Online imitation learning (IL), particularly on-policy distillation, has emerged as a strong LLM post-training approach, often outperforming offline supervised fine-tuning (SFT). Yet a principled understanding of when and why online interaction helps remains unclear. In this work, we challenge the view that error accumulation is the main source of online IL's advantage, and instead show that the benefits of online interaction depend critically on whether the setting is realizable, i.e., whether the student policy class can represent the expert policy. Under realizability, we empirically find that offline IL already matches expert performance. In contrast, in non-realizable (misspecified) settings, we prove that offline IL encounters an information-theoretic bottleneck even when horizon $H=1$, and propose a structural characterization of misspecification relative to the reward, under which online IL provably achieves high performance despite a large distributional mismatch between the expert and student policies.
Post-training is essential for refining the domain-specific capabilities of large language models (LLMs), yet existing reward optimization and distribution matching methods tightly couple policy exploration with distribution alignment. This coupling forces expensive exploration d…
Reinforcement Learning (RL) post-training is increasingly used to adapt foundation models for reasoning, planning, and feedback-driven robot-learning pipelines, but constrained post-training resources are often summarized by a single total FLOP budget. We study the fixed-budget d…
Pretrained vision-language-action (VLA) policies provide strong language-conditioned manipulation knowledge, but they remain largely vision-driven and can struggle once manipulation enters contact states where the scene is occluded, depth is ambiguous, or small force errors push…
Large language model (LLM) post-training is essential for improving reasoning, adaptation, and alignment. Existing methods mainly follow two paradigms: reinforcement learning (RL) and on-policy distillation (OPD). However, RL relies on coarse-grained outcome supervision, resultin…
Reinforcement learning (RL) has become central to improving large language models (LLMs) on complex reasoning tasks, yet RL post-training is largely studied in isolation from the pretraining that precedes it. As a result, two basic questions remain open: (1) how do pretraining ch…
Partial differential equations (PDEs) are foundational to modeling in science and engineering, but constructing reliable numerical solvers remains labor-intensive, demanding expert knowledge of discretization schemes, stability conditions, and boundary treatments. Recent work has…