Impact of Representation Learning in Linear Bandits

• URL: http://arxiv.org/abs/2010.06531v2
• Date: Wed, 5 May 2021 17:01:53 GMT
• Title: Impact of Representation Learning in Linear Bandits
• Authors: Jiaqi Yang, Wei Hu, Jason D. Lee, Simon S. Du
• Abstract summary: We study how representation learning can improve the efficiency of bandit problems. We present a new algorithm which achieves $widetildeO(TsqrtkN + sqrtdkNT)$ regret, where $N$ is the number of rounds we play for each bandit.
• Score: 83.17684841392754
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study how representation learning can improve the efficiency of bandit problems. We study the setting where we play $T$ linear bandits with dimension $d$ concurrently, and these $T$ bandit tasks share a common $k (\ll d)$ dimensional linear representation. For the finite-action setting, we present a new algorithm which achieves $\widetilde{O}(T\sqrt{kN} + \sqrt{dkNT})$ regret, where $N$ is the number of rounds we play for each bandit. When $T$ is sufficiently large, our algorithm significantly outperforms the naive algorithm (playing $T$ bandits independently) that achieves $\widetilde{O}(T\sqrt{d N})$ regret. We also provide an $\Omega(T\sqrt{kN} + \sqrt{dkNT})$ regret lower bound, showing that our algorithm is minimax-optimal up to poly-logarithmic factors. Furthermore, we extend our algorithm to the infinite-action setting and obtain a corresponding regret bound which demonstrates the benefit of representation learning in certain regimes. We also present experiments on synthetic and real-world data to illustrate our theoretical findings and demonstrate the effectiveness of our proposed algorithms.

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