Adaptive Exploration in Linear Contextual Bandit
This work addresses the problem of improving regret in sequential decision-making for applications like recommendation systems, though it is incremental in bridging theoretical and practical gaps.
The paper tackles the suboptimality of existing contextual bandit algorithms by designing an asymptotically optimal algorithm that exploits linear structure and achieves good finite-time performance, with numerical results showing significant regret reductions compared to baselines.
Contextual bandits serve as a fundamental model for many sequential decision making tasks. The most popular theoretically justified approaches are based on the optimism principle. While these algorithms can be practical, they are known to be suboptimal asymptotically. On the other hand, existing asymptotically optimal algorithms for this problem do not exploit the linear structure in an optimal way and suffer from lower-order terms that dominate the regret in all practically interesting regimes. We start to bridge the gap by designing an algorithm that is asymptotically optimal and has good finite-time empirical performance. At the same time, we make connections to the recent literature on when exploration-free methods are effective. Indeed, if the distribution of contexts is well behaved, then our algorithm acts mostly greedily and enjoys sub-logarithmic regret. Furthermore, our approach is adaptive in the sense that it automatically detects the nice case. Numerical results demonstrate significant regret reductions by our method relative to several baselines.