Foundations and Trendsin Signal Processing Learning with Limited Samples Meta-Learning and Applications to

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Foundations and Trends®in Signal Processing

Learning with Limited Samples –

Meta-Learning and Applications to

Communication Systems

Suggested Citation:

Lisha Chen, Sharu Theresa Jose, Ivana Nikoloska, Sangwoo

Park, Tianyi Chen and Osvaldo Simeone (2022), “Learning with Limited Samples –

Meta-Learning and Applications to Communication Systems”, Foundations and Trends

in Signal Processing: Vol. xx, No. xx, pp 1–131. DOI: 10.1561/XXXXXXXXX.

This article may be used only for the purpose of research, teaching,

and/or private study. Commercial use or systematic downloading

(by robots or other automatic processes) is prohibited without ex-

plicit Publisher approval.

arXiv:2210.02515v1 [cs.LG] 3 Oct 2022

Contents

1 Introduction and Background 3

1.1 Introduction......................... 3

1.2 Meta-Learning........................ 5

1.3 Organization of the Monograph . . . . . . . . . . . . . . . 14

2 Meta-Learning Algorithms 16

2.1 Overview of Meta-Learning Algorithms . . . . . . . . . . . 16

2.2 Second-Order Optimization-Based Meta-Learning . . . . . 18

2.3 First-Order Optimization-Based Meta-Learning . . . . . . 24

2.4 Bayesian Meta-Learning . . . . . . . . . . . . . . . . . . . 28

2.5 Modular Meta-Learning . . . . . . . . . . . . . . . . . . . 33

2.6 Model-Based Meta-Learning . . . . . . . . . . . . . . . . 34

2.7 Conclusions ......................... 36

3 Bilevel Optimization for Meta-Learning 37

3.1 A Brief Introduction to Bilevel Optimization . . . . . . . . 37

3.2 A Uniﬁed Bilevel Optimization Framework . . . . . . . . . 40

3.3 Convergence Analysis for Bilevel Optimization . . . . . . . 45

3.4 Conclusions ......................... 47

4 Statistical Learning Theory for Meta-Learning 48

4.1 Generalization Error for Conventional Learning . . . . . . . 49

4.2 Generalization Error in Meta-Learning . . . . . . . . . . . 56

4.3 Information-Theoretic Bounds on Meta-Generalization Error 59

4.4 PAC-Bayes Analysis of Meta-Generalization Error . . . . . 65

4.5 Minimum Excess Meta-Risk for Bayesian Meta-Learning . . 67

4.6 Sharper Meta-Risk Analysis in Meta Linear Regression . . 71

4.7 Conclusions ......................... 71

5 Applications of Meta-Learning to Communications 72

5.1 Overview........................... 72

5.2 Demodulation ........................ 73

5.3 Encoding and Decoding . . . . . . . . . . . . . . . . . . . 80

5.4 Channel Prediction . . . . . . . . . . . . . . . . . . . . . 84

5.5 PowerControl........................ 88

5.6 Conclusions ......................... 93

6 Integration with Emerging Computing Technologies 94

6.1 Neuromorphic Computing . . . . . . . . . . . . . . . . . . 95

6.2 Quantum Computing . . . . . . . . . . . . . . . . . . . . 99

6.3 Conclusions .........................103

7 Outlook 104

7.1 Methods...........................104

7.2 Theory............................109

7.3 Applications.........................110

Acknowledgements 111

References 112

Learning with Limited Samples –

Meta-Learning and Applications to

Communication Systems

Lisha Chen?, Sharu Theresa Jose†, Ivana Nikoloska†, Sangwoo

Park†, Tianyi Chen?and Osvaldo Simeone†

†King’s College London

?Rensselaer Polytechnic Institute

ABSTRACT

Deep learning has achieved remarkable success in many

machine learning tasks such as image classiﬁcation, speech

recognition, and game playing. However, these breakthroughs

are often diﬃcult to translate into real-world engineering

systems because deep learning models require a massive

number of training samples, which are costly to obtain in

practice. To address labeled data scarcity, few-shot meta-

learning optimizes learning algorithms that can eﬃciently

adapt to new tasks quickly. While meta-learning is gaining

signiﬁcant interest in the machine learning literature, its

The ﬁrst four authors are listed in alphabetical order. Lisha Chen is the main

author of Section 2excluding Section 2.5, as well as Sections 3,4.6, and 7.2; Sharu

Theresa Jose is the main author of Section 4; Ivana Nikoloska is the main author of

Sections 2.5,5.5 and 6.2; Sangwoo Park is the main author of Section 5excluding

Section 5.5, as well as Sections 7.1 and 7.3; Tianyi Chen is the main author of

Section 3; and Osvaldo Simeone is the main author of Section 1and Section 6.1. This

monograph is based on a tutorial delivered by Tianyi Chen and Osvaldo Simeone at

IEEE ICASSP 2022. Tianyi Chen and Osvaldo Simeone have supervised the writing

process, and Osvaldo Simeone led the editing of the document.

Lisha Chen, Sharu Theresa Jose, Ivana Nikoloska, Sangwoo Park, Tianyi Chen

and Osvaldo Simeone (2022), “Learning with Limited Samples – Meta-Learning

and Applications to Communication Systems”, Foundations and Trends

in Signal

Processing: Vol. xx, No. xx, pp 1–131. DOI: 10.1561/XXXXXXXXX.

working principles and theoretic fundamentals are not as

well understood in the engineering community.

This review monograph provides an introduction to meta-

learning by covering principles, algorithms, theory, and en-

gineering applications. After introducing meta-learning in

comparison with conventional and joint learning, we de-

scribe the main meta-learning algorithms, as well as a gen-

eral bilevel optimization framework for the deﬁnition of

meta-learning techniques. Then, we summarize known re-

sults on the generalization capabilities of meta-learning from

a statistical learning viewpoint. Applications to communi-

cation systems, including decoding and power allocation,

are discussed next, followed by an introduction to aspects

related to the integration of meta-learning with emerging

computing technologies, namely neuromorphic and quantum

computing. The monograph is concluded with an overview

of open research challenges.

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FoundationsandTrends®inSignalProcessingLearningwithLimitedSamplesMeta-LearningandApplicationstoCommunicationSystemsSuggestedCitation:LishaChen,SharuTheresaJose,IvanaNikoloska,SangwooPark,TianyiChenandOsvaldoSimeone(2022),LearningwithLimitedSamplesMeta-LearningandApplicationstoCommunicationSystems...

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