In policy gradient methods, the gradient of the performance objective is estimated as an expectation over trajectories. Each trajectory's contribution to this estimate is the product of its cumulative reward and the gradient of its log-probability. Given this structure, why can these methods effectively handle tasks with non-differentiable reward functions, such as a simple binary reward for winning or losing a game?

For a policy gradient method to be applicable, the cumulative reward function must be differentiable, as its derivative is required when computing the gradient of the policy performance objective.