  Policy gradient methods are appealing in deep reinforcement learning but
suffer from high variance of gradient estimate. To reduce the variance, the
state value function is applied commonly. However, the effect of the state
value function becomes limited in stochastic dynamic environments, where the
unexpected state dynamics and rewards will increase the variance. In this
paper, we propose to replace the state value function with a novel hindsight
value function, which leverages the information from the future to reduce the
variance of the gradient estimate for stochastic dynamic environments.
  Particularly, to obtain an ideally unbiased gradient estimate, we propose an
information-theoretic approach, which optimizes the embeddings of the future to
be independent of previous actions. In our experiments, we apply the proposed
hindsight value function in stochastic dynamic environments, including
discrete-action environments and continuous-action environments. Compared with
the standard state value function, the proposed hindsight value function
consistently reduces the variance, stabilizes the training, and improves the
eventual policy.
