Learning Compositional Neural Programs with Recursive Tree Search and
  Planning
  We propose a novel reinforcement learning algorithm, AlphaNPI, that
incorporates the strengths of Neural Programmer-Interpreters (NPI) and
AlphaZero. NPI contributes structural biases in the form of modularity,
hierarchy and recursion, which are helpful to reduce sample complexity, improve
generalization and increase interpretability. AlphaZero contributes powerful
neural network guided search algorithms, which we augment with recursion.
AlphaNPI only assumes a hierarchical program specification with sparse rewards:
1 when the program execution satisfies the specification, and 0 otherwise.
Using this specification, AlphaNPI is able to train NPI models effectively with
RL for the first time, completely eliminating the need for strong supervision
in the form of execution traces. The experiments show that AlphaNPI can sort as
well as previous strongly supervised NPI variants. The AlphaNPI agent is also
trained on a Tower of Hanoi puzzle with two disks and is shown to generalize to
puzzles with an arbitrary number of disk
