We study a sequential decision-making problem motivated by recent regulatory and technological shifts that limit access to individual user data in recommender systems (RSs), leaving only population-level preference information. This privacy-aware setting poses fundamental challenges in planning under uncertainty: Effective personalization requires exploration to infer user preferences, yet unsatisfactory recommendations risk immediate user churn. To address this, we introduce the Rec-APC model, in which an anonymous user is drawn from a known prior over latent user types (e.g., personas or clusters), and the decision-maker sequentially selects items to recommend. Feedback is binary -- positive responses refine the posterior via Bayesian updates, while negative responses result in the termination of the session. We prove that optimal policies converge to pure exploitation in finite time and propose a branch-and-bound algorithm to efficiently compute them. Experiments on synthetic and MovieLens data confirm rapid convergence and demonstrate that our method outperforms the POMDP solver SARSOP, particularly when the number of user types is large or comparable to the number of content categories. Our results highlight the applicability of this approach and inspire new ways to improve decision-making under the constraints imposed by aggregated preference data.

Recent advancements in large language models (LLMs) have significantly improved the capabilities of web agents. However, effectively navigating complex and dynamic web environments still requires more advanced trajectory-level planning and execution. Prior studies have addressed self-improving agents by collecting extensive GUI trajectories from real-environment interactions. Despite their effectiveness, these approaches encounter two critical challenges: (1) Uncontrollable environment states, where real or sandboxed web environments often yield unstable and non-deterministic feedback, complicating the reproduction and debugging of agent behaviors; and (2) High API costs, as generating even a single interaction trajectory can involve hundreds of queries, leading to considerable API usage and computational expenses. To address these limitations and enable scalable self-improvement for agents, we propose WebSynthesis, a novel framework for trajectory synthesis and training. WebSynthesis leverages a learned world model to simulate virtual web environments, allowing a policy agent to perform efficient and reversible tree-based planning. This approach supports the large-scale generation of diverse and high-quality trajectories, which are subsequently utilized to refine the agent's policy. Experimental results demonstrate that an agent trained using WebSynthesis on a small-scale synthetic dataset achieves performance comparable to or even surpassing that of models trained on large-scale real-world data.

Deep reinforcement learning (RL) has gained widespread adoption in recent years but faces significant challenges, particularly in unknown and complex environments. Among these, high-dimensional action selection stands out as a critical problem. Existing works often require a sophisticated prior design to eliminate redundancy in the action space, relying heavily on domain expert experience or involving high computational complexity, which limits their generalizability across different RL tasks. In this paper, we address these challenges by proposing a general data-driven action selection approach with model-free and computationally friendly properties. Our method not only selects minimal sufficient actions but also controls the false discovery rate via knockoff sampling. More importantly, we seamlessly integrate the action selection into deep RL methods during online training. Empirical experiments validate the established theoretical guarantees, demonstrating that our method surpasses various alternative techniques in terms of both performance in variable selection and overall achieved rewards.

Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present a general framework of runtime verification of algorithmic fairness for systems whose models are unknown, but are assumed to have a Markov chain structure, with or without full observation of the state space. We introduce a specification language that can model many common algorithmic fairness properties, such as demographic parity, equal opportunity, and social burden. We build monitors that observe a long sequence of events as generated by a given system, and output, after each observation, a quantitative estimate of how fair or biased the system was on that run until that point in time. The estimate is proven to be correct modulo a variable error bound and a given confidence level, where the error bound gets tighter as the observed sequence gets longer. We present two categories of monitoring algorithms, namely ones with a uniform error bound across all time points, and ones with weaker non-uniform, pointwise error bounds at different time points. Our monitoring algorithms use statistical tools that are adapted to suit the dynamic requirements of monitoring and the special needs of the fairness specifications. Using a prototype implementation, we show how we can monitor if a bank is fair in giving loans to applicants from different social backgrounds, and if a college is fair in admitting students while maintaining a reasonable financial burden on the society. In these experiments, our monitors took less than a millisecond to update their verdicts after each observation.

The proliferation of ride-hailing aggregator platforms presents significant growth opportunities for ride-service providers by increasing order volume and gross merchandise value (GMV). On most ride-hailing aggregator platforms, service providers that offer lower fares are ranked higher in listings and, consequently, are more likely to be selected by passengers. This competitive ranking mechanism creates a strong incentive for service providers to adopt coupon strategies that lower prices to secure a greater number of orders, as order volume directly influences their long-term viability and sustainability. Thus, designing an effective coupon strategy that can dynamically adapt to market fluctuations while optimizing order acquisition under budget constraints is a critical research challenge. However, existing studies in this area remain scarce. To bridge this gap, we propose FCA-RL, a novel reinforcement learning-based subsidy strategy framework designed to rapidly adapt to competitors' pricing adjustments. Our approach integrates two key techniques: Fast Competition Adaptation (FCA), which enables swift responses to dynamic price changes, and Reinforced Lagrangian Adjustment (RLA), which ensures adherence to budget constraints while optimizing coupon decisions on new price landscape. Furthermore, we introduce RideGym, the first dedicated simulation environment tailored for ride-hailing aggregators, facilitating comprehensive evaluation and benchmarking of different pricing strategies without compromising real-world operational efficiency. Experimental results demonstrate that our proposed method consistently outperforms baseline approaches across diverse market conditions, highlighting its effectiveness in subsidy optimization for ride-hailing service providers.

