  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.
