# Should we multiply the target of actor by the importance sampling ratio when prioritized replay is applied to DDPG?

According to PER, we have to multiply the $$Q$$ error $$\delta_i$$ by the importance sampling ratio to correct the bias introduced by the imbalance sampling of PER, where importance sampling ratio is defined $$w_i=\left({1\over N}{1\over P(i)}\right)^\beta$$ in which $$1/N$$ is the probability of drawing a sample uniformly from the buffer, and $$P(i)$$ is the probability of drawing a sample from PER.

I'm wondering if we have to do the same to the target of the actor when we apply PER to DDPG. That is, multiplying $$-Q(s_i, \mu(s_i))$$ by $$w_i$$, where $$\mu$$ is the outcome of the actor.

In my opinion, it is necessary. And I've done some experiments in the gym environment BipedalWalker-v2. The results, however, is quite confusing: I constantly get better performance when I do not apply importance sampling to the actor. Why would this be the case?