IEEE Computational Intelligence Magazine - May 2022 - 70

update their weights with a higher learning
rate. Moreover, due to the failure in
using the geometry knowledge of the data
observed in the online learning process,
Ding et al. [4] proposed an adaptive online
AUC maximization by exploiting the
knowledge of historical gradients to perform
more informative online learning.
Although batch learning methods are
preferable to online AUC optimization
methods in terms of performance, they
cannot handle large-scale datasets due to
the high computational costs in evaluation.
Moreover, online AUC optimization
methods have relatively low accuracy but
can handle large-scale datasets. Thus, it is
necessary to design a strategy to balance
convergence and computational complexity.
Unlike current methods, a multitasking
AUC optimization framework is proposed
by designing a cheap task with a dynamic
adjustment strategy to address the above
issues. Due to the pair learning characteristics
of AUC optimization, a cheap task is
developed by sampling mini-batches of
positive/negative instance pairs to avoid
the limitation of batch AUC optimization
methods. Moreover, due to the fast convergence
of the cheap task and the local
knowledge of the sampling dataset,
dynamically adjusting the data structure of
the cheap task is designed to make full use
of the knowledge carried by the whole
data. Then, any general EMTO algorithm
can be employed to optimize the cheap
and expensive tasks.
III. EMTO
This section gives background knowledge
on the multitasking optimization
(MTO) problem first. Then, an overview
of existing state-of-the-art methods for
EMTO is also introduced, including multifactorial
EA with online transfer parameter
estimation (MFEAII) [28], symbiosis
in biocoenosis optimization (SBO) [27],
and evolutionary multitasking via explicit
autoencoding (EMEA) [26].
A. MTO Problem
MTO is an emerging topic for solving
multiple tasks simultaneously with the
benefits of implicit parallelism of EAs.
Generally, for the K minimization tasks, the
MTO problem can be expressed as follows:
minfX iK
Xx xx Di
ii
Xi
..
=12
st ==i ii
12
mi
i !
i
(),, ,...,
[, , ..., ], ,,...,
12
3) Skill Factor :{ } indixx
=
K
(1)
where fi (Xi) represents the objective
function of task i, and Xi is the decision
variable. mi is the dimension of Xi, and
Di is the decision space for task i. MTO
aims to find a set of solutions Xi
) =
argmin fi(Xi) in the vast decision space
by effective knowledge transfer across
tasks. Generally speaking, EMTO
algorithms need to consider two
issues: 1. How to ensure knowledge
flow in different decision spaces? 2.
How to transfer the common knowledge
across tasks? For the former, a
unified search space X of dimensionality
DDi
in the multifactorial
= ma {}x
EA (MFEA) [25] is designed for all
decision variables to ensure the flow of
knowledge and then the key value of
each variable is between 0 and 1.
Unlike the establishment of a unified
search space X in MFEA, each task
maintains its own search space's independence
in EMEA [26]. The current
mainstream EMTO algorithms can be
divided into implicit and explicit paradigms.
In the implicit paradigm, the
common knowledge across tasks is
transferred by genetic operators. In the
explicit paradigm, the transferred solutions,
including useful knowledge, are
shared explicitly.
B. MFEAII
MFEAII is
the second generation of
MFEA, the most popular MTO algorithm,
which uses probabilistic models to
effectively adjust the degree of knowledge
transfer between tasks. In MFEAII,
to provide a platform for knowledge
sharing, the individual in a population is
encoded in a unified search space introduced
in Section III.A. Each task is
viewed as a factor of the individual.
Some concepts related to this factor are
as follows.
1) Factorial Cost fj
i : fj
2) Factorial Rank rj
i is the objective
value of individual i on task j.
i : rj
i is the rank index
of individual i on the ascending factor
cost list corresponding to task j.
70 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2022
i
ii argmin rj
cates the task associated with individual
i.
{{ =
i
4) Scalar Fitness :/r1ii
xi
is the
scaled fitness of individual i.
In the evolutionary process of
MFEAII, according to the skill factor,
individuals in a population are implicitly
divided into K groups dedicated to K
tasks. Two genetic mechanisms, i.e.,
assortative mating and selective imitation,
are designed to ensure that knowledge
is transferred between tasks. More
details of MFEAII can be found in [28].
C. SBO
SBO is a novel paradigm for solving
MTO problems, which leverages symbiosis
in biocoenosis (SB) to transfer useful
information across tasks. If a species has a
positive/no positive/negative effect on
other species, it is said that the species is
beneficial/neutral/harmful to other species.
According to the relationships
between two species, SB is divided into
six main types, including mutualism,
commensalism, parasitism, neutralism,
amensalism, and competition. The SB can
reasonably simulate the information
transmission in EMTO. The populations
of various tasks form multiple species, and
the information transmission across tasks
can be regarded as symbiosis. The main
framework of SBO holds three main
components: 1) individual replacement
strategy across paired tasks, 2) measurement
of symbiosis by inter-task paired
evaluations, and 3) dynamic adjustment
strategy for the frequency and quantity of
knowledge transfer based on SB. More
details of SBO can be found in [27].
D. EMEA
An explicit EMTO algorithm (called
EMEA in this paper) was first proposed
by Feng et al. [26], in which evolutionary
solvers with different biases are used to
solve different tasks simultaneously, and
the common knowledge across tasks is
transferred based on autoencoding. In this
method, to make use of biases of multiple
search operators, each task is assigned an
independent solver. For any two tasks, a
single-layer denoising autoencoder M
establishes the connection across tasks,
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