Clipped Utility Function with Upper-Bound Clipping

An agent's policy is being updated using an objective function that relies on importance sampling. Consider a single time step t in a trajectory where the calculated advantage A(s_t, a_t) is large and positive. At the same time, the importance sampling ratio π_θ(a_t|s_t) / π_θ_ref(a_t|s_t) is also large (e.g., 5.0), indicating the current policy is much more likely to choose action a_t than the reference policy was.

Given the objective function U(τ; θ) = Σ [π_θ(a_t|s_t) / π_θ_ref(a_t|s_t)] * A(s_t, a_t), what is the most direct consequence of this situation for this specific time step's contribution to the policy update?

Calculating Trajectory Utility with Importance Sampling

In the context of updating a policy using an objective function with importance sampling, if the ratio of the current policy's probability to the reference policy's probability for a given action is greater than 1, this will always increase the likelihood of that action being selected in the subsequent policy update.