By recursively nesting sums and products, probabilistic circuits have emerged in recent years as an attractive class of generative models as they enjoy, for instance, polytime marginalization of random variables. In this work we study these machine learning models using the framework of quantum information theory, leading to the introduction of positive unital circuits (PUnCs), which generalize circuit evaluations over positive real-valued probabilities to circuit evaluations over positive semi-definite matrices. As a consequence, PUnCs strictly generalize probabilistic circuits as well as recently introduced circuit classes such as PSD circuits.

In many real-world planning tasks, agents must tackle uncertainty about the environment's state and variability in the outcomes of any chosen policy. We address both forms of uncertainty as a first step toward safer algorithms in partially observable settings. Specifically, we extend Distributional Reinforcement Learning (DistRL)--which models the entire return distribution for fully observable domains--to Partially Observable Markov Decision Processes (POMDPs), allowing an agent to learn the distribution of returns for each conditional plan. Concretely, we introduce new distributional Bellman operators for partial observability and prove their convergence under the supremum p-Wasserstein metric. We also propose a finite representation of these return distributions via ψ -vectors, generalizing the classical α -vectors in POMDP solvers. Building on this, we develop Distributional Point-Based V alue Iteration (DPBVI), which integrates ψ -vectors into a standard point-based backup procedure-- bridging DistRL and POMDP planning . By tracking return distributions, DPBVI lays the foundation for future risk-sensitive control in domains where rare, high-impact events must be carefully managed. We provide source code to foster further research in robust decision-making under partial observability.

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic) gradient descent, and related topics into dynamical statements. We also tackle three concrete challenges. First, we consider the process of information propagation through a neural network, i.e., we study the input-output map for different architectures. We explain the universal embedding property for augmented neural ODEs representing arbitrary functions of given regularity, the classification of multilayer perceptrons and neural ODEs in terms of suitable function classes, and the memory-dependence in neural delay equations. Second, we consider the training aspect of neural networks dynamically. We describe a dynamical systems perspective on gradient descent and study stability for overdetermined problems. We then extend this analysis to the overparameterized setting and describe the edge of stability phenomenon, also in the context of possible explanations for implicit bias. For stochastic gradient descent, we present stability results for the overparameterized setting via Lyapunov exponents of interpolation solutions. Third, we explain several results regarding mean-field limits of neural networks. We describe a result that extends existing techniques to heterogeneous neural networks involving graph limits via digraph measures. This shows how large classes of neural networks naturally fall within the framework of Kuramoto-type models on graphs and their large-graph limits. Finally, we point out that similar strategies to use dynamics to study explainable and reliable AI can also be applied to settings such as generative models or fundamental issues in gradient training methods, such as backpropagation or vanishing/exploding gradients.

Research, innovation and practical capital investment have been increasing rapidly toward the realization of autonomous physical agents. This includes industrial and service robots, unmanned aerial vehicles, embedded control devices, and a number of other realizations of cybernetic/mechatronic implementations of intelligent autonomous devices. In this paper, we consider a stylized version of robotic care, which would normally involve a two-level Reinforcement Learning procedure that trains a policy for both lower level physical movement decisions as well as higher level conceptual tasks and their sub-components. In order to deliver greater safety and reliability in the system, we present the general formulation of this as a two-level optimization scheme which incorporates control at the lower level, and classical planning at the higher level, integrated with a capacity for learning. This synergistic integration of multiple methodologies -- control, classical planning, and RL -- presents an opportunity for greater insight for algorithm development, leading to more efficient and reliable performance. Here, the notion of reliability pertains to physical safety and interpretability into an otherwise black box operation of autonomous agents, concerning users and regulators. This work presents the necessary background and general formulation of the optimization framework, detailing each component and its integration with the others.

The limitations of the Poisson process were more evident when modeling high-speed network traffic, particularly real-time data traffic modeling for next-generation networks. For example, Liji et al. [85] demonstrated that the Stationary Poison Increment Process can only model Short Range Dependence (SRD) but not LRD. To address this limitation, the authors proposed using second-order self-similarity models, such as fractional Gaussian noise and fractional ARIMA processes, as a more appropriate approach. In the meantime, researchers also explored modeling data center network traffic using poisson processes. To better simulate realistic traffic in data center environments, the generation of flow-level network traffic matrices based on the poisson shot-noise model is proposed in [172]. By incorporating factors such as flow arrival rates, intra-rack traffic ratios, flow sizes and durations, the poisson shot-noise process offers a more accurate representation of traffic patterns in data centers. B. Weibull distribution As discussed earlier, the limitations of Poisson processes for modeling network traffic led to exploring other distributions. One such promising model was the Weibull distribution, mainly due to its flexibility to model both heavy and non-heavy tailed distributions [11].