Contextual Bandits and Imitation Learning with Preference-Based Active Queries

We consider the problem of contextual bandits and imitation learning, where the learner lacks direct knowledge of the executed action's reward. Instead, the learner can actively request the expert at each round to compare two actions and receive noisy preference feedback. The learner's objective is two-fold: to minimize regret associated with the executed actions, while simultaneously, minimizing the number of comparison queries made to the expert. In this paper, we assume that the learner has access to a function class that can represent the expert's preference model under appropriate link functions and present an algorithm that leverages an online regression oracle with respect to this function class. For the contextual bandit setting, our algorithm achieves a regret bound that combines the best of both worlds, scaling as $O(\min\\{\sqrt{T}, d/\Delta\\})$, where $T$ represents the number of interactions, $d$ represents the eluder dimension of the function class, and $\Delta$ represents the minimum preference of the optimal action over any suboptimal action under all contexts. Our algorithm does not require the knowledge of $\Delta$, and the obtained regret bound is comparable to what can be achieved in the standard contextual bandits setting where the learner observes reward signals at each round. Additionally, our algorithm makes only $O(\min\\{T, d^2/\Delta^2\\})$ queries to the expert. We then extend our algorithm to the imitation learning setting, where the agent engages with an unknown environment in episodes of length $H$, and provide similar guarantees regarding regret and query complexity. Interestingly, with preference-based feedback, our imitation learning algorithm can learn a policy outperforming a sub-optimal expert, matching the result from interactive imitation learning algorithms [Ross and Bagnell, 2014] that require access to the expert's actions and also reward signals.