Robust partially observable Markov decision processes (RPOMDPs) model sequential decision-making problems under partial observability, where an agent must be robust against a range of dynamics. RPOMDPs can be viewed as a two-player game between an agent, who selects actions, and nature, who adversarially selects the dynamics. Evaluating an agent policy requires finding an adversarial nature policy, which is computationally challenging. In this paper, we advance the evaluation of agent policies for RPOMDPs in three ways. First, we discuss suitable benchmarks.

Inverse problems, where the goal is to recover an unknown signal from noisy or incomplete measurements, are central to applications in medical imaging, remote sensing, and computational biology. Diffusion models have recently emerged as powerful priors for solving such problems. However, existing methods either rely on projection-based techniques that enforce measurement consistency through heuristic updates, or they approximate the likelihood p(y | x), often resulting in artifacts and instability under complex or high-noise conditions. To address these limitations, we propose a novel framework called coupled data and measurement space diffusion posterior sampling (C-DPS), which eliminates the need for constraint tuning or likelihood approximation. C-DPS introduces a forward stochastic process in the measurement space {yt}, evolving in parallel with the data-space diffusion {xt}, which enables the derivation of a closed-form posterior p(xt 1 | xt,yt 1). This coupling allows for accurate and recursive sampling based on a well-defined posterior distribution. Empirical results demonstrate that C-DPS consistently outperforms existing baselines, both qualitatively and quantitatively, across multiple inverse problem benchmarks.

Task planning under uncertainty is essential for home-service robots operating in the real world. Tasks involve ambiguous human instructions, hidden or unknown object locations, and open-vocabulary object types, leading to significant open-ended uncertainty and a boundlessly large planning space. To address these challenges, we propose Tru-POMDP, a planner that combines structured belief generation using Large Language Models (LLMs) with principled POMDP planning. Tru-POMDP introduces a hierarchical Tree of Hypotheses (TOH), which systematically queries an LLM to construct high-quality particle beliefs over possible world states and human goals. We further formulate an open-ended POMDP model that enables rigorous Bayesian belief tracking and efficient belief-space planning over these LLM-generated hypotheses. Experiments on complex object rearrangement tasks across diverse kitchen environments show that Tru-POMDP significantly outperforms state-of-the-art LLM-based and LLM-tree-search hybrid planners, achieving higher success rates with significantly better plans, stronger robustness to ambiguity and occlusion, and greater planning efficiency.1

One way to address the known limitations of backpropagation through time is to directly adjust neural activities during the learning process. However, it remains unclear how to effectively use feedback to shape RNN dynamics. Here, we introduce error forcing (EF), where the network activity is guided orthogonally toward the zero-error manifold during learning. This method contrasts with alternatives like teaching forcing, which impose stronger constraints on neural activity and thus induce larger feedback influence on circuit dynamics. Furthermore, EF can be understood from a Bayesian perspective as a form of approximate dynamic inference. Empirically, EF consistently outperforms other learning algorithms across several tasks and its benefits persist when additional biological constraints are taken into account. Overall, EF is a powerful temporal credit assignment mechanism and a promising candidate model for learning in biological systems.

Neural simulation-based inference (SBI) is a popular set of methods for Bayesian inference when models are only available in the form of a simulator. These methods are widely used in the sciences and engineering, where writing down a likelihood can be significantly more challenging than constructing a simulator. However, the performance of neural SBI can suffer when simulators are computationally expensive, thereby limiting the number of simulations that can be performed. In this paper, we propose a novel approach to neural SBI which leverages multilevel Monte Carlo techniques for settings where several simulators of varying cost and fidelity are available. We demonstrate through both theoretical analysis and extensive experiments that our method can significantly enhance the accuracy of SBI methods given a fixed computational budget.

We address the learning problem in the context of infinite-horizon average-reward POMDPs. Traditionally, this problem has been approached using Spectral Decomposition (SD) methods applied to samples collected under non-adaptive policies, such as uniform or round-robin policies. Recently, SD techniques have been extended to accommodate a restricted class of adaptive policies such as memoryless policies. However, the use of adaptive policies has introduced challenges related to data inefficiency, as SD methods typically require all samples to be drawn from a single policy. In this work, we propose Mixed Spectral Estimation, which generalizes spectral estimation techniques to support a broader class of belief-based policies.

To learn approximately optimal acting policies for decision problems, modern Actor Critic algorithms rely on deep Neural Networks (DNNs) to parameterize the acting policy and greedification operators to iteratively improve it. The reliance on DNNs suggests an improvement that is gradient based, which is per step much less greedy than the improvement possible by greedier operators such as the greedy update used by Q-learning algorithms. On the other hand, slow changes to the policy can also be beneficial for the stability of the learning process, resulting in a tradeoff between greedification and stability. To better address this tradeoff, we propose to decouple the acting policy from the policy evaluated by the critic. This allows the agent to separately improve the critic's policy (e.g.

Quantifying uncertainty in deep regression models is important both for understanding the confidence of the model and for safe decision-making in high-risk domains. Existing approaches that yield prediction intervals overlook distributional information, neglecting the effect of multimodal or asymmetric distributions on decision-making.

Understanding how individual metro usage evolves over multi-year horizons is essential for transit planning and passenger retention. However, existing approaches typically characterize mobility patterns as static clusters or short-term variability, leaving the lifecycle dynamics of transit participation underexplored. This study proposes a state-based lifecycle modeling framework that integrates Hidden Semi-Markov Models (HSMM) with discrete-time survival analysis to characterize the evolution of individual metro mobility. The HSMM infers latent mobility states with explicit duration distributions and a transition matrix governing regime changes, while the survival component models exit and re-entry events via state-dependent hazard functions conditioned on mobility-state trajectories and behavioral history. Applied to four years of smart card data from the Shanghai metro system (2021-2024), the framework enables the identification of interpretable mobility states, the characterization of transition dynamics, and the quantification of state-dependent exit and re-entry processes. The analysis reveals five robust mobility states with a directional transition hierarchy centered on an occasional-usage gateway state, and fundamentally different temporal mechanisms governing disengagement and return: exit hazard is state-dependent but duration-independent, whereas re-entry hazard decays sharply with inactivity length. These findings provide a methodological foundation for lifecycle-oriented mobility analysis and practical guidance for transit operators to identify at-risk users and time retention interventions.

The nested sampling (NS) technique has gained widespread attention, particularly in cosmology and astronomy, due to its ability to efficiently explore high-likelihood regions - a feature akin to an implicit likelihood optimization that underlies its success. While the full theoretical derivation of NS is complex and involves several approximations, the central challenge lies in sampling from the likelihood-constrained priors, which is crucial for its performance. This work provides a comprehensive and detailed exposition of NS derivation, clarifying both its theoretical foundations and practical challenges. We provide a thorough description of the NS procedure, emphasizing both its strengths and potential limitations. In doing so, this work seeks to deepen understanding of the method and to foster the development of future enhancements, novel variants, and more efficient implementations across a wide range of scientific applications. Thus, the main contribution of this work is twofold: it serves both as a tutorial for newcomers to the field and as a critical review for experienced practitioners.