Thanks Flo for pointing this out. I agree with your reasoning for why we want the Markov property. For the second modification, we can sample a rollout from the agent policy rather than computing a penalty over all possible rollouts. For example, we could randomly choose an integer N, roll out the agent policy and the inaction policy for N steps, and then compare the resulting states. This does require a complete environment model (which does make it more complicated to apply standard RL), while inaction rollouts only require a partial environment model (predicting the outcome of the noop action in each state). If you don’t have a complete environment model, then you can still use the first modification (sampling a baseline state from the inaction rollout).
Thanks Flo for pointing this out. I agree with your reasoning for why we want the Markov property. For the second modification, we can sample a rollout from the agent policy rather than computing a penalty over all possible rollouts. For example, we could randomly choose an integer N, roll out the agent policy and the inaction policy for N steps, and then compare the resulting states. This does require a complete environment model (which does make it more complicated to apply standard RL), while inaction rollouts only require a partial environment model (predicting the outcome of the noop action in each state). If you don’t have a complete environment model, then you can still use the first modification (sampling a baseline state from the inaction rollout).