IEEE Computational Intelligence Magazine - May 2022 - 81

computational costs and the convergence
and result in the low AUC accuracy. In
Fig. 6(c), the performance of EMTAUC
is the best in all cases when s is set
to 0.1. With the increase of s, the
performance of EMTAUC decreases.
This phenomenon appears because a
higher value of s may break the balance
of the computational costs and the convergence
and result in low AUC accuracy.
This case can also be found in Fig. S4(i)
and Fig. S4(j).
Figure 7 shows the average AUC
value of EMTAUC versus varying m on
diabetes and fourclass datasets. The average
AUC value of EMTAUC varies with
m on all datasets as shown in Fig. S5 (see
Supplementary Material). The value of
m is set to 2i, i = −5, −4, −3, ..., 1. m
balances the feasibility and sparsity of
model f. Figure 7 shows that the smaller
value of m denotes the lower average
AUC value. To achieve the high performance
of EMTAUC, more attention
should be paid to the first term of (5).
Thus, m should be set to a value small
than 2−3.
VII. Conclusions
This paper proposes a multitasking AUC
optimization framework to overcome
the limitations of batch and online AUC
optimization methods. First, an auxiliary
task by sampling the mini-batches of the
original dataset is designed. The other
task is to optimize the original problem
with the whole dataset. Moreover, a
dynamic adjustment strategy is proposed
to enhance the representation ability of
the sampled dataset by replacing the
items with the cases with low AUC
scores in the original dataset. The results
compared with the batch EA method
have demonstrated the advantage of the
proposed multitasking AUC framework.
Compared with the online AUC optimization
methods, EMTAUC is highly
competitive in small-scale and largescale
datasets.
Our work raises many questions to
further the development of the evolutionary
multitasking AUC optimization
problem. For example, the parameters
have a significant effect on the performance
of EMTAUC. In future work, we
will develop an effective tuning-free
EMTAUC with a policy network. In
addition, applying EMTAUC to solve
other machine learning problems is also
a promising research topic. Due to its
extensibility, EMTAUC has preliminarily
been applied to tune hyperparameters
of LightGBM [57] to further illustrate
the advanced nature of our proposal,
which can be found in the Supplementary
Material. The experimental results
conducted on 11 datasets have shown
the advantages of our proposal over single
task optimization.
Acknowledgment
This work was supported in part by
the Key Project of Science and Technology
Innovation 2030 supported by
the Ministry of Science and Technology
of China under Grant 2018AAA0101302
and in part by the General Program
of National Natural Science Found
a t ion of China (NSFC) under
Grant 61773300.
References
[1] J. A. Hanley and B. J. McNeil, " The meaning and
use of the area under of receiver operating characteristic
(ROC) curve, " Radiology, vol. 143, no. 1, pp. 29-36,
1982, doi: 10.1148/radiology.143.1.7063747.
[2] P. Kar, B. K. Sriperumbudur, P. Jain, and H. Karnick,
" On the generalization ability of online learning
algorithms for pairwise loss functions, " in Proc. ICML,
2013, pp. 441-449.
[3] W. Gao, R. Jin, S. Zhu, and Z.-H. Zhou, " One-pass
AUC optimization, " in Proc. ICML, 2013, pp. 906-914.
[4] Y. Ding, P. Zhao, S. C. Hoi, and Y.-S. Ong, " An
adaptive gradient method for online AUC maximization. "
in Proc. AAAI, 2015, pp. 2568-2574.
[5] R.-E. Fan, K.-W. Chang, C.-J. Hsieh, X.-R. Wang,
and C.-J. Lin, " LIBLINEAR: A library for large linear
classification, " J. Machine Learn. Res., vol. 9, pp.1871-
1874, Jan. 2008.
[6] S. Clémençon and N. Vayatis, " Ranking the best instances, "
J. Machine Learn. Res., vol. 8, pp. 2671-2699,
Dec. 2007.
[7] T. Joachims, " A support vector method for multivariate
performance measures, " in Proc. ICML, 2005, pp.
377-384, doi: 10.1145/1102351.1102399.
[8] C.-P. Lee and C.-J. Lin, " Large-scale linear RankSVM, "
Neural Comput., vol. 26, no. 4, pp. 781-817, 2014,
doi: 10.1162/NECO_a_00571.
[9] S. Gultekin, A. Saha, A. Ratnaparkhi, and J. Paisley,
" MBA: Mini-batch AUC optimization, " IEEE Trans.
Neural Netw. Learn. Syst., vol. 31, no. 12, pp. 5561-5574,
Dec. 2020, doi: 10.1109/TNNLS.2020.2969527.
[10] S. Clémençon, G. Lugosi, and N. Vayatis, " Ranking
and empirical minimization of u- statistics, " Annals
Statist., vol. 36, no. 2, pp. 844-874, 2008, doi:
10.1214/009052607000000910.
[11] K. C. Tan, L. Feng, and M. Jiang, " Evolutionary transfer
optimization - A new frontier in evolutionary computation
research, " IEEE Comput. Intell. Mag., vol. 16, no.
1, pp. 22-33, Feb. 2021, doi: 10.1109/MCI.2020.3039066.
[12] F. Cheng, X. Zhang, C. Zhang, J. Qiu, and L. Zhang,
" An adaptive mini-batch stochastic gradient method for
AUC maximization, " Neurocomputing, vol. 318, pp. 137-
150, Nov. 2018, doi: 10.1016/j.neucom.2018.08.041.
