Improper Learning with Gradient-based Policy Optimization

We consider an improper reinforcement learning setting where the learner is given M base controllers for an unknown Markov Decision Process, and wishes to combine them optimally to produce a potentially new controller that can outperform each of the base ones. We propose a gradient-based approach that operates over a class of improper mixtures of the controllers. The value function of the mixture and its gradient may not be available in closed-form; however, we show that we can employ rollouts and simultaneous perturbation stochastic approximation (SPSA) for explicit gradient descent optimization. We derive convergence and convergence rate guarantees for the approach assuming access to a gradient oracle. Numerical results on a challenging constrained queueing task show that our improper policy optimization algorithm can stabilize the system even when each constituent policy at its disposal is unstable.