In this paper, we study offline-to-online Imitation Learning (IL) that pretrains an imitation policy from static demonstration data, followed by fast finetuning with minimal environmental interaction. We find the na\"ive combination of existing offline IL and online IL methods tends to behave poorly in this context, because the initial discriminator (often used in online IL) operates randomly and discordantly against the policy initialization, leading to misguided policy optimization and $\textit{unlearning}$ of pretraining knowledge. To overcome this challenge, we propose a principled offline-to-online IL method, named $\texttt{OLLIE}$, that simultaneously learns a near-expert policy initialization along with an $\textit{aligned discriminator initialization}$, which can be seamlessly integrated into online IL, achieving smooth and fast finetuning. Empirically, $\texttt{OLLIE}$ consistently and significantly outperforms the baseline methods in $\textbf{20}$ challenging tasks, from continuous control to vision-based domains, in terms of performance, demonstration efficiency, and convergence speed. This work may serve as a foundation for further exploration of pretraining and finetuning in the context of IL.

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