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

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 • Choose a pair to experiment with 2

Application: Drug discovery drugs proteins • Choose a pair to experiment with • Goal: Find as many pairs with the desired interaction as possible online dating clothing recommendation 3

Bilinear bandits ! = # $ Θ & + ( protein features desired interaction? (0/1) drug features unknown parameter ( ) by ) ) • A natural model: already used for predicting drug-protein interaction. [Luo et al., “A network integration approach for drug-target interaction prediction and computational drug repositioning from heterogeneous information”, Nature Communications, 2017] 4

Bilinear bandits ) = + , Θ - + / protein features desired interaction? (0/1) drug features unknown parameter ( ! by ! ) • A natural model: already used for predicting drug-protein interaction. [Luo et al., “A network integration approach for drug-target interaction prediction and computational drug repositioning from heterogeneous information”, Nature Communications, 2017] • Issue: ! " number of unknowns • What if rank Θ ≪ ! ? 4 , Θ = 0 5 6 7 6 8 6 ~ !: unknowns 123 • Many real-world problems exhibit the low-rank structure. 5

Summary of the result • A naïve method: reduction "[$] = ' ( Θ * = ⟨vec Θ , vec '* ( 〉 • Invoking linear algorithms [Abbasi-Yadkori’11] , convergence rate is 1 2 3 • No dependence of the rank ! 6

Summary of the result • A naïve method: reduction "[$] = ' ( Θ * = ⟨vec Θ , vec '* ( 〉 • Invoking linear algorithms [Abbasi-Yadkori’11] , convergence rate is 1 2 3 • No dependence of the rank ! • Can we obtain faster rates as the rank ! becomes smaller? 7

Summary of the result • A naïve method: reduction "[$] = ' ( Θ * = ⟨vec Θ , vec '* ( 〉 • Invoking linear algorithms [Abbasi-Yadkori’11] , convergence rate is 1 2 3 • No dependence of the rank ! • Can we obtain faster rates as the rank ! becomes smaller? YES, we achieve 4 5/7 8 (factor 1/! better) 9 • Is this optimal? 8

Explore-Subspace-Then-Refine (ESTR) • Stage 1: estimate the subspace V & Θ U Σ ≈ • Stage 2: linear bandit within the “subspace” 9

Explore-Subspace-Then-Refine (ESTR) • Stage 1: estimate the subspace V & Θ U Σ ≈ • Stage 2: linear bandit within the “subspace” • Turns out, it doesn’t work. Θ • Our solution: allow “refining” the subspace. our search space • The devil is in the detail. 10

Explore-Subspace-Then-Refine (ESTR) • Stage 1: estimate the subspace V & Θ U Σ ≈ • Stage 2: linear bandit within the “subspace” • Turns out, it doesn’t work. Θ • Our solution: allow “refining” the subspace. our search space • The devil is in the detail. Let’s chat! #127 @ Pacific Ballroom 11