Geometry and convergence of natural policy gradient methods

Global Convergence of Policy Gradient Methods for Linearized Control Problems

Direct policy gradient methods for reinforcement learning and continuous control problems are a popular approach for a variety of reasons: 1) they are easy to implement without explicit knowledge of the underlying model 2) they are an “end-to-end” approach, directly optimizing the performance metric of interest 3) they inherently allow for richly parameterized policies. A notable drawback is th...

Gradient Convergence in Gradient Methods

For the classical gradient method xt+1 = xt − γt∇f(xt) and several deterministic and stochastic variants, we discuss the issue of convergence of the gradient sequence ∇f(xt) and the attendant issue of stationarity of limit points of xt. We assume that ∇f is Lipschitz continuous, and that the stepsize γt diminishes to 0 and satisfies standard stochastic approximation conditions. We show that eit...

A Natural Policy Gradient

We provide a natural gradient method that represents the steepest descent direction based on the underlying structure of the parameter space. Although gradient methods cannot make large changes in the values of the parameters, we show that the natural gradient is moving toward choosing a greedy optimal action rather than just a better action. These greedy optimal actions are those that would be...

A Natural Policy Gradient

Gradient Convergence in Gradient methods with Errors

We consider the gradient method xt+1 = xt + γt(st + wt), where st is a descent direction of a function f : �n → � and wt is a deterministic or stochastic error. We assume that ∇f is Lipschitz continuous, that the stepsize γt diminishes to 0, and that st and wt satisfy standard conditions. We show that either f(xt) → −∞ or f(xt) converges to a finite value and ∇f(xt) → 0 (with probability 1 in t...