Pascal Van Der Vaart

Moritz A. Zanger, Yijun Wu, Pascal R. Van der Vaart et al.

Uncertainty quantification is central to safe and efficient deployments of deep learning models, yet many computationally practical methods lack lacking rigorous theoretical motivation. Random network distillation (RND) is a lightweight technique that measures novelty via prediction errors against a fixed random target. While empirically effective, it has remained unclear what uncertainties RND measures and how its estimates relate to other approaches, e.g. Bayesian inference or deep ensembles. This paper establishes these missing theoretical connections by analyzing RND within the neural tangent kernel framework in the limit of infinite network width. Our analysis reveals two central findings in this limit: (1) The uncertainty signal from RND -- its squared self-predictive error -- is equivalent to the predictive variance of a deep ensemble. (2) By constructing a specific RND target function, we show that the RND error distribution can be made to mirror the centered posterior predictive distribution of Bayesian inference with wide neural networks. Based on this equivalence, we moreover devise a posterior sampling algorithm that generates i.i.d. samples from an exact Bayesian posterior predictive distribution using this modified \textit{Bayesian RND} model. Collectively, our findings provide a unified theoretical perspective that places RND within the principled frameworks of deep ensembles and Bayesian inference, and offer new avenues for efficient yet theoretically grounded uncertainty quantification methods.

Joery A. de Vries, Jinke He, Yaniv Oren et al.

Optimally trading-off exploration and exploitation is the holy grail of reinforcement learning as it promises maximal data-efficiency for solving any task. Bayes-optimal agents achieve this, but obtaining the belief-state and performing planning are both typically intractable. Although deep learning methods can greatly help in scaling this computation, existing methods are still costly to train. To accelerate this, this paper proposes a variational framework for learning and planning in Bayes-adaptive Markov decision processes that coalesces variational belief learning, sequential Monte-Carlo planning, and meta-reinforcement learning. In a single-GPU setup, our new method VariBASeD exhibits favorable scaling to larger planning budgets, improving sample- and runtime-efficiency over prior methods.

Pascal Van Der Vaart, Anuj Mahajan, Shimon Whiteson

A challenge in multi-agent reinforcement learning is to be able to generalize over intractable state-action spaces. Inspired from Tesseract [Mahajan et al., 2021], this position paper investigates generalisation in state-action space over unexplored state-action pairs by modelling the transition and reward functions as tensors of low CP-rank. Initial experiments on synthetic MDPs show that using tensor decompositions in a model-based reinforcement learning algorithm can lead to much faster convergence if the true transition and reward functions are indeed of low rank.