Sample inefficiency is a long-lasting challenge in deep reinforcement learning (DRL). Despite dramatic improvements have been made, the problem is far from being solved and is especially challenging in environments with sparse or delayed rewards. In our work, we propose to use Adversarial Estimates as a new, simple and efficient approach to mitigate this problem for a class of feedback-based DRL algorithms. Our approach leverages latent similarity search from a small set of human-collected trajectories to boost learning, using only five minutes of human-recorded experience. The results of our study show algorithms trained with Adversarial Estimates converge faster than their original version. Moreover, we discuss how our approach could enable learning in feedback-based algorithms in extreme scenarios with very sparse rewards.

What computational structures emerge in transformers trained on next-token prediction? In this work, we provide evidence that transformers implement constrained Bayesian belief updating -- a parallelized version of partial Bayesian inference shaped by architectural constraints. To do this, we integrate the model-agnostic theory of optimal prediction with mechanistic interpretability to analyze transformers trained on a tractable family of hidden Markov models that generate rich geometric patterns in neural activations. We find that attention heads carry out an algorithm with a natural interpretation in the probability simplex, and create representations with distinctive geometric structure. We show how both the algorithmic behavior and the underlying geometry of these representations can be theoretically predicted in detail -- including the attention pattern, OV-vectors, and embedding vectors -- by modifying the equations for optimal future token predictions to account for the architectural constraints of attention. Our approach provides a principled lens on how gradient descent resolves the tension between optimal prediction and architectural design.

In this paper, we propose a novel censoring policy for energy-efficient transmissions in energy-harvesting sensors. The problem is formulated as an infinite-horizon Markov Decision Process (MDP). The objective to be optimized is the expected sum of the importance (utility) of all transmitted messages. Assuming that such importance can be evaluated at the transmitting node, we show that, under certain conditions on the battery model, the optimal censoring policy is a threshold function on the importance value. Specifically, messages are transmitted only if their importance is above a threshold whose value depends on the battery level. Exploiting this property, we propose a model-based stochastic scheme that approximates the optimal solution, with less computational complexity and faster convergence speed than a conventional Q-learning algorithm. Numerical experiments in single-hop and multi-hop networks confirm the analytical advantages of the proposed scheme.

Advancements in mobility services, navigation systems, and smart transportation technologies have made it possible to collect large amounts of path data. Modeling the distribution of this path data, known as the Path Generation (PG) problem, is crucial for understanding urban mobility patterns and developing intelligent transportation systems. Recent studies have explored using diffusion models to address the PG problem due to their ability to capture multimodal distributions and support conditional generation. A recent work devises a diffusion process explicitly in graph space and achieves state-of-the-art performance. However, this method suffers a high computation cost in terms of both time and memory, which prohibits its application. In this paper, we analyze this method both theoretically and experimentally and find that the main culprit of its high computation cost is its explicit design of the diffusion process in graph space. To improve efficiency, we devise a Latent-space Path Diffusion (LPD) model, which operates in latent space instead of graph space. Our LPD significantly reduces both time and memory costs by up to 82.8% and 83.1%, respectively. Despite these reductions, our approach does not suffer from performance degradation. It outperforms the state-of-the-art method in most scenarios by 24.5%~34.0%.

A key paradigm to improve the reasoning capabilities of large language models (LLMs) is to allocate more inference-time compute to search against a verifier or reward model. This process can then be utilized to refine the pretrained model or distill its reasoning patterns into more efficient models. In this paper, we study inference-time compute by viewing chain-of-thought (CoT) generation as a metastable Markov process: easy reasoning steps (e.g., algebraic manipulations) form densely connected clusters, while hard reasoning steps (e.g., applying a relevant theorem) create sparse, low-probability edges between clusters, leading to phase transitions at longer timescales. Under this framework, we prove that implementing a search protocol that rewards sparse edges improves CoT by decreasing the expected number of steps to reach different clusters. In contrast, we establish a limit on reasoning capability when the model is restricted to local information of the pretrained graph. We also show that the information gained by search can be utilized to obtain a better reasoning model: (1) the pretrained model can be directly finetuned to favor sparse edges via policy gradient methods, and moreover (2) a compressed metastable representation of the reasoning dynamics can be distilled into a smaller, more efficient model.

