Global Optimality Guarantees For Policy Gradient Methods
This addresses convergence issues in reinforcement learning for control problems, offering theoretical guarantees that are incremental but important for improving algorithm reliability.
The paper tackles the non-convex optimization problem in policy gradient methods for control by identifying structural properties that eliminate suboptimal stationary points, ensuring global optimality guarantees and providing convergence rates under stronger conditions.
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.