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The policy gradient theorem states that the policy should only be updated instates that are visited by the current policy, which leads to insufficientplanning in the off-policy states, and thus to convergence to suboptimalpolicies. We tackle this planning issue by extending the policy gradient theoryto policy updates with respect to any state density. Under these generalizedpolicy updates, we show convergence to optimality under a necessary andsufficient condition on the updates' state densities, and thereby solve theaforementioned planning issue. We also prove asymptotic convergence rates thatsignificantly improve those in the policy gradient literature.  To implement the principles prescribed by our theory, we propose an agent, DrJekyll & Mr Hyde (JH), with a double personality: Dr Jekyll purely exploitswhile Mr Hyde purely explores. JH's independent policies allow to record twoseparate replay buffers: one on-policy (Dr Jekyll's) and one off-policy (MrHyde's), and therefore to update JH's models with a mixture of on-policy andoff-policy updates. More than an algorithm, JH defines principles foractor-critic algorithms to satisfy the requirements we identify in ouranalysis. We extensively test on finite MDPs where JH demonstrates a superiorability to recover from converging to a suboptimal policy without impairing itsspeed of convergence. We also implement a deep version of the algorithm andtest it on a simple problem where it shows promising results.

Dr Jekyll and Mr Hyde: the Strange Case of Off-Policy Policy Updates