[13] L. Gräning, Y. Jin, and B. Sendhoff, " Generalization
improvement in multiobjective learning, " in Proc.
IJCNN, 2006, pp. 4839-4846.
[14] P. Wang, K. Tang, T. Weise, E. P. K. Tsang, and X.
Yao, " Multiobjective genetic programming for maximizing
ROC performance, " Neurocomputing, vol. 125, no. 3,
pp. 102-118, 2014, doi: 10.1016/j.neucom.2012.06.054.
[15] P. Wang, M. Emmerich, R. Li, K. Tang, T. Bäck,
and X. Yao, " Convex hull-based multiobjective genetic
programming for maximizing receiver operating characteristic
performance, " IEEE Trans. Evol. Comput.,
vol. 19, no. 2, pp. 188-200, Apr. 2015, doi: 10.1109/
TEVC.2014.2305671.
[16] W. Hong and K. Tang, " Convex hull-based multiobjective
evolutionary computation for maximizing
receiver operating characteristics performance, " Memetic
Comput., vol. 8, no. 1, pp. 35-44, 2016, doi: 10.1007/
s12293-015-0176-8.
[17] J. Zhao et al., " Multiobjective optimization of classifiers
by means of 3D convex-hull-based evolutionary
algorithms, " Inf. Sci., vol. 367, pp. 80-104, Nov. 2016,
doi: 10.1016/j.ins.2016.05.026.
[18] J. Zhao et al., " 3D fast convex-hull-based evolutionary
multiobjective optimization algorithm, " Appl. Soft
Comput., vol. 67, pp. 322-336, Jun. 2018, doi: 10.1016/j.
asoc.2018.03.005.
[19] F. Cheng, G. Fu, X. Zhang, and J. Qiu, " Multiobjective
evolutionary algorithm for optimizing the partial
area under the ROC curve, " Knowl.-Based Syst., vol. 170,
pp. 61-69, Apr. 2019, doi: 10.1016/j.knosys.2019.01.029.
[20] J. Qiu, M. Liu, L. Zhang, W. Li, and F. Cheng, " A
multi-level knee point based multiobjective evolutionary
algorithm for AUC maximization, " Memetic Comput., vol.
11, no. 3, pp. 285-296, 2019, doi: 10.1007/s12293-01900280-7.
[21]
P. Zhao, S. C. H. Hoi, R. Jin, and T. Yang, " Online
AUC maximization, " in Proc. ICML, 2011.
[22] F. Rosenblatt, " The perceptron: A probabilistic
model for information storage and organization in the
brain, " Psychol. Rev., vol. 65, pp. 386-407, 1958, doi:
10.1037/h0042519.
[23] K. Crammer, O. Dekel, J. Keshet, S. Shalev-Shwartz,
and Y. Singer, " Online passive-aggressive algorithms, " J.
Machine Learn. Res., vol. 7, pp. 551-585, Mar. 2006.
[24] K. Crammer, M. Dredze, and F. Pereira, " Exact convex
confidence-weighted learning, " in Proc. NIPS, 2008,
pp. 345-352.
[25] A. Gupta, Y. S. Ong, and L. Feng, " Multifactorial
evolution: toward evolutionary multitasking, " IEEE
Trans. Evol. Comput., vol. 20, no. 3, pp. 343−357, Jun.
2016, doi: 10.1109/TEVC.2015.2458037.
[26] L. Feng et al., " Evolutionary multitasking via explicit
autoencoding, " IEEE Trans. Cybern., vol. 49,
no. 9, pp. 3457-3470, Sep. 2019, doi: 10.1109/TCYB.
2018.2845361.
[27] R. T. Liaw and C. K. Ting, " Evolutionary many
tasking optimization based on symbiosis in biocoenosis, "
in Proc. AAAI, 2019, vol. 33, pp. 4295-4303, doi:
10.1609/aaai.v33i01.33014295.
[28] K. K. Bali, Y. S. Ong, A. Gupta, and P. S. Tan,
" Multifactorial evolutionary algorithm with online
transfer parameter estimation: MFEA-II, " IEEE Trans.
Evol. Comput., vol. 24, no. 1, pp. 69-83, Feb. 2020, doi:
10.1109/TEVC.2019.2906927.
[29] X. Zheng, A. K. Qin, M. Gong, and D. Zhou, " Selfregulated
evolutionary multitask optimization, " IEEE
Trans. Evol. Comput., vol. 24, no. 1, pp. 16-28, Feb. 2020,
doi: 10.1109/TEVC.2019.2904696.
[30] Y. Chen, J. Zhong, L. Feng, and J. Zhang, " An adaptive
archive-based evolutionary framework for many-task
optimization, " IEEE Trans. Emerg. Topics Comput. Intell.,
vol. 4, no. 3, pp. 369-384, Jun. 2020, doi: 10.1109/TETCI.2019.2916051.
[31]
A. Gupta, Y. S. Ong, L. Feng, and K. C. Tan, " Multiobjective
multifactorial optimization in evolutionary
multitasking, " IEEE Trans. Cybern., vol. 47, no. 7, pp.
1652-1665, Jul. 2017, doi: 10.1109/TCYB.2016.2554622.
[32] K. K. Bali, A. Gupta, Y. S. Ong, and P. S. Tan,
" Cognizant multitasking in multiobjective multifactorial
evolution: MO-MFEA-II, " IEEE Trans. Cybern.,
vol. 51, no. 4, pp. 1784-1796, Apr. 2021, doi: 10.1109/
TCYB.2020.2981733.
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