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We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. In particular, we focus on characterizing the variance over values induced by a distribution over MDPs. Previous work upper bounds the posterior variance over values by solving a so-called uncertainty Bellman equation, but the over-approximation may result in inefficient exploration. We propose a new uncertainty Bellman equation whose solution converges to the true posterior variance over values and explicitly characterizes the gap in previous work. Moreover, our uncertainty quantification technique is easily integrated into common exploration strategies and scales naturally beyond the tabular setting by using standard deep reinforcement learning architectures. Experiments in difficult exploration tasks, both in tabular and continuous control settings, show that our sharper uncertainty estimates improve sample-efficiency., Comment: AISTATS 2023

We consider a sequential decision making task where we are not allowed to evaluate parameters that violate an a priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on the unknown constraint and allow evaluations only in regions that are safe with high probability. Most current methods rely on a discretization of the domain and cannot be directly extended to the continuous case. Moreover, the way in which they exploit regularity assumptions about the constraint introduces an additional critical hyperparameter. In this paper, we propose an information-theoretic safe exploration criterion that directly exploits the GP posterior to identify the most informative safe parameters to evaluate. Our approach is naturally applicable to continuous domains and does not require additional hyperparameters. We theoretically analyze the method and show that we do not violate the safety constraint with high probability and that we explore by learning about the constraint up to arbitrary precision. Empirical evaluations demonstrate improved data-efficiency and scalability., Submitted to NeurIPS 2022

Bayesian optimization is a powerful paradigm to optimize black-box functions based on scarce and noisy data. Its data efficiency can be further improved by transfer learning from related tasks. While recent transfer models meta-learn a prior based on large amount of data, in the low-data regime methods that exploit the closed-form posterior of Gaussian processes (GPs) have an advantage. In this setting, several analytically tractable transfer-model posteriors have been proposed, but the relative advantages of these methods are not well understood. In this paper, we provide a unified view on hierarchical GP models for transfer learning, which allows us to analyze the relationship between methods. As part of the analysis, we develop a novel closed-form boosted GP transfer model that fits between existing approaches in terms of complexity. We evaluate the performance of the different approaches in large-scale experiments and highlight strengths and weaknesses of the different transfer-learning methods.

We consider the problem of robust optimization within the well-established Bayesian Optimization (BO) framework.While BO is intrinsically robust to noisy evaluations of the objective function, standard approaches do not consider the case of uncertainty about the input parameters.In this paper, we propose Noisy-Input Entropy Search (NES), a novel information-theoretic acquisition function that is designed to find robust optima for problems with both input and measurement noise.NES is based on the key insight that the robust objective in many cases can be modeled as a Gaussian process, however, it cannot be observed directly.We evaluate NES on several benchmark problems from the optimization literature and from engineering.The results show that NES reliably finds robust optima, outperforming existing methods from the literature on all benchmarks. ISSN:2640-3498