In the pursuit of finding an optimal policy, reinforcement learning (RL) methods generally ignore the properties of learned policies apart from their expected return. Thus, even when successful, it is difficult to characterize which policies will be learned and what they will do. In this work, we present a theoretical framework for policy optimization that guarantees convergence to a particular optimal policy, via vanishing entropy regularization and a *temperature decoupling gambit*. Our approach realizes an interpretable, diversity-preserving optimal policy as the regularization temperature vanishes and ensures the convergence of policy derived objects--value functions and return distributions. In a particular instance of our method, for example, the realized policy samples all optimal actions uniformly. Leveraging our temperature decoupling gambit, we present an algorithm that estimates, to arbitrary accuracy, the return distribution associated to its interpretable, diversity-preserving optimal policy.

When decisions are made at high frequency, traditional reinforcement learning (RL) methods struggle to accurately estimate action values. In turn, their performance is inconsistent and often poor. Whether the performance of distributional RL (DRL) agents suffers similarly, however, is unknown. In this work, we establish that DRL agents *are* sensitive to the decision frequency. We prove that action-conditioned return distributions collapse to their underlying policy's return distribution as the decision frequency increases. We quantify the rate of collapse of these return distributions and exhibit that their statistics collapse at different rates. Moreover, we define distributional perspectives on action gaps and advantages. In particular, we introduce the *superiority* as a probabilistic generalization of the advantage---the core object of approaches to mitigating performance issues in high-frequency value-based RL. In addition, we build a superiority-based DRL algorithm. Through simulations in an option-trading domain, we validate that proper modeling of the superiority distribution produces improved controllers at high decision frequencies.

Cooperative communication plays a fundamental role in theories of human-human interaction--cognition, culture, development, language, etc.--as well as human-robot interaction. The core challenge in cooperative communication is the problem of common ground: having enough shared knowledge and understanding to successfully communicate. Prior models of cooperative communication, however, uniformly assume the strongest form of common ground, perfect and complete knowledge sharing, and, therefore, fail to capture the core challenge of cooperative communication. We propose a general theory of cooperative communication that is mathematically principled and explicitly defines a spectrum of common ground possibilities, going well beyond that of perfect and complete knowledge sharing, on spaces that permit arbitrary representations of data and hypotheses. Our framework is a strict generalization of prior models of cooperative communication. After considering a parametric form of common ground and viewing the data selection and hypothesis inference processes of communication as encoding and decoding, we establish a connection to variational autoencoding, a powerful model in modern machine learning. Finally, we carry out a series of empirical simulations to support and elaborate on our theoretical results.