Linear temporal logic (LTL) and, more generally, $\omega$-regular objectives are alternatives to the traditional discount sum and average reward objectives in reinforcement learning (RL), offering the advantage of greater comprehensibility and hence explainability. In this work, we study the relationship between these objectives. Our main result is that each RL problem for $\omega$-regular objectives can be reduced to a limit-average reward problem in an optimality-preserving fashion, via (finite-memory) reward machines. Furthermore, we demonstrate the efficacy of this approach by showing that optimal policies for limit-average problems can be found asymptotically by solving a sequence of discount-sum problems approximately. Consequently, we resolve an open problem: optimal policies for LTL and $\omega$-regular objectives can be learned asymptotically.

Language models strongly rely on frequency information because they maximize the likelihood of tokens during pre-training. As a consequence, language models tend to not generalize well to tokens that are seldom seen during training. Moreover, maximum likelihood training has been discovered to give rise to anisotropy: representations of tokens in a model tend to cluster tightly in a high-dimensional cone, rather than spreading out over their representational capacity. Our work introduces a method for quantifying the frequency bias of a language model by assessing sentence-level perplexity with respect to token-level frequency. We then present a method for reducing the frequency bias of a language model by inducing a syntactic prior over token representations during pre-training. Our Syntactic Smoothing method adjusts the maximum likelihood objective function to distribute the learning signal to syntactically similar tokens. This approach results in better performance on infrequent English tokens and a decrease in anisotropy. We empirically show that the degree of anisotropy in a model correlates with its frequency bias.

Optimal Bayesian decision making on what geoscientific data to acquire requires stating a prior model of uncertainty. Data acquisition is then optimized by reducing uncertainty on some property of interest maximally, and on average. In the context of exploration, very few, sometimes no data at all, is available prior to data acquisition planning. The prior model therefore needs to include human interpretations on the nature of spatial variability, or on analogue data deemed relevant for the area being explored. In mineral exploration, for example, humans may rely on conceptual models on the genesis of the mineralization to define multiple hypotheses, each representing a specific spatial variability of mineralization. More often than not, after the data is acquired, all of the stated hypotheses may be proven incorrect, i.e. falsified, hence prior hypotheses need to be revised, or additional hypotheses generated. Planning data acquisition under wrong geological priors is likely to be inefficient since the estimated uncertainty on the target property is incorrect, hence uncertainty may not be reduced at all. In this paper, we develop an intelligent agent based on partially observable Markov decision processes that plans optimally in the case of multiple geological or geoscientific hypotheses on the nature of spatial variability. Additionally, the artificial intelligence is equipped with a method that allows detecting, early on, whether the human stated hypotheses are incorrect, thereby saving considerable expense in data acquisition. Our approach is tested on a sediment-hosted copper deposit, and the algorithm presented has aided in the characterization of an ultra high-grade deposit in Zambia in 2023.

Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of differentiable programming to computational plasma physics. First, we consider how differentiable programming can be used to simplify and improve stellarator optimization. We introduce a stellarator coil design code (FOCUSADD) that uses gradient-based optimization to produce stellarator coils with finite build. Because we use reverse mode AD, which can compute gradients of scalar functions with the same computational complexity as the function, FOCUSADD is simple, flexible, and efficient. We then discuss two additional applications of AD in stellarator optimization. Second, we explore how machine learning (ML) can be used to improve or replace the numerical methods used to solve partial differential equations (PDEs), focusing on time-dependent PDEs in fluid mechanics relevant to plasma physics. Differentiable programming allows neural networks and other techniques from ML to be embedded within numerical methods. This is a promising, but relatively new, research area. We focus on two basic questions. First, can we design ML-based PDE solvers that have the same guarantees of conservation, stability, and positivity that standard numerical methods do? The answer is yes; we introduce error-correcting algorithms that preserve invariants of time-dependent PDEs. Second, which types of ML-based solvers work best at solving PDEs? We perform a systematic review of the scientific literature on solving PDEs with ML. Unfortunately we discover two issues, weak baselines and reporting biases, that affect the interpretation reproducibility of a significant majority of published research. We conclude that using ML to solve PDEs is not as promising as we initially believed.

Offline reinforcement learning (RL) is a powerful approach for data-driven decision-making and control. Compared to model-free methods, offline model-based reinforcement learning (MBRL) explicitly learns world models from a static dataset and uses them as surrogate simulators, improving the data efficiency and enabling the learned policy to potentially generalize beyond the dataset support. However, there could be various MDPs that behave identically on the offline dataset and so dealing with the uncertainty about the true MDP can be challenging. In this paper, we propose modeling offline MBRL as a Bayes Adaptive Markov Decision Process (BAMDP), which is a principled framework for addressing model uncertainty. We further introduce a novel Bayes Adaptive Monte-Carlo planning algorithm capable of solving BAMDPs in continuous state and action spaces with stochastic transitions. This planning process is based on Monte Carlo Tree Search and can be integrated into offline MBRL as a policy improvement operator in policy iteration. Our ``RL + Search" framework follows in the footsteps of superhuman AIs like AlphaZero, improving on current offline MBRL methods by incorporating more computation input. The proposed algorithm significantly outperforms state-of-the-art model-based and model-free offline RL methods on twelve D4RL MuJoCo benchmark tasks and three target tracking tasks in a challenging, stochastic tokamak control simulator.

