Distributional Reinforcement Learning with Unconstrained Monotonic Neural Networks
This work addresses a specific challenge in distributional RL for researchers and practitioners by enabling more flexible distribution modeling, though it appears incremental as it builds on existing distributional RL methods with a novel architectural choice.
The paper tackles the problem of representing the full probability distribution of returns in reinforcement learning by introducing a method that learns three continuous representations (PDF, CDF, QF) using unconstrained monotonic neural networks, resulting in a new algorithm (UMDQN) that empirically compares probability metrics like KL divergence, Cramer distance, and Wasserstein distance, highlighting their strengths and weaknesses.
The distributional reinforcement learning (RL) approach advocates for representing the complete probability distribution of the random return instead of only modelling its expectation. A distributional RL algorithm may be characterised by two main components, namely the representation of the distribution together with its parameterisation and the probability metric defining the loss. The present research work considers the unconstrained monotonic neural network (UMNN) architecture, a universal approximator of continuous monotonic functions which is particularly well suited for modelling different representations of a distribution. This property enables the efficient decoupling of the effect of the function approximator class from that of the probability metric. The research paper firstly introduces a methodology for learning different representations of the random return distribution (PDF, CDF and QF). Secondly, a novel distributional RL algorithm named unconstrained monotonic deep Q-network (UMDQN) is presented. To the authors' knowledge, it is the first distributional RL method supporting the learning of three, valid and continuous representations of the random return distribution. Lastly, in light of this new algorithm, an empirical comparison is performed between three probability quasi-metrics, namely the Kullback-Leibler divergence, Cramer distance, and Wasserstein distance. The results highlight the main strengths and weaknesses associated with each probability metric together with an important limitation of the Wasserstein distance.