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.

研究表征学习如何提高赌博机问题的效率，提出一种可以共享线性表征的新算法来减少后悔，实验结果证明该算法在合适的情况下优于独立运行赌博机的朴素算法，并将该算法推广到无限动作集的情况中。

线性赌博机中表示学习的影响