Convex quadratic programming (QP) is an important sub-field of mathematical
optimization. The alternating direction method of multipliers (ADMM) is a
successful method to solve QP. Even though ADMM shows promising results in
solving various types of QP, its convergence speed is known to be highly
dependent on the step-size parameter $\rho$. Due to the absence of a general
rule for setting $\rho$, it is often tuned manually or heuristically. In this
paper, we propose CA-ADMM (Context-aware Adaptive ADMM)) which learns to
adaptively adjust $\rho$ to accelerate ADMM. CA-ADMM extracts the
spatio-temporal context, which captures the dependency of the primal and dual
variables of QP and their temporal evolution during the ADMM iterations.
CA-ADMM chooses $\rho$ based on the extracted context. Through extensive
numerical experiments, we validated that CA-ADMM effectively generalizes to
unseen QP problems with different sizes and classes (i.e., having different QP
parameter structures). Furthermore, we verified that CA-ADMM could dynamically
adjust $\rho$ considering the stage of the optimization process to accelerate
the convergence speed further.

本文提出了一种基于上下文自适应 ADMM 的参数调节方法 CA-ADMM，通过提取 QP 问题的时空依赖，动态调节参数 rho，达到了加速优化过程的效果。

学习上下文感知的自适应求解器以加速二次规划问题

Learning context-aware adaptive solvers to accelerate quadratic programming

We study the problem of computing the minimum adversarial perturbation of the
Nearest Neighbor (NN) classifiers. Previous attempts either conduct attacks on
continuous approximations of NN models or search for the perturbation by some
heuristic methods. In this paper, we propose the first algorithm that is able
to compute the minimum adversarial perturbation. The main idea is to formulate
the problem as a list of convex quadratic programming (QP) problems that can be
efficiently solved by the proposed algorithms for 1-NN models. Furthermore, we
show that dual solutions for these QP problems could give us a valid lower
bound of the adversarial perturbation that can be used for formal robustness
verification, giving us a nice view of attack/verification for NN models. For
$K$-NN models with larger $K$, we show that the same formulation can help us
efficiently compute the upper and lower bounds of the minimum adversarial
perturbation, which can be used for attack and verification.

本篇论文的研究内容为：计算最小对抗性扰动的问题。研究者们提出了第一个能够计算最小对抗性扰动的算法，将问题用凸二次规划问题的列表进行了表示，用于 1-NN 模型的算法能够有效地解决这个问题。对于更大的 $K$-NN 模型，我们表明同样的表示形式可以帮助我们有效地计算最小对抗性扰动的上限和下限，这可用于攻击和验证。