The relationship between inverse reinforcement learning (IRL) and inverse optimization (IO) for Markov decision processes (MDPs) has been relatively underexplored in the literature, despite addressing the same problem. In this work, we revisit the relationship between the IO framework for MDPs, IRL, and apprenticeship learning (AL). We incorporate prior beliefs on the structure of the cost function into the IRL and AL problems, and demonstrate that the convex-analytic view of the AL formalism (Kamoutsi et al., 2021) emerges as a relaxation of our framework. Notably, the AL formalism is a special case in our framework when the regularization term is absent. Focusing on the suboptimal expert setting, we formulate the AL problem as a regularized min-max problem. The regularizer plays a key role in addressing the ill-posedness of IRL by guiding the search for plausible cost functions. To solve the resulting regularized-convex-concave-min-max problem, we use stochastic mirror descent (SMD) and establish convergence bounds for the proposed method. Numerical experiments highlight the critical role of regularization in learning cost vectors and apprentice policies.

-- We introduce a novel self-improving framework that enhances Embodied Visual Tracking (EVT) with Vision-Language Models (VLMs) to address the limitations of current active visual tracking systems in recovering from tracking failure. Our approach combines the off-the-shelf active tracking methods with VLMs' reasoning capabilities, deploying a fast visual policy for normal tracking and activating VLM reasoning only upon failure detection. The framework features a memory-augmented self-reflection mechanism that enables the VLM to progressively improve by learning from past experiences, effectively addressing VLMs' limitations in 3D spatial reasoning. Experimental results demonstrate significant performance improvements, with our framework boosting success rates by 72% with state-of-the-art RL-based approaches and 220% with PID-based methods in challenging environments. This work represents the first integration of VLM-based reasoning to assist EVT agents in proactive failure recovery, offering substantial advances for real-world robotic applications that require continuous target monitoring in dynamic, unstructured environments. I. INTRODUCTION Embodied Visual Tracking (EVT) is a critical task for embodied AI, requiring agents to track dynamic targets while navigating through unstructured environments. Unlike traditional visual tracking tasks [13], EVT requires agents to not only understand their surroundings but also to control their movements and camera angles to continuously monitor a target in an ever-changing context. This capability forms the foundation for numerous real-world robotic applications, such as social navigation and person-following robots [5], [22], [11], which must maintain awareness of a target human in dynamic environments, assistive robots that shadow users while avoiding obstacles.

Generative modeling of non-negative, discrete data, such as symbolic music, remains challenging due to two persistent limitations in existing methods. Firstly, many approaches rely on modeling continuous embeddings, which is suboptimal for inherently discrete data distributions. Secondly, most models optimize variational bounds rather than exact data likelihood, resulting in inaccurate likelihood estimates and degraded sampling quality. While recent diffusion-based models have addressed these issues separately, we tackle them jointly. In this work, we introduce the Information-Theoretic Discrete Poisson Diffusion Model (ItDPDM), inspired by photon arrival process, which combines exact likelihood estimation with fully discrete-state modeling. Central to our approach is an information-theoretic Poisson Reconstruction Loss (PRL) that has a provable exact relationship with the true data likelihood. ItDPDM achieves improved likelihood and sampling performance over prior discrete and continuous diffusion models on a variety of synthetic discrete datasets. Furthermore, on real-world datasets such as symbolic music and images, ItDPDM attains superior likelihood estimates and competitive generation quality-demonstrating a proof of concept for distribution-robust discrete generative modeling.

Predicting the trajectories of vehicles is crucial for the development of autonomous driving (AD) systems, particularly in complex and dynamic traffic environments. In this study, we introduce HiT (Human-like Trajectory Prediction), a novel model designed to enhance trajectory prediction by incorporating behavior-aware modules and dynamic centrality measures. Unlike traditional methods that primarily rely on static graph structures, HiT leverages a dynamic framework that accounts for both direct and indirect interactions among traffic participants. This allows the model to capture the subtle yet significant influences of surrounding vehicles, enabling more accurate and human-like predictions. To evaluate HiT's performance, we conducted extensive experiments using diverse and challenging real-world datasets, including NGSIM, HighD, RounD, ApolloScape, and MoCAD++. The results demonstrate that HiT consistently outperforms other top models across multiple metrics, particularly excelling in scenarios involving aggressive driving behaviors. This research presents a significant step forward in trajectory prediction, offering a more reliable and interpretable approach for enhancing the safety and efficiency of fully autonomous driving systems.

Probabilistic integral circuits (PICs) have been recently introduced as probabilistic models enjoying the key ingredient behind expressive generative models: continuous latent variables (LVs). PICs are symbolic computational graphs defining continuous LV models as hierarchies of functions that are summed and multiplied together, or integrated over some LVs. They are tractable if LVs can be analytically integrated out, otherwise they can be approximated by tractable probabilistic circuits (PC) encoding a hierarchical numerical quadrature process, called QPCs.So far, only tree-shaped PICs have been explored, and training them via numerical quadrature requires memory-intensive processing at scale. In this paper, we address these issues, and present: (i) a pipeline for building DAG-shaped PICs out of arbitrary variable decompositions, (ii) a procedure for training PICs using tensorized circuit architectures, and (iii) neural functional sharing techniques to allow scalable training.

