Reinforcement learning (RL) has achieved remarkable success in real-world decision-making across diverse domains, including gaming, robotics, online advertising, public health, and natural language processing. Despite these advances, a substantial gap remains between RL research and its deployment in many practical settings. Two recurring challenges often underlie this gap. First, many settings offer limited opportunity for the agent to interact extensively with the target environment due to practical constraints. Second, many target environments often undergo substantial changes, requiring redesign and redeployment of RL systems (e.g., advancements in science and technology that change the landscape of healthcare delivery). Addressing these challenges and bridging the gap between basic research and application requires theory and methodology that directly inform the design, implementation, and continual improvement of RL systems in real-world settings. In this paper, we frame the application of RL in practice as a three-component process: (i) online learning and optimization during deployment, (ii) post- or between-deployment offline analyses, and (iii) repeated cycles of deployment and redeployment to continually improve the RL system. We provide a narrative review of recent advances in statistical RL that address these components, including methods for maximizing data utility for between-deployment inference, enhancing sample efficiency for online learning within-deployment, and designing sequences of deployments for continual improvement. We also outline future research directions in statistical RL that are use-inspired -- aiming for impactful application of RL in practice.

We consider the problem of modifying a description logic concept in light of models represented as pointed interpretations. We call this setting model change, and distinguish three main kinds of changes: eviction, which consists of only removing models; reception, which incorporates models; and revision, which combines removal with incorporation of models in a single operation. We introduce a formal notion of revision and argue that it does not reduce to a simple combination of eviction and reception, contrary to intuition. We provide positive and negative results on the compatibility of eviction and reception for EL-bottom and ALC description logic concepts and on the compatibility of revision for ALC concepts.

Abstract--This paper presents a semi-supervised learning framework for Gaussian mixture modelling under a Missing at Random (MAR) mechanism. T o quantify classification uncertainty, we introduce margin confidence and incorporate the Aranda-Ordaz (AO) link function to flexibly capture the asymmetric relationships between uncertainty and missing probability. Based on this formulation, we develop an efficient Expectation-Conditional Maximization (ECM) algorithm that jointly estimates all parameters appearing in both the Gaussian mixture model (GMM) and the missingness mechanism, and subsequently imputes the missing labels by a Bayesian classifier derived from the fitted mixture model. This method effectively alleviates the bias induced by ignoring the missingness mechanism while enhancing the robustness of semi-supervised learning. The resulting uncertainty-aware framework delivers reliable classification performance in realistic MAR scenarios with substantial proportions of missing labels.

Fairness and privacy are two vital pillars of trustworthy machine learning. Despite extensive research on these individual topics, the relationship between fairness and privacy has received significantly less attention. In this paper, we utilize the information-theoretic measure Chernoff Information to highlight the data-dependent nature of the relationship among the triad of fairness, privacy, and accuracy. We first define Noisy Chernoff Difference, a tool that allows us to analyze the relationship among the triad simultaneously. We then show that for synthetic data, this value behaves in 3 distinct ways (depending on the distribution of the data). We highlight the data distributions involved in these cases and explore their fairness and privacy implications. Additionally, we show that Noisy Chernoff Difference acts as a proxy for the steepness of the fairness-accuracy curves. Finally, we propose a method for estimating Chernoff Information on data from unknown distributions and utilize this framework to examine the triad dynamic on real datasets. This work builds towards a unified understanding of the fairness-privacy-accuracy relationship and highlights its data-dependent nature.

Average-reward reinforcement learning offers a principled framework for long-term decision-making by maximizing the mean reward per time step. Although Q-learning is a widely used model-free algorithm with established sample complexity in discounted and finite-horizon Markov decision processes (MDPs), its theoretical guarantees for average-reward settings remain limited. This work studies a simple but effective Q-learning algorithm for average-reward MDPs with finite state and action spaces under the weakly communicating assumption, covering both single-agent and federated scenarios. For the single-agent case, we show that Q-learning with carefully chosen parameters achieves sample complexity $\widetilde{O}\left(\frac{|\mathcal{S}||\mathcal{A}|\|h^{\star}\|_{\mathsf{sp}}^3}{\varepsilon^3}\right)$, where $\|h^{\star}\|_{\mathsf{sp}}$ is the span norm of the bias function, improving previous results by at least a factor of $\frac{\|h^{\star}\|_{\mathsf{sp}}^2}{\varepsilon^2}$. In the federated setting with $M$ agents, we prove that collaboration reduces the per-agent sample complexity to $\widetilde{O}\left(\frac{|\mathcal{S}||\mathcal{A}|\|h^{\star}\|_{\mathsf{sp}}^3}{M\varepsilon^3}\right)$, with only $\widetilde{O}\left(\frac{\|h^{\star}\|_{\mathsf{sp}}}{\varepsilon}\right)$ communication rounds required. These results establish the first federated Q-learning algorithm for average-reward MDPs, with provable efficiency in both sample and communication complexity.

