Optimal cross-learning for contextual bandits with unknown context distributions
This work addresses a theoretical challenge in online learning for researchers, offering incremental improvements by extending prior cross-learning frameworks to handle unknown distributions.
The paper tackles the problem of designing contextual bandit algorithms in a cross-learning setting with adversarial losses and unknown context distributions, achieving a nearly tight regret bound of O~(√(TK)) independent of context count. This result resolves an open problem and provides the first nearly tight bounds for applications like learning to bid in first-price auctions and sleeping bandits.
We consider the problem of designing contextual bandit algorithms in the ``cross-learning'' setting of Balseiro et al., where the learner observes the loss for the action they play in all possible contexts, not just the context of the current round. We specifically consider the setting where losses are chosen adversarially and contexts are sampled i.i.d. from an unknown distribution. In this setting, we resolve an open problem of Balseiro et al. by providing an efficient algorithm with a nearly tight (up to logarithmic factors) regret bound of $\widetilde{O}(\sqrt{TK})$, independent of the number of contexts. As a consequence, we obtain the first nearly tight regret bounds for the problems of learning to bid in first-price auctions (under unknown value distributions) and sleeping bandits with a stochastic action set. At the core of our algorithm is a novel technique for coordinating the execution of a learning algorithm over multiple epochs in such a way to remove correlations between estimation of the unknown distribution and the actions played by the algorithm. This technique may be of independent interest for other learning problems involving estimation of an unknown context distribution.