Finding Nash equilibria in imperfect-information games remains a central challenge in multi-agent reinforcement learning. While regularization-based methods have recently achieved last-iteration convergence to a regularized equilibrium, they require the regularization strength to shrink toward zero to approximate a Nash equilibrium, often leading to unstable learning in practice. Instead, we fix the regularization strength at a large value for robustness and achieve convergence by iteratively refining the reference policy. Our main theoretical result shows that this procedure guarantees strictly monotonic improvement and convergence to an exact Nash equilibrium in two-player zero-sum games, without requiring a uniqueness assumption. Building on this framework, we develop a practical algorithm, Nash Policy Gradient (NashPG), which preserves the generalizability of policy gradient methods while relying solely on the current and reference policies. Empirically, NashPG achieves comparable or lower exploitability than prior model-free methods on classic benchmark games and scales to large domains such as Battleship and No-Limit Texas Hold'em, where NashPG consistently attains higher Elo ratings.

We study a web-deployed, tool-augmented LLM health coach with real users. In a pilot with seven users (280 rated turns), offline policy evaluation (OPE) over factorized decision heads (Tool/Style) shows that a uniform heavy-tool policy raises average value on logs but harms specific subgroups, most notably low-health-literacy/high-self-efficacy users. A lightweight simulator with hidden archetypes further shows that adding a small early information-gain bonus reliably shortens trait identification and improves goal success and pass@3. Together, these early findings indicate an evaluation-first path to personalization: freeze the generator, learn subgroup-aware decision heads on typed rewards (objective tool outcomes and satisfaction), and always report per-archetype metrics to surface subgroup harms that averages obscure.

Safety is a major concern in reinforcement learning (RL): we aim at developing RL systems that not only perform optimally, but are also safe to deploy by providing formal guarantees about their safety. To this end, we introduce Probabilistic Shielding via Risk Augmentation (ProSh), a model-free algorithm for safe reinforcement learning under cost constraints. ProSh augments the Constrained MDP state space with a risk budget and enforces safety by applying a shield to the agent's policy distribution using a learned cost critic. The shield ensures that all sampled actions remain safe in expectation. We also show that optimality is preserved when the environment is deterministic. Since ProSh is model-free, safety during training depends on the knowledge we have acquired about the environment. We provide a tight upper-bound on the cost in expectation, depending only on the backup-critic accuracy, that is always satisfied during training. Under mild, practically achievable assumptions, ProSh guarantees safety even at training time, as shown in the experiments.

Achieving persistent tracking of multiple dynamic targets over a large spatial area poses significant challenges for a single-robot system with constrained sensing capabilities. As the robot moves to track different targets, the ones outside the field of view accumulate uncertainty, making them progressively harder to track. An effective path planning algorithm must manage uncertainty over a long horizon and account for the risk of permanently losing track of targets that remain unseen for too long. However, most existing approaches rely on short planning horizons and assume small, bounded environments, resulting in poor tracking performance and target loss in large-scale scenarios. In this paper, we present a hierarchical planner for tracking multiple moving targets with an aerial vehicle. To address the challenge of tracking non-static targets, our method incorporates motion models and uncertainty propagation during path execution, allowing for more informed decision-making. We decompose the multi-target tracking task into sub-tasks of single target search and detection, and our proposed pipeline consists a novel low-level coverage planner that enables searching for a target in an evolving belief area, and an estimation method to assess the likelihood of success for each sub-task, making it possible to convert the active target tracking task to a Markov decision process (MDP) that we solve with a tree-based algorithm to determine the sequence of sub-tasks. We validate our approach in simulation, demonstrating its effectiveness compared to existing planners for active target tracking tasks, and our proposed planner outperforms existing approaches, achieving a reduction of 11-70% in final uncertainty across different environments.

Humanoid table tennis (TT) demands rapid perception, proactive whole-body motion, and agile footwork under strict timing -- capabilities that remain difficult for unified controllers. We propose a reinforcement learning framework that maps ball-position observations directly to whole-body joint commands for both arm striking and leg locomotion, strengthened by predictive signals and dense, physics-guided rewards. A lightweight learned predictor, fed with recent ball positions, estimates future ball states and augments the policy's observations for proactive decision-making. During training, a physics-based predictor supplies precise future states to construct dense, informative rewards that lead to effective exploration. The resulting policy attains strong performance across varied serve ranges (hit rate $\geq$ 96% and success rate $\geq$ 92%) in simulations. Ablation studies confirm that both the learned predictor and the predictive reward design are critical for end-to-end learning. Deployed zero-shot on a physical Booster T1 humanoid with 23 revolute joints, the policy produces coordinated lateral and forward-backward footwork with accurate, fast returns, suggesting a practical path toward versatile, competitive humanoid TT.

