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.

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.

This paper studies the safe reinforcement learning problem formulated as an episodic finite-horizon tabular constrained Markov decision process with an unknown transition kernel and stochastic reward and cost functions. We propose a model-based algorithm based on novel cost and reward function estimators that provide tighter cost pessimism and reward optimism. While guaranteeing no constraint violation in every episode, our algorithm achieves a regret upper bound of $\widetilde{\mathcal{O}}((\bar C - \bar C_b)^{-1}H^{2.5} S\sqrt{AK})$ where $\bar C$ is the cost budget for an episode, $\bar C_b$ is the expected cost under a safe baseline policy over an episode, $H$ is the horizon, and $S$, $A$ and $K$ are the number of states, actions, and episodes, respectively. This improves upon the best-known regret upper bound, and when $\bar C- \bar C_b=\Omega(H)$, it nearly matches the regret lower bound of $\Omega(H^{1.5}\sqrt{SAK})$. We deduce our cost and reward function estimators via a Bellman-type law of total variance to obtain tight bounds on the expected sum of the variances of value function estimates. This leads to a tighter dependence on the horizon in the function estimators. We also present numerical results to demonstrate the computational effectiveness of our proposed framework.

Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the functional central limit theorem, are known for weakly dependent variables. We demonstrate the transfer of mixing properties from the exogenous regressor to the response via coupling arguments. Additionally, we study Markov chains in random environments with drift and minorization conditions, even under non-stationary environments with favorable mixing properties, and apply this framework to single-server queuing models.

We study the mixing time of two popular discrete time Markov chains in continuous space, the unadjusted Langevin algorithm and the proximal sampler, which are discretizations of the Langevin dynamics. We extend mixing time analyses for these Markov chains to hold in $\Phi$-divergence. We show that any $\Phi$-divergence arising from a twice-differentiable strictly convex function $\Phi$ converges to $0$ exponentially fast along these Markov chains, under the assumption that their stationary distributions satisfies the corresponding $\Phi$-Sobolev inequality. Our rates of convergence are tight and include as special cases popular mixing time regimes, namely the mixing in chi-squared divergence under a Poincar\'e inequality, and the mixing in relative entropy under a log-Sobolev inequality. Our results follow by bounding the contraction coefficients arising in the appropriate strong data processing inequalities.

The aim of the notes is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems and/or data assimilation who wish to see a mathematical presentation of machine learning as it pertains to their fields. As a by-product of the presentation we present a succinct mathematical treatment of various topics in machine learning. The material on machine learning, along with some other related topics, is summarized in Part III, Appendix. Part I of the notes is concerned with inverse problems, employing material from Part III; Part II of the notes is concerned with data assimilation, employing material from Parts I and III.

We study a class of structured Markov Decision Processes (MDPs) known as Exo-MDPs. They are characterized by a partition of the state space into two components: the exogenous states evolve stochastically in a manner not affected by the agent's actions, whereas the endogenous states can be affected by actions, and evolve according to deterministic dynamics involving both the endogenous and exogenous states. Exo-MDPs provide a natural model for various applications, including inventory control, portfolio management, power systems, and ride-sharing, among others. While seemingly restrictive on the surface, our first result establishes that any discrete MDP can be represented as an Exo-MDP. The underlying argument reveals how transition and reward dynamics can be written as linear functions of the exogenous state distribution, showing how Exo-MDPs are instances of linear mixture MDPs, thereby showing a representational equivalence between discrete MDPs, Exo-MDPs, and linear mixture MDPs. The connection between Exo-MDPs and linear mixture MDPs leads to algorithms that are near sample-optimal, with regret guarantees scaling with the (effective) size of the exogenous state space $d$, independent of the sizes of the endogenous state and action spaces, even when the exogenous state is {\em unobserved}. When the exogenous state is unobserved, we establish a regret upper bound of $O(H^{3/2}d\sqrt{K})$ with $K$ trajectories of horizon $H$ and unobserved exogenous state of dimension $d$. We also establish a matching regret lower bound of $\Omega(H^{3/2}d\sqrt{K})$ for non-stationary Exo-MDPs and a lower bound of $\Omega(Hd\sqrt{K})$ for stationary Exo-MDPs. We complement our theoretical findings with an experimental study on inventory control problems.

Recent advancements in Model-Based Reinforcement Learning (MBRL) have made it a powerful tool for visual control tasks. Despite improved data efficiency, it remains challenging to train MBRL agents with generalizable perception. Training in the presence of visual distractions is particularly difficult due to the high variation they introduce to representation learning. Building on DREAMER, a popular MBRL method, we propose a simple yet effective auxiliary task to facilitate representation learning in distracting environments. Under the assumption that task-relevant components of image observations are straightforward to identify with prior knowledge in a given task, we use a segmentation mask on image observations to only reconstruct task-relevant components. In doing so, we greatly reduce the complexity of representation learning by removing the need to encode task-irrelevant objects in the latent representation. Our method, Segmentation Dreamer (SD), can be used either with ground-truth masks easily accessible in simulation or by leveraging potentially imperfect segmentation foundation models. The latter is further improved by selectively applying the reconstruction loss to avoid providing misleading learning signals due to mask prediction errors. In modified DeepMind Control suite (DMC) and Meta-World tasks with added visual distractions, SD achieves significantly better sample efficiency and greater final performance than prior work. We find that SD is especially helpful in sparse reward tasks otherwise unsolvable by prior work, enabling the training of visually robust agents without the need for extensive reward engineering.

This paper explores the challenges posed by nominal adjectives (NAs) in natural language processing (NLP) tasks, particularly in part-of-speech (POS) tagging. We propose treating NAs as a distinct POS tag, "JN," and investigate its impact on POS tagging, BIO chunking, and coreference resolution. Our study shows that reclassifying NAs can improve the accuracy of syntactic analysis and structural understanding in NLP. We present experimental results using Hidden Markov Models (HMMs), Maximum Entropy (MaxEnt) models, and Spacy, demonstrating the feasibility and potential benefits of this approach. Additionally we finetuned a bert model to identify the NA in untagged text.

Effective decision-making in partially observable environments demands robust memory management. Despite their success in supervised learning, current deep-learning memory models struggle in reinforcement learning environments that are partially observable and long-term. They fail to efficiently capture relevant past information, adapt flexibly to changing observations, and maintain stable updates over long episodes. We theoretically analyze the limitations of existing memory models within a unified framework and introduce the Stable Hadamard Memory, a novel memory model for reinforcement learning agents. Our model dynamically adjusts memory by erasing no longer needed experiences and reinforcing crucial ones computationally efficiently. To this end, we leverage the Hadamard product for calibrating and updating memory, specifically designed to enhance memory capacity while mitigating numerical and learning challenges. Our approach significantly outperforms state-of-the-art memory-based methods on challenging partially observable benchmarks, such as meta-reinforcement learning, long-horizon credit assignment, and POPGym, demonstrating superior performance in handling long-term and evolving contexts.