  Reinforcement learning algorithms such as the deep deterministic policy
gradient algorithm (DDPG) has been widely used in continuous control tasks.
However, the model-free DDPG algorithm suffers from high sample complexity. In
this paper we consider the deterministic value gradients to improve the sample
efficiency of deep reinforcement learning algorithms. Previous works consider
deterministic value gradients with the finite horizon, but it is too myopic
compared with infinite horizon. We firstly give a theoretical guarantee of the
existence of the value gradients in this infinite setting. Based on this
theoretical guarantee, we propose a class of the deterministic value gradient
algorithm (DVG) with infinite horizon, and different rollout steps of the
analytical gradients by the learned model trade off between the variance of the
value gradients and the model bias. Furthermore, to better combine the
model-based deterministic value gradient estimators with the model-free
deterministic policy gradient estimator, we propose the deterministic
value-policy gradient (DVPG) algorithm. We finally conduct extensive
experiments comparing DVPG with state-of-the-art methods on several standard
continuous control benchmarks. Results demonstrate that DVPG substantially
outperforms other baselines.
