  Value function is the central notion of Reinforcement Learning (RL). Value
estimation, especially with function approximation, can be challenging since it
involves the stochasticity of environmental dynamics and reward signals that
can be sparse and delayed in some cases. A typical model-free RL algorithm
usually estimates the values of a policy by Temporal Difference (TD) or Monte
Carlo (MC) algorithms directly from rewards, without explicitly taking dynamics
into consideration. In this paper, we propose Value Decomposition with Future
Prediction (VDFP), providing an explicit two-step understanding of the value
estimation process: 1) first foresee the latent future, 2) and then evaluate
it. We analytically decompose the value function into a latent future dynamics
part and a policy-independent trajectory return part, inducing a way to model
latent dynamics and returns separately in value estimation. Further, we derive
a practical deep RL algorithm, consisting of a convolutional model to learn
compact trajectory representation from past experiences, a conditional
variational auto-encoder to predict the latent future dynamics and a convex
return model that evaluates trajectory representation. In experiments, we
empirically demonstrate the effectiveness of our approach for both off-policy
and on-policy RL in several OpenAI Gym continuous control tasks as well as a
few challenging variants with delayed reward.
