Improper Reinforcement Learning with Gradient-based Policy Optimization

We consider an improper reinforcement learning setting where a 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. This can be useful in tuning across controllers, learnt possibly in mismatched or simulated environments, to obtain a good controller for a given target environment with relatively few trials. \par We propose a gradient-based approach that operates over a class of improper mixtures of the controllers. We derive convergence rate guarantees for the approach assuming access to a gradient oracle. 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. Numerical results on (i) the standard control theoretic benchmark of stabilizing an inverted pendulum and (ii) a constrained queueing task show that our improper policy optimization algorithm can stabilize the system even when the base policies at its disposal are unstable\footnote{Under review. Please do not distribute.}.