Points-based rewards programs are a prevalent way to incentivize customer loyalty; in these programs, customers who make repeated purchases from a seller accumulate points, working toward eventual redemption of a free reward. These programs have recently come under scrutiny due to accusations of unfair practices in their implementation. Motivated by these concerns, we study the problem of fairly designing points-based rewards programs, with a focus on two obstacles that put fairness at odds with their effectiveness. First, due to customer heterogeneity, the seller should set different redemption thresholds for different customers to generate high revenue. Second, the relationship between customer behavior and the number of accumulated points is typically unknown; this requires experimentation which may unfairly devalue customers' previously earned points. We first show that an individually fair rewards program that uses the same redemption threshold for all customers suffers a loss in revenue of at most a factor of $1+\ln 2$, compared to the optimal personalized strategy that differentiates between customers. We then tackle the problem of designing temporally fair learning algorithms in the presence of demand uncertainty. Toward this goal, we design a learning algorithm that limits the risk of point devaluation due to experimentation by only changing the redemption threshold $O(\log T)$ times, over a horizon of length $T$. This algorithm achieves the optimal (up to polylogarithmic factors) $\widetilde{O}(\sqrt{T})$ regret in expectation. We then modify this algorithm to only ever decrease redemption thresholds, leading to improved fairness at a cost of only a constant factor in regret. Extensive numerical experiments show the limited value of personalization in average-case settings, in addition to demonstrating the strong practical performance of our proposed learning algorithms.

Large language models (LLMs) have enabled agents to perform complex reasoning and decision-making through free-form language interactions. However, in open-ended language action environments (e.g., negotiation or question-asking games), the action space can be formulated as a joint distribution over tokens, resulting in an exponentially large action space. Sampling actions in such a space can lead to extreme reward sparsity, which brings large reward variance, hindering effective reinforcement learning (RL). To address this, we propose ARIA, a method that Aggregates Rewards in Intention space to enable efficient and effective language Agents training. ARIA aims to project natural language actions from the high-dimensional joint token distribution space into a low-dimensional intention space, where semantically similar actions are clustered and assigned shared rewards. This intention-aware reward aggregation reduces reward variance by densifying reward signals, fostering better policy optimization. Extensive experiments demonstrate that ARIA not only significantly reduces policy gradient variance, but also delivers substantial performance gains of an average of 9.95% across four downstream tasks, consistently outperforming offline and online RL baselines.

Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning Dirichlet-to-Neumann maps on graphs using Gaussian processes, specifically for problems where the data obey a conservation constraint from an underlying partial differential equation. Our approach combines discrete exterior calculus and nonlinear optimal recovery to infer relationships between vertex and edge values. This framework yields data-driven predictions with uncertainty quantification across the entire graph, even when observations are limited to a subset of vertices and edges. By optimizing over the reproducing kernel Hilbert space norm while applying a maximum likelihood estimation penalty on kernel complexity, our method ensures that the resulting surrogate strictly enforces conservation laws without overfitting. We demonstrate our method on two representative applications: subsurface fracture networks and arterial blood flow. Our results show that the method maintains high accuracy and well-calibrated uncertainty estimates even under severe data scarcity, highlighting its potential for scientific applications where limited data and reliable uncertainty quantification are critical.

The Multi-Armed Bandit (MAB) problem is challenging in non-stationary environments where reward distributions evolve dynamically. We introduce RAVEN-UCB, a novel algorithm that combines theoretical rigor with practical efficiency via variance-aware adaptation. It achieves tighter regret bounds than UCB1 and UCB-V, with gap-dependent regret of order $K σ_{\max}^2 \log T / Δ$ and gap-independent regret of order $\sqrt{K T \log T}$. RAVEN-UCB incorporates three innovations: (1) variance-driven exploration using $\sqrt{\hatσ_k^2 / (N_k + 1)}$ in confidence bounds, (2) adaptive control via $α_t = α_0 / \log(t + ε)$, and (3) constant-time recursive updates for efficiency. Experiments across non-stationary patterns - distributional changes, periodic shifts, and temporary fluctuations - in synthetic and logistics scenarios demonstrate its superiority over state-of-the-art baselines, confirming theoretical and practical robustness.

Dynamic microsimulation has long been recognized as a powerful tool for policy analysis, but in fact most major health policy simulations lack path dependency, a critical feature for evaluating policies that depend on accumulated outcomes such as retirement savings, wealth, or debt. We propose the Longitudinal Health, Income and Employment Model (LHIEM), a path-dependent discrete-time microsimulation that predicts annual health care expenditures, family income, and health status for the U.S. population over a multi-year period. LHIEM advances the population from year to year as a Markov chain with modules capturing the particular dynamics of each predictive attribute. LHIEM was designed to assess a health care financing proposal that would allow individuals to borrow from the U.S. government to cover health care costs, requiring careful tracking of medical expenditures and medical debt over time. However, LHIEM is flexible enough to be used for a range of modeling needs related to predicting health care spending and income over time. In this paper, we present the details of the model and all dynamic modules, and include a case study to demonstrate how LHIEM can be used to evaluate proposed policy changes.

