The linear contextual bandit literature is mostly focused on the design of efficient learning algorithms for a given representation. However, a contextual bandit problem may admit multiple linear representations, each one with different characteristics that directly impact the regret of the learning algorithm. In particular, recent works showed that there exist "good" representations for which constant problem-dependent regret can be achieved. In this paper, we first provide a systematic analysis of the different definitions of "good" representations proposed in the literature. We then propose a novel selection algorithm able to adapt to the best representation in a set of $M$ candidates. We show that the regret is indeed never worse than the regret obtained by running LinUCB on the best representation (up to a $\ln M$ factor). As a result, our algorithm achieves constant regret whenever a "good" representation is available in the set. Furthermore, we show that the algorithm may still achieve constant regret by implicitly constructing a "good" representation, even when none of the initial representations is "good". Finally, we empirically validate our theoretical findings in a number of standard contextual bandit problems.

本文针对线性语境劫掠问题，提出新的选择算法来适应多种线性表示方法，通过实验证明了我们算法的可行性和优越性。

在线性情境下利用良好表示的策略性宝藏