  Reward-Weighted Regression (RWR) belongs to a family of widely known
iterative Reinforcement Learning algorithms based on the
Expectation-Maximization framework. In this family, learning at each iteration
consists of sampling a batch of trajectories using the current policy and
fitting a new policy to maximize a return-weighted log-likelihood of actions.
Although RWR is known to yield monotonic improvement of the policy under
certain circumstances, whether and under which conditions RWR converges to the
optimal policy have remained open questions. In this paper, we provide for the
first time a proof that RWR converges to a global optimum when no function
approximation is used, in a general compact setting. Furthermore, for the
simpler case with finite state and action spaces we prove R-linear convergence
of the state-value function to the optimum.
