement Learning

We propose a method to impose homogeneous linear inequality constraints of
the form $Ax\leq 0$ on neural network activations. The proposed method allows a
data-driven training approach to be combined with modeling prior knowledge
about the task. One way to achieve this task is by means of a projection step
at test time after unconstrained training. However, this is an expensive
operation. By directly incorporating the constraints into the architecture, we
can significantly speed-up inference at test time; for instance, our
experiments show a speed-up of up to two orders of magnitude over a projection
method. Our algorithm computes a suitable parameterization of the feasible set
at initialization and uses standard variants of stochastic gradient descent to
find solutions to the constrained network. Thus, the modeling constraints are
always satisfied during training. Crucially, our approach avoids to solve an
optimization problem at each training step or to manually trade-off data and
constraint fidelity with additional hyperparameters. We consider constrained
generative modeling as an important application domain and experimentally
demonstrate the proposed method by constraining a variational autoencoder.

本文提出了一种方法来在神经网络激活中施加均匀的线性不等式约束，以结合数据驱动的训练方法和先前任务的先验知识。该算法可在测试时间内显著加速推理速度，并避免了在每个训练步骤中求解优化问题或手动调整超参数。该方法通过约束变分自编码器进行实验演示。

神经网络激活的齐次线性不等式约束

Homogeneous Linear Inequality Constraints for Neural Network Activations

This paper deals with faces and facets of the family-variable polytope and
the characteristic-imset polytope, which are special polytopes used in integer
linear programming approaches to statistically learn Bayesian network
structure. A common form of linear objectives to be maximized in this area
leads to the concept of score equivalence (SE), both for linear objectives and
for faces of the family-variable polytope. We characterize the linear space of
SE objectives and establish a one-to-one correspondence between SE faces of the
family-variable polytope, the faces of the characteristic-imset polytope, and
standardized supermodular functions. The characterization of SE facets in terms
of extremality of the corresponding supermodular function gives an elegant
method to verify whether an inequality is SE-facet-defining for the
family-variable polytope. We also show that when maximizing an SE objective one
can eliminate linear constraints of the family-variable polytope that
correspond to non-SE facets. However, we show that solely considering SE facets
is not enough as a counter-example shows; one has to consider the linear
inequality constraints that correspond to facets of the characteristic-imset
polytope despite the fact that they may not define facets in the
family-variable mode.

研究了用于整数线性规划建模贝叶斯网络结构的两种特殊多面体，阐述了它们之间的关系并探究了它们的性质，包括面和顶点的可描述性、可重合性及极大性等，研究了基于超模函数的等价性判定及其对不等式约束的影响。