Robotic Information Gathering (RIG) is a foundational research topic that answers how a robot (team) collects informative data to efficiently build an accurate model of an unknown target function under robot embodiment constraints. RIG has many applications, including but not limited to autonomous exploration and mapping, 3D reconstruction or inspection, search and rescue, and environmental monitoring. A RIG system relies on a probabilistic model's prediction uncertainty to identify critical areas for informative data collection. Gaussian Processes (GPs) with stationary kernels have been widely adopted for spatial modeling. However, real-world spatial data is typically non-stationary -- different locations do not have the same degree of variability. As a result, the prediction uncertainty does not accurately reveal prediction error, limiting the success of RIG algorithms. We propose a family of non-stationary kernels named Attentive Kernel (AK), which is simple, robust, and can extend any existing kernel to a non-stationary one. We evaluate the new kernel in elevation mapping tasks, where AK provides better accuracy and uncertainty quantification over the commonly used stationary kernels and the leading non-stationary kernels. The improved uncertainty quantification guides the downstream informative planner to collect more valuable data around the high-error area, further increasing prediction accuracy. A field experiment demonstrates that the proposed method can guide an Autonomous Surface Vehicle (ASV) to prioritize data collection in locations with significant spatial variations, enabling the model to characterize salient environmental features.

The solution of probabilistic inverse problems for which the corresponding forward problem is constrained by physical principles is challenging. This is especially true if the dimension of the inferred vector is large and the prior information about it is in the form of a collection of samples. In this work, a novel deep learning based approach is developed and applied to solving these types of problems. The approach utilizes samples of the inferred vector drawn from the prior distribution and a physics-based forward model to generate training data for a conditional Wasserstein generative adversarial network (cWGAN). The cWGAN learns the probability distribution for the inferred vector conditioned on the measurement and produces samples from this distribution. The cWGAN developed in this work differs from earlier versions in that its critic is required to be 1-Lipschitz with respect to both the inferred and the measurement vectors and not just the former. This leads to a loss term with the full (and not partial) gradient penalty. It is shown that this rather simple change leads to a stronger notion of convergence for the conditional density learned by the cWGAN and a more robust and accurate sampling strategy. Through numerical examples it is shown that this change also translates to better accuracy when solving inverse problems. The numerical examples considered include illustrative problems where the true distribution and/or statistics are known, and a more complex inverse problem motivated by applications in biomechanics.

Bayesian optimisation is a powerful method for optimising black-box functions, popular in settings where the true function is expensive to evaluate and no gradient information is available. Bayesian optimisation can improve responses to many optimisation problems within climate change for which simulator models are unavailable or expensive to sample from. While there have been several feasibility demonstrations of Bayesian optimisation in climate-related applications, there has been no unifying review of applications and benchmarks. We provide such a review here, to encourage the use of Bayesian optimisation in important and well-suited application domains. We identify four main application domains: material discovery, wind farm layout, optimal renewable control and environmental monitoring. For each domain we identify a public benchmark or data set that is easy to use and evaluate systems against, while being representative of real-world problems. Due to the lack of a suitable benchmark for environmental monitoring, we propose LAQN-BO, based on air pollution data. Our contributions are: a) identifying a representative range of benchmarks, providing example code where necessary; b) introducing a new benchmark, LAQN-BO; and c) promoting a wider use of climate change applications among Bayesian optimisation practitioners.

We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced by Zermelo almost a century ago. Here we describe an alternative and similarly simple iteration that provably returns identical results but does so much faster -- over a hundred times faster in some cases. We demonstrate this algorithm with applications to a range of example data sets and derive a number of results regarding its convergence.

The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to note that existing methods often struggle to identify the underlying equation accurately in the presence of noise. In this study, we present a new approach to discovering PDEs by combining variational Bayes and sparse linear regression. The problem of PDE discovery has been posed as a problem to learn relevant basis from a predefined dictionary of basis functions. To accelerate the overall process, a variational Bayes-based approach for discovering partial differential equations is proposed. To ensure sparsity, we employ a spike and slab prior. We illustrate the efficacy of our strategy in several examples, including Burgers, Korteweg-de Vries, Kuramoto Sivashinsky, wave equation, and heat equation (1D as well as 2D). Our method offers a promising avenue for discovering PDEs from data and has potential applications in fields such as physics, engineering, and biology.

In many robotics problems, there is a significant gain in collaborative information sharing between multiple robots, for exploration, search and rescue, tracking multiple targets, or mapping large environments. One of the key implicit assumptions when solving cooperative multi-robot problems is that all robots use the same (homogeneous) underlying algorithm. However, in practice, we want to allow collaboration between robots possessing different capabilities and that therefore must rely on heterogeneous algorithms. We present a system architecture and the supporting theory, to enable collaboration in a decentralized network of robots, where each robot relies on different estimation algorithms. To develop our approach, we focus on multi-robot simultaneous localization and mapping (SLAM) with multi-target tracking. Our theoretical framework builds on our idea of exploiting the conditional independence structure inherent to many robotics applications to separate between each robot's local inference (estimation) tasks and fuse only relevant parts of their non-equal, but overlapping probability density function (pdfs). We present a new decentralized graph-based approach to the multi-robot SLAM and tracking problem. We leverage factor graphs to split between different parts of the problem for efficient data sharing between robots in the network while enabling robots to use different local sparse landmark/dense/metric-semantic SLAM algorithms.

The reinforcement learning algorithm SARSA combined with linear function approximation has been shown to converge for infinite horizon discounted Markov decision problems (MDPs). In this paper, we investigate the convergence of the algorithm for random horizon MDPs, which has not previously been shown. We show, similar to earlier results for infinite horizon discounted MDPs, that if the behaviour policy is $\varepsilon$-soft and Lipschitz continuous with respect to the weight vector of the linear function approximation, with small enough Lipschitz constant, then the algorithm will converge with probability one when considering a random horizon MDP.

The Blackboard Architecture provides a mechanism for embodying data, decision making and actuation. Its versatility has been demonstrated across a wide number of application areas. However, it lacks the capability to directly model organizational, spatial and other relationships which may be useful in decision-making, in addition to the propositional logic embodied in the rule-fact-action network. Previous work has proposed the use of container objects and links as a mechanism to simultaneously model these organizational and other relationships, while leaving the operational logic modeled in the rules, facts and actions. While containers facilitate this modeling, their utility is limited by the need to manually define them. For systems which may have multiple instances of a particular type of object and which may build their network autonomously, based on sensing, the reuse of logical structures facilitates operations and reduces storage and processing needs. This paper, thus, presents and assesses two additional concepts to add to the Blackboard Architecture: common properties and generic rules. Common properties are facts associated with containers which are defined as representing the same information across the various objects that they are associated with. Generic rules provide logical propositions that use these generic rules across links and apply to any objects matching their definition. The potential uses of these two new concepts are discussed herein and their impact on system performance is characterized.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

Control variates can be a powerful tool to reduce the variance of Monte Carlo estimators, but constructing effective control variates can be challenging when the number of samples is small. In this paper, we show that when a large number of related integrals need to be computed, it is possible to leverage the similarity between these integration tasks to improve performance even when the number of samples per task is very small. Our approach, called meta learning CVs (Meta-CVs), can be used for up to hundreds or thousands of tasks. Our empirical assessment indicates that Meta-CVs can lead to significant variance reduction in such settings, and our theoretical analysis establishes general conditions under which Meta-CVs can be successfully trained.