World models allow agents to simulate the consequences of actions in imagined environments for planning, control, and long-horizon decision-making. However, existing autoregressive world models struggle with visually coherent predictions due to disrupted spatial structure, inefficient decoding, and inadequate motion modeling. In response, we propose \textbf{S}cale-wise \textbf{A}utoregression with \textbf{M}otion \textbf{P}r\textbf{O}mpt (\textbf{SAMPO}), a hybrid framework that combines visual autoregressive modeling for intra-frame generation with causal modeling for next-frame generation. Specifically, SAMPO integrates temporal causal decoding with bidirectional spatial attention, which preserves spatial locality and supports parallel decoding within each scale. This design significantly enhances both temporal consistency and rollout efficiency. To further improve dynamic scene understanding, we devise an asymmetric multi-scale tokenizer that preserves spatial details in observed frames and extracts compact dynamic representations for future frames, optimizing both memory usage and model performance. Additionally, we introduce a trajectory-aware motion prompt module that injects spatiotemporal cues about object and robot trajectories, focusing attention on dynamic regions and improving temporal consistency and physical realism. Extensive experiments show that SAMPO achieves competitive performance in action-conditioned video prediction and model-based control, improving generation quality with 4.4$\times$ faster inference. We also evaluate SAMPO's zero-shot generalization and scaling behavior, demonstrating its ability to generalize to unseen tasks and benefit from larger model sizes.

Inference in dynamic probabilistic models is a complex task involving expensive operations. In particular, for Hidden Markov Models, the whole state space has to be enumerated for advancing in time. Even states with negligible probabilities are considered, resulting in computational inefficiency and increased noise due to the propagation of unlikely probability mass. We propose to denoise the future and speed up inference by using only the top-p states, i.e., the most probable states with accumulated probability p. We show that the error introduced by using only the top-p states is bound by p and the so-called minimal mixing rate of the underlying model. Moreover, in our empirical evaluation, we show that we can expect speedups of at least an order of magnitude, while the error in terms of total variation distance is below 0.09.

While Variational Inference (VI) is central to modern generative models like Variational Autoencoders (VAEs) and Denoising Diffusion Models (DDMs), its pedagogical treatment is split across disciplines. In statistics, VI is typically framed as a Bayesian method for posterior approximation. In machine learning, however, VAEs and DDMs are developed from a Frequentist viewpoint, where VI is used to approximate a maximum likelihood estimator. This creates a barrier for statisticians, as the principles behind VAEs and DDMs are hard to contextualize without a corresponding Frequentist introduction to VI. This paper provides that introduction: we explain the theory for VI, VAEs, and DDMs from a purely Frequentist perspective, starting with the classical Expectation-Maximization (EM) algorithm. We show how VI arises as a scalable solution for intractable E-steps and how VAEs and DDMs are natural, deep-learning-based extensions of this framework, thereby bridging the gap between classical statistical inference and modern generative AI.

Modeling dynamical systems and unraveling their underlying causal relationships is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and stochastic in nature, and admit only partial, noisy state measurements. This poses a significant challenge for addressing the problems of modeling the underlying dynamics and inferring the network structure of these systems. Existing methods are typically tailored either for structure learning or modeling dynamics at the population level, but are limited in their ability to address both problems together. In this work, we address both problems simultaneously: we present StructureFlow, a novel and principled simulation-free approach for jointly learning the structure and stochastic population dynamics of physical systems. We showcase the utility of StructureFlow for the tasks of structure learning from interventions and dynamical (trajectory) inference of conditional population dynamics. We empirically evaluate our approach on high-dimensional synthetic systems, a set of biologically plausible simulated systems, and an experimental single-cell dataset. We show that StructureFlow can learn the structure of underlying systems while simultaneously modeling their conditional population dynamics -- a key step toward the mechanistic understanding of systems behavior.

The intricate dynamics of stock markets have led to extensive research on models that are able to effectively explain their inherent complexities. This study leverages the econometrics literature to explore the dynamic factor model as an interpretable model with sufficient predictive capabilities for capturing essential market phenomena. Although the model has been extensively applied for predictive purposes, this study focuses on analyzing the extracted loadings and common factors as an alternative framework for understanding stock price dynamics. The results reveal novel insights into traditional market theories when applied to the Philippine Stock Exchange using the Kalman method and maximum likelihood estimation, with subsequent validation against the capital asset pricing model. Notably, a one-factor model extracts a common factor representing systematic or market dynamics similar to the composite index, whereas a two-factor model extracts common factors representing market trends and volatility. Furthermore, an application of the model for nowcasting the growth rates of the Philippine gross domestic product highlights the potential of the extracted common factors as viable real-time market indicators, yielding over a 34% decrease in the out-of-sample prediction error. Overall, the results underscore the value of dynamic factor analysis in gaining a deeper understanding of market price movement dynamics.