Support vector regression (SVR) has garnered significant popularity over the
past two decades owing to its wide range of applications across various fields.
Despite its versatility, SVR encounters challenges when confronted with
outliers and noise, primarily due to the use of the $\varepsilon$-insensitive
loss function. To address this limitation, SVR with bounded loss functions has
emerged as an appealing alternative, offering enhanced generalization
performance and robustness. Notably, recent developments focus on designing
bounded loss functions with smooth characteristics, facilitating the adoption
of gradient-based optimization algorithms. However, it's crucial to highlight
that these bounded and smooth loss functions do not possess an insensitive
zone. In this paper, we address the aforementioned constraints by introducing a
novel symmetric loss function named the HawkEye loss function. It is worth
noting that the HawkEye loss function stands out as the first loss function in
SVR literature to be bounded, smooth, and simultaneously possess an insensitive
zone. Leveraging this breakthrough, we integrate the HawkEye loss function into
the least squares framework of SVR and yield a new fast and robust model termed
HE-LSSVR. The optimization problem inherent to HE-LSSVR is addressed by
harnessing the adaptive moment estimation (Adam) algorithm, known for its
adaptive learning rate and efficacy in handling large-scale problems. To our
knowledge, this is the first time Adam has been employed to solve an SVR
problem. To empirically validate the proposed HE-LSSVR model, we evaluate it on
UCI, synthetic, and time series datasets. The experimental outcomes
unequivocally reveal the superiority of the HE-LSSVR model both in terms of its
remarkable generalization performance and its efficiency in training time.

提出了一种新型的对称损失函数 HawkEye 损失函数，将其整合到支持向量回归（SVR）的最小二乘框架中，得到了一种新的快速鲁棒模型 HE-LSSVR，通过应用自适应矩估计（Adam）算法解决 HE-LSSVR 的优化问题，并在 UCI、合成和时序数据集上验证了其卓越的泛化性能和训练效率。

提升支持向量回归的效率和鲁棒性：鹰眼损失

Enhancing Efficiency and Robustness in Support Vector Regression with  HawkEye Loss

In this paper, we study the convergence of the Adaptive Moment Estimation
(Adam) algorithm under unconstrained non-convex smooth stochastic
optimizations. Despite the widespread usage in machine learning areas, its
theoretical properties remain limited. Prior researches primarily investigated
Adam's convergence from an expectation view, often necessitating strong
assumptions like uniformly stochastic bounded gradients or problem-dependent
knowledge in prior. As a result, the applicability of these findings in
practical real-world scenarios has been constrained. To overcome these
limitations, we provide a deep analysis and show that Adam could converge to
the stationary point in high probability with a rate of $\mathcal{O}\left({\rm
poly}(\log T)/\sqrt{T}\right)$ under coordinate-wise "affine" variance noise,
not requiring any bounded gradient assumption and any problem-dependent
knowledge in prior to tune hyper-parameters. Additionally, it is revealed that
Adam confines its gradients' magnitudes within an order of
$\mathcal{O}\left({\rm poly}(\log T)\right)$. Finally, we also investigate a
simplified version of Adam without one of the corrective terms and obtain a
convergence rate that is adaptive to the noise level.

研究了自适应矩估计算法（Adam）在无约束非凸平滑随机优化中的收敛性，证明了 Adam 能够在很高的概率下以 $O (poly (log T)/√T)$ 的速率收敛到稳定点，不需要任何有界梯度假设和问题相关的先验知识来调整超参数，同时还研究了一个简化版本的 Adam 算法以适应噪声水平。