Distributional Meta-Gradient Reinforcement Learning

Meta-gradient reinforcement learning (RL) algorithms have substantially boosted the performance of RL agents by learning an adaptive return. All the existing algorithms adhere to the same reward learning regime, where the adaptive return is simply formulated in the form of expected cumulative rewards, upon which the policy and critic update rules are specified under well adopted distance metrics. In this paper, we present a novel algorithm which builds on the success of meta-gradient RL algorithms and effectively improves such algorithms by following a simple recipe, i.e., going beyond the expected return to formulate and learn the return in a more expressive form, value distributions. To this end, we first formulate a distributional return that could effectively capture bootstrapping and discounting behaviors over distributions, to form an informative distributional return target in value update. Then we derive an efficient meta update rule to learn the adaptive distributional return with meta-gradients. For empirical evaluation, we first present an illustrative example on a toy two-color grid-world domain, which validates the benefit of learning distributional return; then we conduct extensive comparisons on a large-scale RL benchmark Atari 2600, where we confirm that our proposed method with distributional return works seamlessly well with the actor-critic framework and leads to state-of-the-art median human normalized score among meta-gradient RL literature.