Global Optimality Guarantees For Policy Gradient Methods

Policy gradients methods apply to complex, poorly understood, control problems by performing stochastic gradient descent over a parameterized class of polices. Unfortunately, even for simple control problems solvable by standard dynamic programming techniques, policy gradient algorithms face non-convex optimization problems and are widely understood to converge only to a stationary point. This work identifies structural properties -- shared by several classic control problems -- that ensure the policy gradient objective function has no suboptimal stationary points despite being non-convex. When these conditions are strengthened, this objective satisfies a Polyak-lojasiewicz (gradient dominance) condition that yields convergence rates. We also provide bounds on the optimality gap of any stationary point when some of these conditions are relaxed.