Policy Gradient For Multidimensional Action Spaces: Action Sampling and Entropy Bonus

In recent years deep reinforcement learning has been shown to be adept at solving sequential decision processes with high-dimensional state spaces such as in the Atari games. Many reinforcement learning problems, however, involve high-dimensional discrete action spaces as well as high-dimensional state spaces. In this paper, we develop a novel policy gradient methodology for the case of large multidimensional discrete action spaces. We propose two approaches for creating parameterized policies: LSTM parameterization and a Modified MDP (MMDP) giving rise to Feed-Forward Network (FFN) parameterization. Both of these approaches provide expressive models to which backpropagation can be applied for training. We then consider entropy bonus, which is typically added to the reward function to enhance exploration. In the case of high-dimensional action spaces, calculating the entropy and the gradient of the entropy requires enumerating all the actions in the action space and running forward and backpropagation for each action, which may be computationally infeasible. We develop several novel unbiased estimators for the entropy bonus and its gradient. Finally, we test our algorithms on two environments: a multi-hunter multi-rabbit grid game and a multi-agent multi-arm bandit problem.