LEARNING TO REPRESENT ACTION VALUES AS A HYPERGRAPH ON THE ACTION VERTICES

Abstract

Action-value estimation is a critical component of many reinforcement learning (RL) methods whereby sample complexity relies heavily on how fast a good estimator for action value can be learned. By viewing this problem through the lens of representation learning, good representations of both state and action can facilitate action-value estimation. While advances in deep learning have seamlessly driven progress in learning state representations, given the specificity of the notion of agency to RL, little attention has been paid to learning action representations. We conjecture that leveraging the combinatorial structure of multi-dimensional action spaces is a key ingredient for learning good representations of action. To test this, we set forth the action hypergraph networks framework-a class of functions for learning action representations in multi-dimensional discrete action spaces with a structural inductive bias. Using this framework we realise an agent class based on a combination with deep Q-networks, which we dub hypergraph Q-networks. We show the effectiveness of our approach on a myriad of domains: illustrative prediction problems under minimal confounding effects, Atari 2600 games, and discretised physical control benchmarks.

1. INTRODUCTION

Representation learning methods have helped shape recent progress in RL by enabling a capacity for learning good representations of state. This is in spite of the fact that, traditionally, representation learning was less often explored in the RL context. As such, the de facto representation learning techniques which are widely used in RL were developed under other machine learning paradigms (Bengio et al., 2013) . Nevertheless, RL brings some unique problems to the topic of representation learning, with exciting headway being made in identifying and exploring such topics. Action-value estimation is a critical component of the RL paradigm (Sutton & Barto, 2018) . Hence, how to effectively learn estimators for action value from training samples is one of the major problems studied in RL. We set out to study this problem through the lens of representation learning, focusing particularly on learning representations of action in multi-dimensional discrete action spaces. While action values are conditioned on both state and action and as such good representations of both would be beneficial, there has been comparatively little research on learning action representations. We frame this problem as learning a decomposition of the action-value function that is structured in such a way to leverage the combinatorial structure of multi-dimensional discrete action spaces. This structure is an inductive bias which we incorporate in the form of architectural assumptions. We present this approach as a framework to flexibly build architectures for learning representations of multi-dimensional discrete actions by leveraging various orders of their underlying sub-action combinations. Our architectures can be combined in succession with any other architecture for learning state representations and trained end-to-end using backpropagation, without imposing any change to the RL algorithm. We remark that designing representation learning methods by incorporating some form of structural inductive biases is highly common in deep learning, resulting in highly-publicised architectures such as convolutional, recurrent, and graph networks (Battaglia et al., 2018) . We first demonstrate the effectiveness of our approach in illustrative, structured prediction problems. Then, we argue for the ubiquity of similar structures and test our approach in standard RL problems. * Correspondence to: Arash Tavakoli <a.tavakoli@imperial.ac.uk>. 1

