  Combining deep model-free reinforcement learning with on-line planning is a
promising approach to building on the successes of deep RL. On-line planning
with look-ahead trees has proven successful in environments where transition
models are known a priori. However, in complex environments where transition
models need to be learned from data, the deficiencies of learned models have
limited their utility for planning. To address these challenges, we propose
TreeQN, a differentiable, recursive, tree-structured model that serves as a
drop-in replacement for any value function network in deep RL with discrete
actions. TreeQN dynamically constructs a tree by recursively applying a
transition model in a learned abstract state space and then aggregating
predicted rewards and state-values using a tree backup to estimate Q-values. We
also propose ATreeC, an actor-critic variant that augments TreeQN with a
softmax layer to form a stochastic policy network. Both approaches are trained
end-to-end, such that the learned model is optimised for its actual use in the
tree. We show that TreeQN and ATreeC outperform n-step DQN and A2C on a
box-pushing task, as well as n-step DQN and value prediction networks (Oh et
al. 2017) on multiple Atari games. Furthermore, we present ablation studies
that demonstrate the effect of different auxiliary losses on learning
transition models.
