Bi Bilinear Ba Bandits wi with Low-ra rank Structure Kwang-Sung - - PowerPoint PPT Presentation

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Bi Bilinear Ba Bandits wi with Low-ra rank Structure Kwang-Sung - - PowerPoint PPT Presentation

Mar 19, 2024 48 likes •159 views

Bi Bilinear Ba Bandits wi with Low-ra rank Structure Kwang-Sung Jun Boston University (will join the U of Arizona ) Rebecca Willett Stephen Wright Robert Nowak U of Chicago UW-Madison 1 Application: Drug discovery drugs proteins

slide-1
SLIDE 1

Bi Bilinear Ba Bandits wi with Low-ra rank Structure

Kwang-Sung Jun

Boston University (will join the U of Arizona)

1

U of Chicago UW-Madison Rebecca Willett Stephen Wright Robert Nowak

slide-2
SLIDE 2
  • Choose a pair to experiment with

Application: Drug discovery

2

drugs proteins

slide-3
SLIDE 3
  • Choose a pair to experiment with
  • Goal: Find as many pairs with the desired interaction as possible

Application: Drug discovery

3

drugs proteins

  • nline dating

clothing recommendation

slide-4
SLIDE 4
  • A natural model: already used for predicting drug-protein

interaction.

Bilinear bandits

4

! = #$ Θ & + (

desired interaction? (0/1) drug features unknown parameter () by )) protein features

[Luo et al., “A network integration approach for drug-target interaction prediction and computational drug repositioning from heterogeneous information”, Nature Communications, 2017]

slide-5
SLIDE 5
  • A natural model: already used for predicting drug-protein

interaction.

  • Issue: !" number of unknowns
  • What if rank Θ ≪ !?
  • Many real-world problems exhibit the low-rank structure.

Bilinear bandits

5

) = +, Θ - + /

desired interaction? (0/1) drug features unknown parameter (! by !) protein features

Θ = 0

123 4

56 7686

,

~ !: unknowns

[Luo et al., “A network integration approach for drug-target interaction prediction and computational drug repositioning from heterogeneous information”, Nature Communications, 2017]

slide-6
SLIDE 6
  • A naïve method: reduction
  • Invoking linear algorithms [Abbasi-Yadkori’11], convergence rate is
  • No dependence of the rank !

Summary of the result

6

"[$] = '( Θ * = ⟨vec Θ , vec '*( 〉

12 3

slide-7
SLIDE 7
  • A naïve method: reduction
  • Invoking linear algorithms [Abbasi-Yadkori’11], convergence rate is
  • No dependence of the rank !
  • Can we obtain faster rates as the rank ! becomes smaller?

Summary of the result

7

"[$] = '( Θ * = ⟨vec Θ , vec '*( 〉

12 3

slide-8
SLIDE 8
  • A naïve method: reduction
  • Invoking linear algorithms [Abbasi-Yadkori’11], convergence rate is
  • No dependence of the rank !
  • Can we obtain faster rates as the rank ! becomes smaller?
  • Is this optimal?

Summary of the result

8

"[$] = '( Θ * = ⟨vec Θ , vec '*( 〉

12 3

YES, we achieve 45/7 8

9

(factor 1/! better)

slide-9
SLIDE 9
  • Stage 1: estimate the subspace
  • Stage 2: linear bandit within the “subspace”

Explore-Subspace-Then-Refine (ESTR)

9

≈

Θ U Σ V&

slide-10
SLIDE 10
  • Stage 1: estimate the subspace
  • Stage 2: linear bandit within the “subspace”
  • Turns out, it doesn’t work.
  • Our solution: allow “refining” the subspace.
  • The devil is in the detail.

Explore-Subspace-Then-Refine (ESTR)

10

≈

  • ur search space

Θ

Θ U Σ V&

slide-11
SLIDE 11
  • Stage 1: estimate the subspace
  • Stage 2: linear bandit within the “subspace”
  • Turns out, it doesn’t work.
  • Our solution: allow “refining” the subspace.
  • The devil is in the detail.

Explore-Subspace-Then-Refine (ESTR)

11

≈

  • ur search space

Θ

Θ U Σ V&

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