We show when maximizing a properly defined $f$-divergence measure with
respect to a classifier's predictions and the supervised labels is robust with
label noise. Leveraging its variational form, we derive a nice decoupling
property for a family of $f$-divergence measures when label noise presents,
where the divergence is shown to be a linear combination of the variational
difference defined on the clean distribution and a bias term introduced due to
the noise. The above derivation helps us analyze the robustness of different
$f$-divergence functions. With established robustness, this family of
$f$-divergence functions arises as useful metrics for the problem of learning
with noisy labels, which do not require the specification of the labels' noise
rate. When they are possibly not robust, we propose fixes to make them so. In
addition to the analytical results, we present thorough experimental evidence.
Our code is available at
this https URL

本文利用 $f$-divergence 的变分形式证明了其在标签噪声存在时具有良好的鲁棒性，并将其应用于噪声标签下的学习问题中，并提出了可能不具鲁棒性的解决方法，并通过实证研究证明了该方法的有效性。

当优化 $f$- 散度对标签噪声具有鲁棒性时

When Optimizing $f$-divergence is Robust with Label Noise

Hybrid quantum-classical algorithms such as the quantum approximate
optimization algorithm (QAOA) are considered one of the most promising
approaches for leveraging near-term quantum computers for practical
applications. Such algorithms are often implemented in a variational form,
combining classical optimization methods with a quantum machine to find
parameters to maximize performance. The quality of the QAOA solution depends
heavily on quality of the parameters produced by the classical optimizer.
Moreover, the presence of multiple local optima in the space of parameters
makes it harder for the classical optimizer. In this paper we study the use of
a multistart optimization approach within a QAOA framework to improve the
performance of quantum machines on important graph clustering problems. We also
demonstrate that reusing the optimal parameters from similar problems can
improve the performance of classical optimization methods, expanding on similar
results for MAXCUT.

本研究使用多次启动优化方法优化量子近似优化算法在图形聚类问题中的性能，并证明重用类似问题的最优参数可以扩展用于 MAXCUT 的相似结果。

多起点方法用于量子近似优化

Multistart Methods for Quantum Approximate Optimization

Generative adversarial networks are a novel method for statistical inference
that have achieved much empirical success; however, the factors contributing to
this success remain ill-understood. In this work, we attempt to analyze
generative adversarial learning -- that is, statistical inference as the result
of a game between a generator and a discriminator -- with the view of
understanding how it differs from classical statistical inference solutions
such as maximum likelihood inference and the method of moments.
Specifically, we provide a theoretical characterization of the distribution
inferred by a simple form of generative adversarial learning called restricted
f-GANs -- where the discriminator is a function in a given function class, the
distribution induced by the generator is restricted to lie in a pre-specified
distribution class and the objective is similar to a variational form of the
f-divergence. A consequence of our result is that for linear KL-GANs -- that
is, when the discriminator is a linear function over some feature space and f
corresponds to the KL-divergence -- the distribution induced by the optimal
generator is neither the maximum likelihood nor the method of moments solution,
but an interesting combination of both.

本文对生成对抗网络（GAN）进行了分析，特别是统计推理这一过程的理论特征，提出了一种简单形式的 GAN，称为受限 f-GANs，发现线性 KL-GANs 的最优生成器所推断出的分布是最大似然与矩法解的有趣组合。