Adaptive Adversarial Multi-task Representation Learning Yuren Mao 1 - - PowerPoint PPT Presentation

Adaptive Adversarial Multi-task Representation Learning

Yuren Mao1 Weiwei Liu2 Xuemin Lin1 WHU

C H I N A

1. University of New South Wales, Australia. 2. Wuhan University, China.

ICML 2020

Overview: Adaptive AMTRL (Adversarial Multi-task Representation Learning)

…… ……

Task 1 Task T

……

Shared Layers Task Specific Layers Discriminator

…

MinMax Forward Propagation Backward Propagation

𝜖෠ 𝑀(𝜄𝑡ℎ, 𝜄1) 𝜖𝜄1 𝜖෠ 𝑀(𝜄𝑡ℎ, 𝜄𝑈) 𝜖𝜄𝑈 𝜖෠ 𝑀(𝜄𝑡ℎ, 𝜄1) 𝜖𝜄𝑡ℎ 𝜖෠ 𝑀(𝜄𝑡ℎ, 𝜄𝑈) 𝜖𝜄𝑡ℎ 𝜖෠ 𝑀𝐸 (𝜄𝑡ℎ) 𝜖𝑋 −𝜖෠ 𝑀𝐸 (𝜄𝑡ℎ) 𝜖𝜄𝑡ℎ

Gradient Reversal Layer Input Original MTRL

AMTRL Algorithm PAC Bound

LD(h) − LS(h) ≤ c1ρ Ga(G∗(X1)) n + c2Qsupg∈G∗∥g(X1)∥ √n +

• 9ln(2/δ)

2nT

Generalization Error The number of tasks does not matter Negligible

Better Performance

Task Relatedness for AMTRL Adaptive AMTRL

• Augmented

Lagrangian

• Relatedness based

Weighting Strategy

Content

• Adversarial Multi-task Representation Learning (AMTRL)
• Adaptive AMTRL
• PAC Bound and Analysis
• Experiments

Adversarial Multi-task Representation Learning

…… ……

Task 1 Task T

……

Shared Layers Task Specific Layers Discriminator

…

MinMax Forward Propagation Backward Propagation

𝜖෠ 𝑀(𝜄𝑡ℎ, 𝜄1) 𝜖𝜄1 𝜖෠ 𝑀(𝜄𝑡ℎ, 𝜄𝑈) 𝜖𝜄𝑈 𝜖෠ 𝑀(𝜄𝑡ℎ, 𝜄1) 𝜖𝜄𝑡ℎ 𝜖෠ 𝑀(𝜄𝑡ℎ, 𝜄𝑈) 𝜖𝜄𝑡ℎ 𝜖෠ 𝑀𝐸 (𝜄𝑡ℎ) 𝜖𝑋 −𝜖෠ 𝑀𝐸 (𝜄𝑡ℎ) 𝜖𝜄𝑡ℎ

Gradient Reversal Layer Input Original MTRL

Adversarial Multi-task Representation Learning (AMTRL) has achieved success in various applications, ranging from sentiment analysis to question answering systems.

min

h L(h, λ) = LS(h) + λLadv

Ladv = max

Φ

1 nT

T

• t=1

n

• i=1

etΦ(g(xt

i))

LS(h) = 1 nT

T

• t=1

n

• i=1

lt(f t(g(xt

i)), yt i)

Empirical loss: Loss of the adversarial module:

Adaptive AMTRL

Adversarial AMTRL aims to minimize the task-averaged empirical risk and enforce the representation of each task to share an identical distribution. We formulate it as a constraint optimization problem

min

h

LS(h) s.t. Ladv − c = 0,

and propose to solve the problem with an augmented Lagrangian method.

min

h

1 T LS(h) + λ(Ladv − c) + r 2(Ladv − c)2.

𝜇 and 𝑠 updates in the training process.

Relatedness for AMTRL

(a) Three 2-d Gaussian distributions (b) Discriminator (c) Relatedness changing curve

𝑡𝑝𝑔𝑢𝑛𝑏𝑦(𝑋𝑌 + 𝑐)

Rij = min{ N

n=1 ejΦ(g(xi n)) + eiΦ(g(xj n))

N

n=1 eiΦ(g(xi n)) + ejΦ(g(xj n))

, 1}

Relatedness between task i and task j:

R =      R11 R12 · · · R1T R21 R22 · · · R2T . . . . . . ... . . . RT1 RT2 · · · RTT      .

Relatedness matrix:

Adaptive AMTRL

In multi-task learning, tasks regularize each other and improve the generalization of some tasks. The weights of each task influences the effect of the regularization. This paper proposes a weighting strategy for AMTRL based on the proposed task relatedness. where 1 is a 1×𝑈 vector of all 1, and 𝑆 is the relatedness matrix. Combining the augmented Lagrangian method with the weighting strategy, optimization

• bjective of our adaptive AMTRL method is

w = 1 1R1′1R,

min

h

1 T

T

• t=1

wtLSt(f t ◦ g) + λ(Ladv − c) + r 2(Ladv − c)2.

PAC Bound and Analysis

LD(h) − LS(h) ≤ c1ρ Ga(G∗(X1)) n + c2Qsupg∈G∗∥g(X1)∥ √n +

• 9ln(2/δ)

2nT

Assume the representation of each task share an identical distribution, we have the following generalization error bound.

Generalization Error The number of tasks does not matter Negligible

• The generalization error bound for AMTRL is tighter than that for MTRL.
• The number of tasks slightly influence the generalization bound of AMTRL.

Experiments - Relatedness Evolution

Sentiment Analysis and Topic Classification. Sentiment Analysis. Topic Classification

Rt = 1 T

T

• k=0

Rtk.

Mean of

Experiments - Classification Accuracy

Sentiment Analysis and Topic Classification. Sentiment Analysis. Topic Classification

Experiments - Influence of the Number of Tasks

Sentiment Analysis.

errel = erMTL

1 T

T

1 ert STL

Relative Error: Error rate for the task ’appeal’.

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