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Do off-policy policy gradient methods exist?

I know that policy gradient methods themselves using the policy function for sampling rollouts. But can't we easily have a model for sampling from the environment? If so, I've never seen this done before.

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Absolutely, it’s a really interesting problem. Here is a paper detailing off policy actor critic. This is important because this method can also support continuous actions.

The general idea of off-policy algorithms is to compare the actions performed by a behaviour policy (which is actually acting in the world) with the actions the target policy (the policy we want to learn) would have chosen. Using this comparison we can determine a ratio (0 <= Rho <= 1) which can scale the update to the target policy by the probability of the target policy taking that action. A higher Rho, the more alike the 2 policies are and this increases the magnitude of the learning update for the target policy for that step. A Rho of 0, and the update is ignored.

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