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Contextual bandits serve as a fundamental model for many sequential decisionmaking tasks. The most popular theoretically justified approaches are based onthe optimism principle. While these algorithms can be practical, they are knownto be suboptimal asymptotically. On the other hand, existing asymptoticallyoptimal algorithms for this problem do not exploit the linear structure in anoptimal way and suffer from lower-order terms that dominate the regret in allpractically interesting regimes. We start to bridge the gap by designing analgorithm that is asymptotically optimal and has good finite-time empiricalperformance. At the same time, we make connections to the recent literature onwhen exploration-free methods are effective. Indeed, if the distribution ofcontexts is well behaved, then our algorithm acts mostly greedily and enjoyssub-logarithmic regret. Furthermore, our approach is adaptive in the sense thatit automatically detects the nice case. Numerical results demonstratesignificant regret reductions by our method relative to several baselines.

Adaptive Exploration in Linear Contextual Bandit