Contextual Bandits with Cross-Learning

This variant arises in several strategic settings, such as learning how to bid in non-truthful repeated auctions, which has gained a lot of attention lately as many platforms have switched to running first-price auctions. We call this problem the contextual bandits problem with cross-learning. The best algorithms for the classical contextual bandits problem achieve Õ( CKT) regret against all stationary policies, where C is the number of contexts, K the number of actions, and T the number of rounds. We demonstrate algorithms for the contextual bandits problem with cross-learning that remove the dependence on C and achieve regret Õ( KT). We simulate our algorithms on real auction data from an ad exchange running first-price auctions (showing that they outperform traditional contextual bandit algorithms).