In this paper, the solution to the empirical risk minimization problem with $f$-divergence regularization (ERM-$f$DR) is presented and conditions under which the solution also serves as the solution to the minimization of the expected empirical risk subject to an $f$-divergence constraint are established. The proposed approach extends applicability to a broader class of $f$-divergences than previously reported and yields theoretical results that recover previously known results. Additionally, the difference between the expected empirical risk of the ERM-$f$DR solution and that of its reference measure is characterized, providing insights into previously studied cases of $f$-divergences. A central contribution is the introduction of the normalization function, a mathematical object that is critical in both the dual formulation and practical computation of the ERM-$f$DR solution. This work presents an implicit characterization of the normalization function as a nonlinear ordinary differential equation (ODE), establishes its key properties, and subsequently leverages them to construct a numerical algorithm for approximating the normalization factor under mild assumptions. Further analysis demonstrates structural equivalences between ERM-$f$DR problems with different $f$-divergences via transformations of the empirical risk. Finally, the proposed algorithm is used to compute the training and test risks of ERM-$f$DR solutions under different $f$-divergence regularizers. This numerical example highlights the practical implications of choosing different functions $f$ in ERM-$f$DR problems.

Estimating the unknown reward functions driving agents' behaviors is of central interest in inverse reinforcement learning and game theory. To tackle this problem, we develop a unified framework for reward function recovery in two-player zero-sum matrix games and Markov games with entropy regularization, where we aim to reconstruct the underlying reward functions given observed players' strategies and actions. This task is challenging due to the inherent ambiguity of inverse problems, the non-uniqueness of feasible rewards, and limited observational data coverage. To address these challenges, we establish the reward function's identifiability using the quantal response equilibrium (QRE) under linear assumptions. Building upon this theoretical foundation, we propose a novel algorithm to learn reward functions from observed actions. Our algorithm works in both static and dynamic settings and is adaptable to incorporate different methods, such as Maximum Likelihood Estimation (MLE). We provide strong theoretical guarantees for the reliability and sample efficiency of our algorithm. Further, we conduct extensive numerical studies to demonstrate the practical effectiveness of the proposed framework, offering new insights into decision-making in competitive environments.

Fairness-aware machine learning has recently attracted various communities to mitigate discrimination against certain societal groups in data-driven tasks. For fair supervised learning, particularly in pre-processing, there have been two main categories: data fairness and task-tailored fairness. The former directly finds an intermediate distribution among the groups, independent of the type of the downstream model, so a learned downstream classification/regression model returns similar predictive scores to individuals inputting the same covariates irrespective of their sensitive attributes. The latter explicitly takes the supervised learning task into account when constructing the pre-processing map. In this work, we study algorithmic fairness for supervised learning and argue that the data fairness approaches impose overly strong regularization from the perspective of the HGR correlation. This motivates us to devise a novel pre-processing approach tailored to supervised learning. We account for the trade-off between fairness and utility in obtaining the pre-processing map. Then we study the behavior of arbitrary downstream supervised models learned on the transformed data to find sufficient conditions to guarantee their fairness improvement and utility preservation. To our knowledge, no prior work in the branch of task-tailored methods has theoretically investigated downstream guarantees when using pre-processed data. We further evaluate our framework through comparison studies based on tabular and image data sets, showing the superiority of our framework which preserves consistent trade-offs among multiple downstream models compared to recent competing models. Particularly for computer vision data, we see our method alters only necessary semantic features related to the central machine learning task to achieve fairness.

Directed acyclic graphical (DAG) models are a powerful tool for representing causal relationships among jointly distributed random variables, especially concerning data from across different experimental settings. However, it is not always practical or desirable to estimate a causal model at the granularity of given features in a particular dataset. There is a growing body of research on causal abstraction to address such problems. We contribute to this line of research by (i) providing novel graphical identifiability results for practically-relevant interventional settings, (ii) proposing an efficient, provably consistent algorithm for directly learning abstract causal graphs from interventional data with unknown intervention targets, and (iii) uncovering theoretical insights about the lattice structure of the underlying search space, with connections to the field of causal discovery more generally. As proof of concept, we apply our algorithm on synthetic and real datasets with known ground truths, including measurements from a controlled physical system with interacting light intensity and polarization.

With grid operators confronting rising uncertainty from renewable integration and a broader push toward electrification, Demand-Side Management (DSM) -- particularly Demand Response (DR) -- has attracted significant attention as a cost-effective mechanism for balancing modern electricity systems. Unprecedented volumes of consumption data from a continuing global deployment of smart meters enable consumer segmentation based on real usage behaviours, promising to inform the design of more effective DSM and DR programs. However, existing clustering-based segmentation methods insufficiently reflect the behavioural diversity of consumers, often relying on rigid temporal alignment, and faltering in the presence of anomalies, missing data, or large-scale deployments. To address these challenges, we propose a novel two-stage clustering framework -- Clustered Representations Optimising Consumer Segmentation (CROCS). In the first stage, each consumer's daily load profiles are clustered independently to form a Representative Load Set (RLS), providing a compact summary of their typical diurnal consumption behaviours. In the second stage, consumers are clustered using the Weighted Sum of Minimum Distances (WSMD), a novel set-to-set measure that compares RLSs by accounting for both the prevalence and similarity of those behaviours. Finally, community detection on the WSMD-induced graph reveals higher-order prototypes that embody the shared diurnal behaviours defining consumer groups, enhancing the interpretability of the resulting clusters. Extensive experiments on both synthetic and real Australian smart meter datasets demonstrate that CROCS captures intra-consumer variability, uncovers both synchronous and asynchronous behavioural similarities, and remains robust to anomalies and missing data, while scaling efficiently through natural parallelisation. These results...