Reward-Weighted Regression Converges to a Global Optimum
This provides theoretical guarantees for a widely used reinforcement learning algorithm, addressing a foundational gap in understanding its convergence properties.
The paper tackled the open question of whether Reward-Weighted Regression (RWR) converges to an optimal policy, proving for the first time that it converges to a global optimum without function approximation in a general compact setting, and showing R-linear convergence of the state-value function in finite spaces.
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.