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Main idea: Standard BC minimizes −logπ(a∣s), meaning it learns π(a∣s)≈pdemo(a∣s) by fitting the empirical data distribution.
BC only observes trajectories sampled from the true policy, not the true policy itself.
Example: Suppose you observe “go left” once. Many policies are still possible:
-Policy A: left 100%
-Policy B: left 80%, right 20%
-Policy C: left 50%, right 50%
This affects the system's entropy and changes RL's ability to explore. Posterior BC preserves imitation performance while avoiding unwarranted confidence about poorly observed parts of the state space.
TLDR: preserve entropy/stochasticity for downstream RL during BC training.