Post-processing networks (PPNs) are components that modify the outputs of arbitrary modules in task-oriented dialogue systems and are optimized using reinforcement learning (RL) to improve the overall task completion capability of the system. However, previous PPN-based approaches have been limited to handling only a subset of modules within a system, which poses a significant limitation in improving the system performance. In this study, we propose a joint optimization method for post-processing the outputs of all modules using universal post-processing networks (UniPPNs), which are language-model-based networks that can modify the outputs of arbitrary modules in a system as a sequence-transformation task. Moreover, our RL algorithm, which employs a module-level Markov decision process, enables fine-grained value and advantage estimation for each module, thereby stabilizing joint learning for post-processing the outputs of all modules. Through both simulation-based and human evaluation experiments using the MultiWOZ dataset, we demonstrated that UniPPN outperforms conventional PPNs in the task completion capability of task-oriented dialogue systems.

World models are crucial for enabling agents to simulate and plan within environments, yet existing approaches struggle with long-term dependencies and inconsistent predictions. We introduce EDELINE, a novel framework that integrates diffusion models with linear-time state space modelsto enhance memory retention and temporal consistency. EDELINE employs a recurrent embedding module based on Mamba SSMs for processing unbounded sequences, a unified architecture for joint reward and termination prediction, and dynamic loss harmonization to balance multi-task learning. Our results across multiple benchmarks demonstrate EDELINE's superiority and robustness over prior baselines in long-horizon tasks.

To bridge the gap between empirical success and theoretical understanding in transfer reinforcement learning (RL), we study a principled approach with provable performance guarantees. We introduce a novel composite MDP framework where high-dimensional transition dynamics are modeled as the sum of a low-rank component representing shared structure and a sparse component capturing task-specific variations. This relaxes the common assumption of purely low-rank transition models, allowing for more realistic scenarios where tasks share core dynamics but maintain individual variations. We introduce UCB-TQL (Upper Confidence Bound Transfer Q-Learning), designed for transfer RL scenarios where multiple tasks share core linear MDP dynamics but diverge along sparse dimensions. When applying UCB-TQL to a target task after training on a source task with sufficient trajectories, we achieve a regret bound of $\tilde{O}(\sqrt{eH^5N})$ that scales independently of the ambient dimension. Here, $N$ represents the number of trajectories in the target task, while $e$ quantifies the sparse differences between tasks. This result demonstrates substantial improvement over single task RL by effectively leveraging their structural similarities. Our theoretical analysis provides rigorous guarantees for how UCB-TQL simultaneously exploits shared dynamics while adapting to task-specific variations.

Large Language Models (LLMs) are increasingly adopted in high-stakes scenarios, yet their safety mechanisms often remain fragile. Simple jailbreak prompts or even benign fine-tuning can bypass these protocols, underscoring the need to understand where and how they fail. Recent findings suggest that vulnerabilities emerge when alignment is confined to only the initial output tokens. Unfortunately, even with the introduction of deep safety alignment, determining the optimal safety depth remains an unresolved challenge. By leveraging the equivalence between autoregressive language models and Markov chains, this paper offers the first theoretical result on how to identify the ideal depth for safety alignment, and demonstrates how permutation-based data augmentation can tighten these bounds. Crucially, we reveal a fundamental interaction between alignment depth and ensemble width-indicating that broader ensembles can compensate for shallower alignments. These insights provide a theoretical foundation for designing more robust, scalable safety strategies that complement existing alignment approaches, opening new avenues for research into safer, more reliable LLMs.

Our friend and mentor Peter Caines has, together with his colleagues, created new foundations for studying collective dynamics in complex systems. Of particular inspiration to us has been his pioneering work in mean-field games (MFGs) launched two decades ago [10, 24, 25], and the related field of mean-field control. Peter pointed the way to both formulate and solve the problem of collective dynamics arising in a large population of heterogeneous dynamical systems. In this paper we survey some elements of MFGs within the context of controlled coupled oscillators. We begin by introducing a model for a single oscillator: dθ(t) = (ω + u(t)) dt + σ dξ(t), mod 2π (1) where θ(t) [0, 2π) is the phase of the oscillator at time t, ω is the nominal frequency with units of radiansper-second, {ξ(t): t 0} is a standard Wiener process, and u(t) is a control signal whose interpretation depends on the context. Unless otherwise noted, the SDEs are interpreted in their Itô form.