  This paper considers policy search in continuous state-action reinforcement
learning problems. Typically, one computes search directions using a classic
expression for the policy gradient called the Policy Gradient Theorem, which
decomposes the gradient of the value function into two factors: the score
function and the Q-function. This paper presents four results:(i) an
alternative policy gradient theorem using weak (measure-valued) derivatives
instead of score-function is established; (ii) the stochastic gradient
estimates thus derived are shown to be unbiased and to yield algorithms that
converge almost surely to stationary points of the non-convex value function of
the reinforcement learning problem; (iii) the sample complexity of the
algorithm is derived and is shown to be $O(1/\sqrt(k))$; (iv) finally, the
expected variance of the gradient estimates obtained using weak derivatives is
shown to be lower than those obtained using the popular score-function
approach. Experiments on OpenAI gym pendulum environment show superior
performance of the proposed algorithm.
