In Reinforcement Learning (RL), an agent engages with an environment in a sequential manner.

Emergent phenomena -- onset of epileptic seizures, sudden customer churn, or pandemic outbreaks -- often arise from hidden causal interactions in complex systems. We propose a machine learning method for their early detection that addresses a core challenge: unveiling and harnessing a system's latent causal structure despite the data-generating process being unknown and partially observed. The method learns an optimal feature representation from a one-parameter family of estimators -- powers of the empirical covariance or precision matrix -- offering a principled way to tune in to the underlying structure driving the emergence of critical events. A supervised learning module then classifies the learned representation. We prove structural consistency of the family and demonstrate the empirical soundness of our approach on seizure detection and churn prediction, attaining competitive results in both. Beyond prediction, and toward explainability, we ascertain that the optimal covariance power exhibits evidence of good identifiability while capturing structural signatures, thus reconciling predictive performance with interpretable statistical structure.

Offline Reinforcement Learning (RL) has demonstrated promising results in various applications by learning policies from previously collected datasets, reducing the need for online exploration and interactions. However, real-world scenarios usually involve partial observability, which brings crucial challenges of the deployment of offline RL methods: i) the policy trained on data with full observability is not robust against the masked observations during execution, and ii) the information of which parts of observations are masked is usually unknown during training. In order to address these challenges, we present Offline RL with DiscrEte pRoxy representations (ORDER), a probabilistic framework which leverages novel state representations to improve the robustness against diverse masked observabilities. Specifically, we propose a discrete representation of the states and use a proxy representation to recover the states from masked partial observable trajectories. The training of ORDER can be compactly described as the following three steps.

In real-world reinforcement learning (RL) systems, various forms of {\it impaired observability} can complicate matters. These situations arise when an agent is unable to observe the most recent state of the system due to latency or lossy channels, yet the agent must still make real-time decisions. This paper introduces a theoretical investigation into efficient RL in control systems where agents must act with delayed and missing state observations.

Existing observational approaches for learning human preferences, such as inverse reinforcement learning, usually make strong assumptions about the observability of the human's environment. However, in reality, people make many important decisions under uncertainty. To better understand preference learning in these cases, we study the setting of inverse decision theory (IDT), a previously proposed framework where a human is observed making non-sequential binary decisions under uncertainty. In IDT, the human's preferences are conveyed through their loss function, which expresses a tradeoff between different types of mistakes. We give the first statistical analysis of IDT, providing conditions necessary to identify these preferences and characterizing the sample complexity--the number of decisions that must be observed to learn the tradeoff the human is making to a desired precision. Interestingly, we show that it is actually easier to identify preferences when the decision problem is more uncertain. Furthermore, uncertain decision problems allow us to relax the unrealistic assumption that the human is an optimal decision maker but still identify their exact preferences; we give sample complexities in this suboptimal case as well. Our analysis contradicts the intuition that partial observability should make preference learning more difficult. It also provides a first step towards understanding and improving preference learning methods for uncertain and suboptimal humans.

This chapter argues that the reliability of agentic and generative AI is chiefly an architectural property. We define agentic systems as goal-directed, tool-using decision makers operating in closed loops, and show how reliability emerges from principled componentisation (goal manager, planner, tool-router, executor, memory, verifiers, safety monitor, telemetry), disciplined interfaces (schema-constrained, validated, least-privilege tool calls), and explicit control and assurance loops. Building on classical foundations, we propose a practical taxonomy-tool-using agents, memory-augmented agents, planning and self-improvement agents, multi-agent systems, and embodied or web agents - and analyse how each pattern reshapes the reliability envelope and failure modes. We distil design guidance on typed schemas, idempotency, permissioning, transactional semantics, memory provenance and hygiene, runtime governance (budgets, termination conditions), and simulate-before-actuate safeguards.

Cooperative suspended aerial transportation is highly susceptible to multi-source disturbances such as aerodynamic effects and thrust uncertainties. To achieve precise load manipulation, existing methods often rely on extra sensors to measure cable directions or the payload's pose, which increases the system cost and complexity. A fundamental question remains: is the payload's pose observable under multi-source disturbances using only the drones' odometry information? To answer this question, this work focuses on the two-drone-bar system and proves that the whole system is observable when only two or fewer types of lumped disturbances exist by using the observability rank criterion. To the best of our knowledge, we are the first to present such a conclusion and this result paves the way for more cost-effective and robust systems by minimizing their sensor suites. Next, to validate this analysis, we consider the situation where the disturbances are only exerted on the drones, and develop a composite disturbance filtering scheme. A disturbance observer-based error-state extended Kalman filter is designed for both state and disturbance estimation, which renders improved estimation performance for the whole system evolving on the manifold $(\mathbb{R}^3)^2\times(TS^2)^3$. Our simulation and experimental tests have validated that it is possible to fully estimate the state and disturbance of the system with only odometry information of the drones.

Relative State Estimation perform mutually localization between two mobile agents undergoing six-degree-of-freedom motion. Based on the principle of circular motion, the estimation accuracy is sensitive to nonlinear rotations of the reference platform, particularly under large inter-platform distances. This phenomenon is even obvious for linearized kinematics, because cumulative linearization errors significantly degrade precision. In virtual reality (VR) applications, this manifests as substantial positional errors in 6-DoF controller tracking during rapid rotations of the head-mounted display. The linearization errors introduce drift in the estimate and render the estimator inconsistent. In the field of odometry, IMU preintegration is proposed as a kinematic observation to enable efficient relinearization, thus mitigate linearized error. Building on this theory, we propose dual preintegration, a novel observation integrating IMU preintegration from both platforms. This method serves as kinematic constraints for consecutive relative state and supports efficient relinearization. We also perform observability analysis of the state and analytically formulate the accordingly null space. Algorithm evaluation encompasses both simulations and real-world experiments. Multiple nonlinear rotations on the reference platform are simulated to compare the precision of the proposed method with that of other state-of-the-art (SOTA) algorithms. The field test compares the proposed method and SOTA algorithms in the application of VR controller tracking from the perspectives of bias observability, nonlinear rotation, and background texture. The results demonstrate that the proposed method is more precise and robust than the SOTA algorithms.

In this letter, we present a closed-form initialization method that recovers the full visual-inertial state without nonlinear optimization. Unlike previous approaches that rely on iterative solvers, our formulation yields analytical, easy-to-implement, and numerically stable solutions for reliable start-up. Our method builds on small-rotation and constant-velocity approximations, which keep the formulation compact while preserving the essential coupling between motion and inertial measurements. We further propose an observability-driven, two-stage initialization scheme that balances accuracy with initialization latency. Extensive experiments on the EuRoC dataset validate our assumptions: our method achieves 10-20% lower initialization error than optimization-based approaches, while using 4x shorter initialization windows and reducing computational cost by 5x.