Title: Polyphonic Music Composition: An Adversarial Inverse Reinforcement Learning Approach. Abstract: Most  recent  approaches  to  automatic  music  harmony composition adopt deep supervised learning to  train  a  model  using  a  set  of  human  composed songs as training data.  However, these approaches suffer  from  inherent  limitations  from  the  chosen deep learning models which may lead to unpleasing harmonies.  This paper explores an alternative approach to harmony composition using a combination  of  novel  Deep  Supervised  Learning,  DeepReinforcement  Learning  and  Inverse  Reinforcement Learning techniques.  In this novel approach, our  model  selects  the  next  chord  in  the  composition(action)  based  on  the  previous  notes(states), therefore allowing us to model harmony composition as a reinforcement learning problem in which we  look  to  maximize  an  overall  accumulated  reward.   However,  designing  an  appropriate reward function is known to be a very tricky and difficult process.  To  overcome  this  problem  we  propose learning  a  reward  function  from  a  set  of  human-composed  tracks  using  Adversarial  Inverse  Reinforcement Learning. We start by training a Bi-axial LSTM  model  using  supervised  learning  and  improve upon it by tuning it using Deep Q-learning. Instead of using GANs to generate a similar music composition  to  human  compositions  directly,  we adopt GANs to learn the reward function of the music trajectories from human compositions. We then combine the learned reward function with a reward based on music theory rules to improve the generation of the model trained by supervised learning. The  results  show  improvement  over  a  pre-trained model  without  training  with  reinforcement  learning with respect to a set of objective metrics and preference from subjective user evaluation.