In policy optimization, an importance-sampled surrogate objective is often used to approximate the true on-policy objective. A key mathematical property of this surrogate is that its gradient, when evaluated at the reference policy (i.e., the policy used to collect the data), is identical to the true on-policy policy gradient. What is the most significant implication of this property for the training process?

In a policy optimization algorithm that uses an importance-sampled surrogate objective, a developer observes that the gradient of the surrogate objective is identical to the on-policy policy gradient at the start of an update step. However, after applying a single gradient update to the policy parameters, the two gradients are no longer identical. This divergence indicates a flaw in the algorithm's implementation.

In policy optimization, an objective function is often constructed using data from a fixed, older policy (the 'reference policy') to estimate the performance of a new policy being optimized. This objective uses an importance sampling ratio: Expectation_over_trajectories_from_reference_policy [ (Probability_of_trajectory_under_new_policy / Probability_of_trajectory_under_reference_policy) * Reward_of_trajectory ]. A critical property of this objective is that its gradient, when evaluated at the