Imitation learning (IL)—training an agent to replicate expert behavior from demonstrations—underpins applications from robotics to language model training. Standard approaches such as Behavior Cloning (BC) are known to suffer from compounding errors and performance plateaus, particularly when the learner cannot perfectly represent the expert’s policy (e.g., as is typical in distillation). Two interventions are widely understood empirically to improve performance: querying the expert interactively along the learner’s own trajectories, and using value function estimation en route to generating a policy. We investigate the nature of these improvements and their potentially surprising interplay. Our main finding is that expert interaction relaxes the representational demands on the learner: one only needs a model capable of realizing the expert’s value function, bypassing the (often stricter) requirement of realizing the expert’s policy itself. Concretely, we introduce OVI, an interactive IL algorithm that is statistically and computationally efficient whenever the learner can represent the expert’s value function. We complement this with a negative result showing that interaction is necessary: without significantly stronger representational assumptions than expert-value realizability alone, a broad class of value-based IL algorithms cannot succeed in the offline setting. These findings bear out empirically: OVI outperforms offline policy-based (BC), interactive policy-based (DAgger), and offline value-based IL methods, with the largest gains when the learner network is substantially less expressive than the expert’s.