The widespread use of generative models has created a feedback loop in which each generation of models is trained on data partially produced by its predecessors. This process has raised concerns about model collapse: A critical degradation in performance caused by repeated training on synthetic data. However, different analyses in the literature have reached different conclusions as to the severity of model collapse. As such, it remains unclear how concerning this phenomenon is, and under which assumptions it can be avoided. To address this, we theoretically study model collapse for maximum likelihood estimation (MLE), in a natural setting where synthetic data is gradually added to the original training set. Under standard assumptions (similar to those long used for proving asymptotic consistency and normality of MLE), we establish non-asymptotic bounds showing that collapse can be avoided even as the fraction of real data vanishes. On the other hand, we prove that some assumptions (beyond MLE consistency) are indeed necessary: Without them, model collapse can occur arbitrarily quickly, even when the original data is still present in the training set. To the best of our knowledge, these are the first rigorous examples of iterative generative modeling with accumulating data that rapidly leads to model collapse.

In real-world multi-agent systems (MASs), observation delays are ubiquitous, preventing agents from making decisions based on the environment's true state. An individual agent's local observation typically comprises multiple components from other agents or dynamic entities within the environment. These discrete observation components with varying delay characteristics pose significant challenges for multi-agent reinforcement learning (MARL). In this paper, we first formulate the decentralized stochastic individual delay partially observable Markov decision process (DSID-POMDP) by extending the standard Dec-POMDP. We then propose the Rainbow Delay Compensation (RDC), a MARL training framework for addressing stochastic individual delays, along with recommended implementations for its constituent modules. We implement the DSID-POMDP's observation generation pattern using standard MARL benchmarks, including MPE and SMAC. Experiments demonstrate that baseline MARL methods suffer severe performance degradation under fixed and unfixed delays.

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.

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.

We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes (POMDPs) with unobserved confounding. Recent advances have introduced bridge-function to circumvent unmeasured confounding and develop estimators for the policy value, yet the statistical error bounds of them related to the length of horizon $T$ and the size of the state-action space $|\mathcal{O}||\mathcal{A}|$ remain largely unexplored. In this paper, we systematically investigate the finite-sample error bounds of OPE estimators in finite-horizon tabular confounded POMDPs. Specifically, we show that under certain rank conditions, the estimation error for policy value can achieve a rate of $\mathcal{O}(T^{1.5}/\sqrt{n})$,

Optimal decision-making under partial observability requires agents to balance reducing uncertainty (exploration) against pursuing immediate objectives (exploitation). In this paper, we introduce a novel policy optimization framework for continuous partially observable Markov decision processes (POMDPs) that explicitly addresses this challenge. Our method casts policy learning as probabilistic inference in a non-Markovian Feynman--Kac model that inherently captures the value of information gathering by anticipating future observations, without requiring suboptimal approximations or handcrafted heuristics. To optimize policies under this model, we develop a nested sequential Monte Carlo (SMC) algorithm that efficiently estimates a history-dependent policy gradient under samples from the optimal trajectory distribution induced by the POMDP. We demonstrate the effectiveness of our algorithm across standard continuous POMDP benchmarks, where existing methods struggle to act under uncertainty.

In this paper, we consider a score-based Integer Programming (IP) approach for solving the Bayesian Network Structure Learning (BNSL) problem. State-of-the-art BNSL IP formulations suffer from the exponentially large number of variables and constraints. A standard approach in IP to address such challenges is to employ row and column generation techniques, which dynamically generate rows and columns, while the complex pricing problem remains a computational bottleneck for BNSL. For the general class of $\ell_0$-penalized likelihood scores, we show how the pricing problem can be reformulated as a difference of submodular optimization problem, and how the Difference of Convex Algorithm (DCA) can be applied as an inexact method to efficiently solve the pricing problems. Empirically, we show that, for continuous Gaussian data, our row and column generation approach yields solutions with higher quality than state-of-the-art score-based approaches, especially when the graph density increases, and achieves comparable performance against benchmark constraint-based and hybrid approaches, even when the graph size increases.

Hidden Markov Models (HMMs) are fundamental tools for modeling sequential data with latent states that follow Markovian dynamics. However, they present significant challenges in model fitting and computational efficiency on real-world datasets. In this work, we demonstrate that pre-trained large language models (LLMs) can effectively model data generated by HMMs through in-context learning (ICL) -- their ability to learn patterns from examples within the input context. We evaluate LLMs' performance on diverse synthetic HMMs, showing that their prediction accuracy converges to the theoretical optimum. We discover novel scaling trends influenced by HMM properties and provide theoretical conjectures for these empirical observations.

Continual learning is often motivated by the idea, known as the big world hypothesis, that ``the world is bigger'' than the agent. Recent problem formulations capture this idea by explicitly constraining an agent relative to the environment. These constraints lead to solutions in which the agent continually adapts to best use its limited capacity, rather than converging to a fixed solution. However, explicit constraints can be ad hoc, difficult to incorporate, and may limit the effectiveness of scaling up the agent's capacity. In this paper, we characterize a problem setting in which an agent, regardless of its capacity, is constrained by being embedded in the environment.

This paper introduces the Quotient Bayesian Learning Rule, an extension of natural-gradient Bayesian updates to probability models that fall outside the exponential family. Building on the observation that many heavy-tailed and otherwise non-exponential distributions arise as marginals of minimal exponential families, we prove that such marginals inherit a unique Fisher-Rao information geometry via the quotient-manifold construction. Exploiting this geometry, we derive the Quotient Natural Gradient algorithm, which takes steepest-descent steps in the well-structured covering space, thereby guaranteeing parameterization-invariant optimization in the target space. Empirical results on the Student-$t$ distribution confirm that our method converges more rapidly and attains higher-quality solutions than previous variants of the Bayesian Learning Rule.