IEEE Computational Intelligence Magazine - May 2022 - 69

tasks of AUC optimization. In
EMTAUC, unlike existing methods
that address the expensive AUC optimization
task alone, a multitasking
AUC optimization environment is
established, where the designed cheap
task and the original task are optimized
simultaneously to promote the
AUC performance.
2) Due to the partial knowledge of the
designed cheap task, a strategy is
proposed to bridge the gap between
the original task and the cheap task
by dynamically adjusting the data
structure of cheap tasks. In this way,
EMTAUC can enhance the representation
ability of cheap tasks and
break the limitation of online learning
and batch learning methods.
The remainder of this paper is organized
as follows. The related work on
AUC optimization is introduced in Section
II. Section III presents the background
of the EMTO algorithm. Section
IV gives a brief introduction on AUC
optimization. Then an introduction on
the designed EMTAUC is given in Section
V. Section VI presents the experimental
results to demonstrate the effectiveness
of EMTAUC. Finally, Section VII concludes
the work in this paper.
II. Related Work
The standard process to maximize the
AUC is described as follows. First, a
classifier is trained based on the training
instances. Then, the predicted test scores
are sorted to obtain the AUC performance.
Most of these approaches can be
divided into three groups.
Batch learning methods.
The first group of methods is based on
batch learning. For batch learning,
Joachims [7] firstly developed a general
framework for optimizing multivariate
nonlinear performance measures such as
the AUC and F1. Linear RankSVM [8] is
the most commonly used AUC maximization
method. In addition, Gultekin et al.
[9] employed U-statistics [10] over sampling
mini-batches of positive/negative
instance pairs to optimize the AUC maximization
problem. Cheng et al. [12] proposed
an adaptive stochastic gradient
In a multitasking AUC optimization environment, optimizing
AUC on the whole dataset is regarded as an expensive
task (AUCE) and optimizing AUC on the sampled dataset is
considered as a cheap task (AUCC).
method over mini-batches, which employed
a projection gradient strategy in its inner
optimization. In these algorithms, special
convex loss functions are designed. These
algorithms are computationally challenging,
and their computational costs are usually
proportional to the number of positive-negative
instance pairs.
EA-based methods.
The second group employs EAs to
improve AUC accuracy. The basic idea of
EA-based methods is to transform the
AUC optimization problem into a biobjective
optimization problem, where
the True Positive Rate (TPR) and False
Positive Rate (FPR) are employed as the
two objectives. Gräning et al. [13] proposed
a Pareto-based multiobjective EA
to optimize TPR and FPR simultaneously.
Wang et al. [14] proposed a mult
iobjective genetic programming
(MOGP) algorithm for maximizing
AUC. MOGP regarded AUC maximization
as a ROC convex hull (ROCCH)
maximization problem, of which the target
is to maximize TPR and minimize
FPR simultaneously. Due to the superiority
of MOGP, several other MOEAs
for maximizing AUC have been proposed.
Wang et al. [15] further developed
a convex hull-based MOGP. In this
method, two new sorting and selection
operations were designed to provide better
solutions than MOGP. Hong et al.
[16] proposed a new multiobjective EA
for maximizing the ROCCH of neural
networks (ETriCM), in which convex
hull-based sorting with the convex hull
of individual minima and an extreme
area extraction selection was designed to
avoid a local optimum. Recently, Zhao
et al. [17], [18] proposed two novel
3D-convex-hull-based MOEAs for
AUC maximization by considering three
objectives, which have obtained good
performance in application-oriented
benchmarks. Moreover, the performance
of the algorithms mentioned above
greatly depends on the convex hull in
the ROC space, but the convex hull is
not precisely the same as the Pareto
front. Qiu et al. [20] proposed a novel
multi-level knee point-based EA to
address this limitation. In addition, unlike
the above methods, which optimize the
AUC metric, Cheng et al. [19] proposed
a multiobjective EA to optimize the partial
AUC metric by designing a metric
considering the partial range of the FPR.
Online learning methods.
The third group investigates online
learning methods for AUC optimization
involving large-scale applications. Among
the online AUC optimization methods,
there are two core online AUC optimization
frameworks. The first framework
is based on the idea of buffer sampling
[2], [21]. This framework used a fixedsize
buffer to stand for the observed data
for calculating the pairwise loss functions.
For example, Zhao et al. [21] leveraged
the reservoir sampling strategy to
represent the empirical data by a fixedsize
buffer, and then the pairwise loss
functions are calculated on the fixed-size
buffer. Kar et al. [2] introduced stream
subsampling with replacement as the
buffer update strategy. This strategy can
improve the generalization capability of
online learning algorithms for pairwise
loss functions with buffer sampling.
The second framework takes a different
perspective [3]. These methods
extended the previous online AUC optimization
framework with a regressionbased
one-pass learning mode, scanned
through the training data. Because of the
theoretical consistency between square
loss and AUC, this framework achieved
solid regret bounds by employing square
loss for the AUC optimization task. For
example, Gao et al. [3] exploited secondorder
statistics to identify the importance
of less frequently occurring features and
MAY 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 69
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