Large language models demonstrate remarkable capabilities after learning from enormous volumes of text data (Anil et al., 2023; Hoffmann et al., 2022; OpenAI, 2023). Yet, reinforcement learning from human feedback (RLHF) greatly improves their behavior even after only tens of thousands of interactions (Bai et al., 2022; Glaese et al., 2022; Ouyang et al., 2022; Stiennon et al., 2020). The uptake of chatbots affords opportunities to gather increasing volumes of human feedback, with each engagement eliciting expressions of satisfaction or preference (OpenAI, 2022). It is natural to wonder what new capabilities may emerge with this growing source of data. Superhuman ingenuity remains an alluring possibility. With increasing volumes, more can be inferred from human feedback.

Thompson sampling (TS) is a popular heuristic for action selection, but it requires sampling from a posterior distribution. Unfortunately, this can become computationally intractable in complex environments, such as those modeled using neural networks. Approximate posterior samples can produce effective actions, but only if they reasonably approximate joint predictive distributions of outputs across inputs. Notably, accuracy of marginal predictive distributions does not suffice. Epistemic neural networks (ENNs) are designed to produce accurate joint predictive distributions. We compare a range of ENNs through computational experiments that assess their performance in approximating TS across bandit and reinforcement learning environments. The results indicate that ENNs serve this purpose well and illustrate how the quality of joint predictive distributions drives performance. Further, we demonstrate that the \textit{epinet} -- a small additive network that estimates uncertainty -- matches the performance of large ensembles at orders of magnitude lower computational cost. This enables effective application of TS with computation that scales gracefully to complex environments.

In machine learning, an agent needs to estimate uncertainty to efficiently explore and adapt and to make effective decisions. A common approach to uncertainty estimation maintains an ensemble of models. In recent years, several approaches have been proposed for training ensembles, and conflicting views prevail with regards to the importance of various ingredients of these approaches. In this paper, we aim to address the benefits of two ingredients -- prior functions and bootstrapping -- which have come into question. We show that prior functions can significantly improve an ensemble agent's joint predictions across inputs and that bootstrapping affords additional benefits if the signal-to-noise ratio varies across inputs. Our claims are justified by both theoretical and experimental results.

Posterior predictive distributions quantify uncertainties ignored by point estimates. This paper introduces \textit{The Neural Testbed}, which provides tools for the systematic evaluation of agents that generate such predictions. Crucially, these tools assess not only the quality of marginal predictions per input, but also joint predictions given many inputs. Joint distributions are often critical for useful uncertainty quantification, but they have been largely overlooked by the Bayesian deep learning community. We benchmark several approaches to uncertainty estimation using a neural-network-based data generating process. Our results reveal the importance of evaluation beyond marginal predictions. Further, they reconcile sources of confusion in the field, such as why Bayesian deep learning approaches that generate accurate marginal predictions perform poorly in sequential decision tasks, how incorporating priors can be helpful, and what roles epistemic versus aleatoric uncertainty play when evaluating performance. We also present experiments on real-world challenge datasets, which show a high correlation with testbed results, and that the importance of evaluating joint predictive distributions carries over to real data. As part of this effort, we opensource The Neural Testbed, including all implementations from this paper.

Reinforcement learning agents have demonstrated remarkable achievements in simulated environments. Data efficiency poses an impediment to carrying this success over to real environments. The design of data-efficient agents calls for a deeper understanding of information acquisition and representation. We develop concepts and establish a regret bound that together offer principled guidance. The bound sheds light on questions of what information to seek, how to seek that information, and what information to retain. To illustrate concepts, we design simple agents that build on them and present computational results that demonstrate improvements in data efficiency. Other learning paradigms are about minimization; reinforcement learning is about maximization.

We study the use of hypermodels to represent epistemic uncertainty and guide exploration. This generalizes and extends the use of ensembles to approximate Thompson sampling. The computational cost of training an ensemble grows with its size, and as such, prior work has typically been limited to ensembles with tens of elements. We show that alternative hypermodels can enjoy dramatic efficiency gains, enabling behavior that would otherwise require hundreds or thousands of elements, and even succeed in situations where ensemble methods fail to learn regardless of size. This allows more accurate approximation of Thompson sampling as well as use of more sophisticated exploration schemes. In particular, we consider an approximate form of information-directed sampling and demonstrate performance gains relative to Thompson sampling. As alternatives to ensembles, we consider linear and neural network hypermodels, also known as hypernetworks. We prove that, with neural network base models, a linear hypermodel can represent essentially any distribution over functions, and as such, hypernetworks are no more expressive.