Asynchronous Batch Bayesian Optimisation with Improved Local - - PowerPoint PPT Presentation

Asynchronous Batch Bayesian Optimisation with Improved Local Penalisation

Ahsan Alvi

Binxin Ru, Jan-Peter Calliess, Stephen Roberts, Michael A. Osborne

ICML 2019

Machine Learning Research Group

M L R G

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Talk Overview

• Bayesian optimisation (BO) recap
• Synchronous vs asynchronous BO
• Our Method

– Design of penaliser – Locally estimated Lipschitz constant

• Empirical results

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• 1. Bayesian Optimisation (BO)
• To solve the global optimisation
• The objective function

f( )

Non-convex Expensive Noisy

x y

x∗ = arg min

x∈X

f(x)

3

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.2 0.4 0.6 0.8 1

• 2
• 1

1 2

• 1. Bayesian Optimisation (BO)

f()

x y

x∗ = arg min

x∈X

f(x)

f ∼ GP

• µt, Kt
• xt+1 = arg max

x∈X

αt(x)

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x∗ = arg min

x∈X

f(x)

• Enable multiple evaluations in parallel
• 2. Synchronous Batch BO

Sequential BO Sync Batch BO (B=3)

1 4 C1 6 3 C3 2 5 C2 C1 2 1 Time

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• Maximise utilisation of parallel workers
• 2. Asynchronous Batch BO

Sync Batch BO (B=3)

1 4 C1 6 3 C3 2 5 C2 Time

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• Maximise utilisation of parallel workers
• 2. Asynchronous Batch BO

Async Batch BO (B=3) Sync Batch BO (B=3)

1 4 C1 6 3 C3 2 5 C2 5 2 9 C2 6 3 8 C3 C1 4 1 7 Time

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• 3. Our Method
• A new async batch BO: Penalising Locally for Asynchronous

Bayesian Optimisation on k Workers (PLAyBOOK)

HLP:X3

busy locations (points under evaluation at busy workers ) new point assigned to the free worker

xq = arg maxx∈X n α(x) Qq−1

i=1 ψ(x|xi)

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• 3. Our Method
• Penalising Locally for Asynchronous Bayesian

Optimisation on k Workers (PLAyBOOK)

• Empirically show: PLAyBOOK outperforms

– other async BO methods – its sync. variants in both time and sample efficiency

xq = arg maxx∈X n α(x) Qq−1

i=1 ψ(x|xi)

• 9

b2

LP HLP

• Our hard penaliser (HLP):
• LP (Gonzalez et al., 2016) :
• 4. Penaliser design

ψLP (x|xq) = Φ ⇣ ˆ

Lkxxqk|µ(xq)M| σ(xq)

⌘

1 0.2 0.4 0.6 0.8 1

xb1 , xb2 LP HLP

• 10
• 5

5 10 0.2 0.4 0.6 0.8 1

LP:x3

• 10
• 5

5 10

HLP:x3

ψHLP (x|xq) = min n

ˆ Lkxxqk |µ(xq)M|+σ(xq), 1

• 1

xq 10

• PLAyBOOK-HL: Ackley 5-D: B=4 and B=16
• 5. Empirical Results: Async. vs. Sync.

X-axis:

• No. of Func.

Evaluations X-axis: Run Time B=16 B=4

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• Tuning 9 hyperparameters of a CNN for CIFAR-10
• 5. Empirical Results: Async. methods

B=2 B=4

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Thank you!

Meet us at poster #213!

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