Research map / Bandits and online learning / Contextual bandits and Thompson sampling
Bilinear Bandits with Low-rank Structure
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| exploit low-rank structure with two-stage subspace exploration and refinement | Bilinear bandit · Bilinear bandit, theoretical regret | regret upper bound: \widetilde{\mathcal{O}}(d_1d_2\sqrt{T}) -> \widetilde{\mathcal{O}}((d_1+d_2)^{3/2} \sqrt{r T}) | Helped |
| use ESTR-OS instead of OFUL | Bilinear bandit simulation · Simulation, d=8 and r=1 | average regret | Helped |
| use ESTR-BM instead of ESTR-OS (ablation) | ESTR · Simulation, d=8 and r=1 | average regret | Helped |
| replace explicit exploration with heuristic implicit subspace estimation (ablation) | ESTR, yielding ISSE · Simulation, d=8 and r=1 | average regret | Mixed |
| replace OptSpace with Burer-Monteiro alternating minimization (ablation) | ESTR · Simulation, d=8 and r=1 | average regret | Helped |
| regularize coordinates outside the estimated subspace more strongly | LowOFUL · Almost-low-dimensional linear bandit | regret upper bound dimensional dependence: from p to k | Helped |
| also regularize the two mixed submatrices (ablation) | LowOFUL in ESTR · Bilinear bandit | regret upper bound order | No clear effect |
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