Optimal Batched Linear Bandits

[ICML 2024]

Xuanfei Ren^* · Tianyuan Jin^† · Pan Xu^‡

^* University of Science and Technology of China · ^† National University of Singapore · ^‡ Duke University

Implementation of the paper "Optimal Batched Linear Bandits".

How to run

The "End of Optimism" instances

$\epsilon=0.01,0.2$

Instances: $\theta=(1,0)$, $\mathcal X=(1,0),(1-\epsilon,2\epsilon),(0,1)$

python main.py --d 2 --T 10000 --num_sim 10 --epsilon 0.01

python main.py --d 2 --T 10000 --num_sim 10 --epsilon 0.2

Instances: $\theta=(1,0,0)$, $\mathcal X=(1,0,0),(0,1,0),(0,0,1),(1-\epsilon,2\epsilon,0),(1-\epsilon,0,2\epsilon)$

python main.py --d 3 --T 50000 --num_sim 10 --epsilon 0.01

python main.py --d 3 --T 50000 --num_sim 10 --epsilon 0.2

Instances: $\theta=(1,0,0,0,0)$, $\mathcal X=(1,0,0,0,0),(0,1,0,0,0),(0,0,1,0,0),(0,0,0,1,0),(0,0,0,0,1),(1-\epsilon,2\epsilon,0,0,0),(1-\epsilon,0,2\epsilon,0,0),(1-\epsilon,0,0,2\epsilon,0),(1-\epsilon,0,0,0,2\epsilon)$

python main.py --d 5 --T 100000 --num_sim 10 --epsilon 0.01

python main.py --d 5 --T 100000 --num_sim 10 --epsilon 0.2

research on epsilon

python main.py --d 2 --T 10000 --num_sim 10 --epsilon 0.005 --research_on_epsilon 1

python main.py --d 2 --T 10000 --num_sim 10 --epsilon 0.01 --research_on_epsilon 1

python main.py --d 2 --T 10000 --num_sim 10 --epsilon 0.05 --research_on_epsilon 1

python main.py --d 2 --T 10000 --num_sim 10 --epsilon 0.1 --research_on_epsilon 1

python main.py --d 2 --T 10000 --num_sim 10 --epsilon 0.15 --research_on_epsilon 1

python main.py --d 2 --T 10000 --num_sim 10 --epsilon 0.2 --research_on_epsilon 1

random examples

python main.py --seed 1 --K 3 --d 2 --T 50000 --num_sim 10 --verbose

python main.py --seed 1 --K 5 --d 3 --T 50000 --num_sim 10 --verbose

python main.py --seed 1 --K 9 --d 5 --T 50000 --num_sim 10 --verbose

python main.py --seed 1 --K 50 --d 20 --T 50000 --num_sim 10 --verbose

Citation

@inproceedings{ren2024optimal,
  title={Optimal Batched Linear Bandits},
  author={Ren, Xuanfei and Jin, Tianyuan and Xu, Pan},
  booktitle={International Conference on Machine Learning (ICML)},
  year={2024}
}