Understanding the complex interactions within dynamic multilayer networks is critical for advancements in various scientific domains. Existing models often fail to capture such networks' temporal and cross-layer dynamics. This paper introduces a novel Tensor State Space Model for Dynamic Multilayer Networks (TSSDMN), utilizing a latent space model framework. TSSDMN employs a symmetric Tucker decomposition to represent latent node features, their interaction patterns, and layer transitions. Then by fixing the latent features and allowing the interaction patterns to evolve over time, TSSDMN uniquely captures both the temporal dynamics within layers and across different layers. The model identifiability conditions are discussed. By treating latent features as variables whose posterior distributions are approximated using a mean-field variational inference approach, a variational Expectation Maximization algorithm is developed for efficient model inference. Numerical simulations and case studies demonstrate the efficacy of TSSDMN for understanding dynamic multilayer networks.

What are the essential components of world models? How far do we get with world models that are not employing RNNs, transformers, discrete representations, and image reconstructions? This paper introduces SGF, a Simple, Good, and Fast world model that uses self-supervised representation learning, captures short-time dependencies through frame and action stacking, and enhances robustness against model errors through data augmentation. We extensively discuss SGF's connections to established world models, evaluate the building blocks in ablation studies, and demonstrate good performance through quantitative comparisons on the Atari 100k benchmark.

The importance of clinical variables in the prognosis of the disease is explained using statistical correlation or machine learning (ML). However, the predictive importance of these variables may not represent their causal relationships with diseases. This paper uses clinical variables from a heart failure (HF) patient cohort to investigate the causal explainability of important variables obtained in statistical and ML contexts. Due to inherent regression modeling, popular causal discovery methods strictly assume that the cause and effect variables are numerical and continuous. This paper proposes a new computational framework to enable causal structure discovery (CSD) and score the causal strength of mixed-type (categorical, numerical, binary) clinical variables for binary disease outcomes. In HF classification, we investigate the association between the importance rank order of three feature types: correlated features, features important for ML predictions, and causal features. Our results demonstrate that CSD modeling for nonlinear causal relationships is more meaningful than its linear counterparts. Feature importance obtained from nonlinear classifiers (e.g., gradient-boosting trees) strongly correlates with the causal strength of variables without differentiating cause and effect variables. Correlated variables can be causal for HF, but they are rarely identified as effect variables. These results can be used to add the causal explanation of variables important for ML-based prediction modeling.

We study the recovery of multiple high-dimensional signals from two noisy, correlated modalities: a spiked matrix and a spiked tensor sharing a common low-rank structure. This setting generalizes classical spiked matrix and tensor models, unveiling intricate interactions between inference channels and surprising algorithmic behaviors. Notably, while the spiked tensor model is typically intractable at low signal-to-noise ratios, its correlation with the matrix enables efficient recovery via Bayesian Approximate Message Passing, inducing staircase-like phase transitions reminiscent of neural network phenomena. In contrast, empirical risk minimization for joint learning fails: the tensor component obstructs effective matrix recovery, and joint optimization significantly degrades performance, highlighting the limitations of naive multi-modal learning. We show that a simple Sequential Curriculum Learning strategy-first recovering the matrix, then leveraging it to guide tensor recovery-resolves this bottleneck and achieves optimal weak recovery thresholds. This strategy, implementable with spectral methods, emphasizes the critical role of structural correlation and learning order in multi-modal high-dimensional inference.

The hippocampus enables spatial navigation through place cell populations forming cognitive maps. We propose proximity-preserving neural embeddings to encode multi-scale random walk transitions, where the inner product $\langle h(x, t), h(y, t) \rangle = q(y|x, t)$ represents normalized transition probabilities, with $h(x, t)$ as the embedding at location $x$ and $q(y|x, t)$ as the transition probability at scale $\sqrt{t}$. This scale hierarchy mirrors hippocampal dorsoventral organization. The embeddings $h(x, t)$ reduce pairwise spatial proximity into an environmental map, with Euclidean distances preserving proximity information. We use gradient ascent on $q(y|x, t)$ for straight-forward path planning, employing adaptive scale selection for trap-free, smooth trajectories, equivalent to minimizing embedding space distances. Matrix squaring ($P_{2t} = P_t^2$) efficiently builds global transitions from local ones ($P_1$), enabling preplay-like shortcut prediction. Experiments demonstrate localized place fields, multi-scale tuning, adaptability, and remapping, achieving robust navigation in complex environments. Our biologically plausible framework, extensible to theta-phase precession, unifies spatial and temporal coding for scalable navigation.