In state of the art model-free off-policy deep reinforcement learning (RL), a replay memory is used to store past experience and derive all network updates. Even if both state and action spaces are continuous, the replay memory only holds a finite number of transitions. We represent these transitions in a data graph and link its structure to soft divergence. By selecting a subgraph with a favorable structure, we construct a simple Markov Decision Process (MDP) for which exact Q-values can be computed efficiently as more data comes in -resulting in a QGRAPH. We show that the Q-value for each transition in the simplified MDP is a lower bound of the Q-value for the same transition in the original continuous Q-learning problem. By using these lower bounds in TD learning, our method is less prone to soft divergence and exhibits increased sample efficiency while being more robust to hyperparameters. QGRAPHs also retain information from transitions that have already been overwritten in the replay memory, which can decrease the algorithm's sensitivity to the replay memory capacity.
The paper proposes Qgraph, an algorithm that  addresses the problem of extrapolation error that appear in RL tasks with continuous action spaces. The authors describe a method to construct a graph from transitions generated by some policy. In this graph nodes correspond to states and (s, a, r, s’, t) define transitions between these nodes. Then this representation is simplified and  used to compute Q-values using methods for tabular MDPs.
The related work section is missing several methods that attempt to address the same problem. Batch Constrained Q-learning (Fujimoto etal, 2018) introduces a formulation of Q-learning that constrains action selection with a generative model trained on a replay buffer in order to omit unseen actions. BEAR-QL (Kumar etal, 2019) describes a similar approach that uses a hard constraint based on MMD. It would be interesting to discuss connections with the recent work on off-policy batch RL.
The clarity of the paper can be improved. In particular, I have several questions regarding the method:
1) How are node of the graph are constructed? Does one state correspond to a single node or several states are merged into a different node?
2) How the actions are selected?
3) What are the assumption regarding the initial state distribution? Does the set of initial states have to be finite?
4) If two similar states appear in different branches of the graphs, are the corresponding nodes merged or not?
5) If the considered environments are deterministic, what is the motivation for stochastic approximation of dynamic programming?
The approach has several major limitations. One of the main limitations of the approach is that it can be applied only to deterministic tasks. Although it is not stated clearly in the paper, it seems also requires to have a finite set of initial states. 
The experimental evaluation is performed on a limited set of tasks and it is rather unclear whether the method can be scaled to higher dimensional control problems.
Overall, I feel that the paper needs to be significantly improved.