Policy optimization methods benefit from a simple and tractable policy parametrization, usually the Gaussian for continuous action spaces. In this paper, we consider a broader policy family that remains tractable: the $q$-exponential family. This family of policies is flexible, allowing the specification of both heavy-tailed policies ($q>1$) and light-tailed policies ($q<1$). This paper examines the interplay between $q$-exponential policies for several actor-critic algorithms conducted on both online and offline problems. We find that heavy-tailed policies are more effective in general and can consistently improve on Gaussian. In particular, we find the Student's t-distribution to be more stable than the Gaussian across settings and that a heavy-tailed $q$-Gaussian for Tsallis Advantage Weighted Actor-Critic consistently performs well in offline benchmark problems. In summary, we find that the Student's t policy a strong candidate for drop-in replacement to the Gaussian. Our code is available at \url{https://github.com/lingweizhu/qexp}.

Sparse continuous policies are distributions that can choose some actions at random yet keep strictly zero probability for the other actions, which are radically different from the Gaussian. They have important real-world implications, e.g. in modeling safety-critical tasks like medicine. The combination of offline reinforcement learning and sparse policies provides a novel paradigm that enables learning completely from logged datasets a safety-aware sparse policy. However, sparse policies can cause difficulty with the existing offline algorithms which require evaluating actions that fall outside of the current support. In this paper, we propose the first offline policy optimization algorithm that tackles this challenge: Fat-to-Thin Policy Optimization (FtTPO). Specifically, we maintain a fat (heavy-tailed) proposal policy that effectively learns from the dataset and injects knowledge to a thin (sparse) policy, which is responsible for interacting with the environment. We instantiate FtTPO with the general $q$-Gaussian family that encompasses both heavy-tailed and sparse policies and verify that it performs favorably in a safety-critical treatment simulation and the standard MuJoCo suite. Our code is available at https://github.com/lingweizhu/fat2thin.

In this paper we investigate the properties of representations learned by deep reinforcement learning systems. Much of the early work on representations for reinforcement learning focused on designing fixed-basis architectures to achieve properties thought to be desirable, such as orthogonality and sparsity. In contrast, the idea behind deep reinforcement learning methods is that the agent designer should not encode representational properties, but rather that the data stream should determine the properties of the representation—good representations emerge under appropriate training schemes. In this paper we bring these two perspectives together, empirically investigating the properties of representations that support transfer in reinforcement learning. We introduce and measure six representational properties over more than 25,000 agent-task settings. We consider Deep Q-learning agents with different auxiliary losses in a pixel-based navigation environment, with source and transfer tasks corresponding to different goal locations. We develop a method to better understand why some representations work better for transfer, through a systematic approach varying task similarity and measuring and correlating representation properties with transfer performance. We demonstrate the generality of the methodology by investigating representations learned by a Rainbow agent that successfully transfers across Atari 2600 game modes.