We study Reinforcement Learning for partially observable systems using function approximation. We propose a new PO-bilinear framework, that is general enough to include models such as undercomplete tabular Partially Observable Markov Decision Processes (POMDPs), Linear Quadratic Gaussian (LQG), Predictive State Representations (PSRs), as well as a newly introduced model Hilbert Space Embeddings of POMDPs. Under this framework, we propose an actor-critic style algorithm that is capable to performing agnostic policy learning. Given a policy class that consists of memory based policies (i.e., policy that looks at a fixed-length window of recent observations), and a value function class that consists of functions taking both memory and future observations as inputs, our algorithm learns to compete against the best memory-based policy among the policy class. For certain examples such as undercomplete POMDPs and LQGs, by leveraging their special properties, our algorithm is even capable of competing against the globally optimal policy without paying an exponential dependence on the horizon.

Instrumental variables (IV) analysis is an important applied tool for areas such as healthcare and consumer economics. For IV analysis in high-dimensional settings, the Generalized Method of Moments (GMM) using deep neural networks offers an efficient approach. With non-i.i.d. data sourced from scattered decentralized clients, federated learning is a popular paradigm for training the models while promising data privacy. However, to our knowledge, no federated algorithm for either GMM or IV analysis exists to date. In this work, we introduce federated instrumental variables analysis (FedIV) via federated generalized method of moments (FedGMM). We formulate FedGMM as a federated zero-sum game defined by a federated non-convex non-concave minimax optimization problem, which is solved using federated gradient descent ascent (FedGDA) algorithm. One key challenge arises in theoretically characterizing the federated local optimality. To address this, we present properties and existence results of clients' local equilibria via FedGDA limit points. Thereby, we show that the federated solution consistently estimates the local moment conditions of every participating client. The proposed algorithm is backed by extensive experiments to demonstrate the efficacy of our approach.

Hollmann et al. ( Nature 637 (2025) 319-326) recently introduced TabPFN, a transformer-based deep learning model for regression and classification on tabular data, which they claim "outperforms all previous methods on datasets with up to 10,000 samples by a wide margin, using substantially less training time. " Furthermore, they have called TabPFN a "foundation model" for tabular data, as it can support "data generation, density estimation, learning reusable embeddings and fine-tuning" . If these statements are well-supported, TabPFN may have the potential to supersede existing modeling approaches on a wide range of statistical tasks, mirroring a similar revolution in other areas of artificial intelligence that began with the advent of large language models. In this paper, we provide a tailored explanation of how TabPFN works for a statistics audience, by emphasizing its interpretation as approximate Bayesian inference. We also provide more evidence of TabPFN's "foundation model" capabilities: We show that an out-of-the-box application of TabPFN vastly outperforms specialized state-of-the-art methods for semi-supervised parameter estimation, prediction under covariate shift, and heterogeneous treatment effect estimation. We further show that TabPFN can outperform LASSO at sparse regression and can break a robustness-efficiency trade-off in classification.

We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can simulate model outputs given parameter values. CPE utilizes a normalizing flow-based (NF) approximation to the posterior distribution which carefully incorporates the conditional dependence structure induced by the graphical representation of the model into the neural network. Thereby it is possible to improve the accuracy of the approximation. We introduce both discrete and continuous NF architectures for CPE and propose a constant-time sampling procedure for the continuous case which reduces the computational complexity of drawing samples to O(1) as for discrete NFs. We show, through an extensive experimental evaluation, that by incorporating the conditional dependencies induced by the graphical model directly into the neural network, rather than learning them from data, CPE is able to conduct highly accurate posterior inference either outperforming or matching the state of the art in the field.

Quantifying differences between probability distributions is fundamental to statistics and machine learning, primarily for comparing statistical uncertainty. In contrast, epistemic uncertainty (EU) -- due to incomplete knowledge -- requires richer representations than those offered by classical probability. Imprecise probability (IP) theory offers such models, capturing ambiguity and partial belief. This has driven growing interest in imprecise probabilistic machine learning (IPML), where inference and decision-making rely on broader uncertainty models -- highlighting the need for metrics beyond classical probability. This work introduces the Integral Imprecise Probability Metric (IIPM) framework, a Choquet integral-based generalisation of classical Integral Probability Metric (IPM) to the setting of capacities -- a broad class of IP models encompassing many existing ones, including lower probabilities, probability intervals, belief functions, and more. Theoretically, we establish conditions under which IIPM serves as a valid metric and metrises a form of weak convergence of capacities. Practically, IIPM not only enables comparison across different IP models but also supports the quantification of epistemic uncertainty within a single IP model. In particular, by comparing an IP model with its conjugate, IIPM gives rise to a new class of EU measures -- Maximum Mean Imprecision -- which satisfy key axiomatic properties proposed in the Uncertainty Quantification literature. We validate MMI through selective classification experiments, demonstrating strong empirical performance against established EU measures, and outperforming them when classical methods struggle to scale to a large number of classes. Our work advances both theory and practice in IPML, offering a principled framework for comparing and quantifying epistemic uncertainty under imprecision.