Monitoring networks increasingly aim to assimilate data from a large number of diverse sensors covering many sensing modalities. Bayesian optimal experimental design (OED) seeks to identify data, sensor configurations, or experiments which can optimally reduce uncertainty and hence increase the performance of a monitoring network. Information theory guides OED by formulating the choice of experiment or sensor placement as an optimization problem that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge and models of expected observation data. Therefore, within the context of seismo-acoustic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types, and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize a sensor network's ability to locate seismic events from arrival time data of detected seismic phases at the regional-scale. Bayesian OED requires four elements: 1) A likelihood function that describes the distribution of detection and travel time data from the sensor network, 2) A Bayesian solver that uses a prior and likelihood to identify the posterior distribution of seismic events given the data, 3) An algorithm to compute EIG about seismic events over a dataset of hypothetical prior events, 4) An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we explore many relevant questions to monitoring such as: how to trade off sensor fidelity and earth model uncertainty; how sensor types, number, and locations influence uncertainty; and how prior models and constraints influence sensor placement.

Deep reinforcement learning has emerged as a powerful tool for obtaining high-performance policies. However, the safety of these policies has been a long-standing issue. One promising paradigm to guarantee safety is a shield, which shields a policy from making unsafe actions. However, computing a shield scales exponentially in the number of state variables. This is a particular concern in multi-agent systems with many agents. In this work, we propose a novel approach for multi-agent shielding. We address scalability by computing individual shields for each agent. The challenge is that typical safety specifications are global properties, but the shields of individual agents only ensure local properties. Our key to overcome this challenge is to apply assume-guarantee reasoning. Specifically, we present a sound proof rule that decomposes a (global, complex) safety specification into (local, simple) obligations for the shields of the individual agents. Moreover, we show that applying the shields during reinforcement learning significantly improves the quality of the policies obtained for a given training budget. We demonstrate the effectiveness and scalability of our multi-agent shielding framework in two case studies, reducing the computation time from hours to seconds and achieving fast learning convergence.

We propose a scalable kinetic Langevin dynamics algorithm for sampling parameter spaces of big data and AI applications. Our scheme combines a symmetric forward/backward sweep over minibatches with a symmetric discretization of Langevin dynamics. For a particular Langevin splitting method (UBU), we show that the resulting Symmetric Minibatch Splitting-UBU (SMS-UBU) integrator has bias $O(h^2 d^{1/2})$ in dimension $d>0$ with stepsize $h>0$, despite only using one minibatch per iteration, thus providing excellent control of the sampling bias as a function of the stepsize. We apply the algorithm to explore local modes of the posterior distribution of Bayesian neural networks (BNNs) and evaluate the calibration performance of the posterior predictive probabilities for neural networks with convolutional neural network architectures for classification problems on three different datasets (Fashion-MNIST, Celeb-A and chest X-ray). Our results indicate that BNNs sampled with SMS-UBU can offer significantly better calibration performance compared to standard methods of training and stochastic weight averaging.

Modelling dynamic traffic patterns and especially the continuously changing dependencies between different base stations, which previous studies overlook, is challenging. Traditional algorithms struggle to process large volumes of data and to extract deep insights that help elucidate mobile traffic demands with fine granularity, as well as how these demands will evolve in the future. Therefore, in this thesis we harness the powerful hierarchical feature learning abilities of Deep Learning (DL) techniques in both spatial and temporal domains and develop solutions for precise city-scale mobile traffic analysis and forecasting. Firstly, we design Spider, a mobile traffic measurement collection and reconstruction framework with a view to reducing the cost of measurement collection and inferring traffic consumption with high accuracy, despite working with sparse information. In particular, we train a reinforcement learning agent to selectively sample subsets of target mobile coverage areas and tackle the large action space problem specific to this setting. We then introduce a lightweight neural network model to reconstruct the traffic consumption based on historical sparse measurements. Our proposed framework outperforms existing solutions on a real-world mobile traffic dataset. Secondly, we design SDGNet, a handover-aware graph neural network model for long-term mobile traffic forecasting. We model the cellular network as a graph, and leverage handover frequency to capture the dependencies between base stations across time. Handover information reflects user mobility such as daily commute, which helps in increasing the accuracy of the forecasts made. We proposed dynamic graph convolution to extract features from both traffic consumption and handover data, showing that our model outperforms other benchmark graph models on a mobile traffic dataset collected by a major network operator.

Reasoning is key to many decision making processes. It requires consolidating a set of rule-like premises that are often associated with degrees of uncertainty and observations to draw conclusions. In this work, we address both the case where premises are specified as numeric probabilistic rules and situations in which humans state their estimates using words expressing degrees of certainty. Existing probabilistic reasoning datasets simplify the task, e.g., by requiring the model to only rank textual alternatives, by including only binary random variables, or by making use of a limited set of templates that result in less varied text. In this work, we present QUITE, a question answering dataset of real-world Bayesian reasoning scenarios with categorical random variables and complex relationships. QUITE provides high-quality natural language verbalizations of premises together with evidence statements and expects the answer to a question in the form of an estimated probability. We conduct an extensive set of experiments, finding that logic-based models outperform out-of-the-box large language models on all reasoning types (causal, evidential, and explaining-away). Our results provide evidence that neuro-symbolic models are a promising direction for improving complex reasoning. We release QUITE and code for training and experiments on Github.