Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper provides a comprehensive review of advanced ML methodologies designed to handle unstructured grid data in high-dimensional dynamical systems. Key approaches discussed include graph neural networks, transformer models with spatial attention mechanisms, interpolation-integrated ML methods, and meshless techniques such as physics-informed neural networks. These methodologies have proven effective across diverse fields, including fluid dynamics and environmental simulations. This review is intended as a guidebook for computational scientists seeking to apply ML approaches to unstructured grid data in their domains, as well as for ML researchers looking to address challenges in computational physics. It places special focus on how ML methods can overcome the inherent limitations of traditional numerical techniques and, conversely, how insights from computational physics can inform ML development. To support benchmarking, this review also provides a summary of open-access datasets of unstructured grid data in computational physics. Finally, emerging directions such as generative models with unstructured data, reinforcement learning for mesh generation, and hybrid physics-data-driven paradigms are discussed to inspire future advancements in this evolving field.

Offline Reinforcement Learning (RL) algorithms learn a policy using a fixed training dataset, which is then deployed online to interact with the environment and make decisions. Transformers, a standard choice for modeling time-series data, are gaining popularity in offline RL. In this context, Beam Search (BS), an approximate inference algorithm, is the go-to decoding method. Offline RL eliminates the need for costly or risky online data collection. However, the restricted dataset induces uncertainty as the agent may encounter unfamiliar sequences of states and actions during execution that were not covered in the training data. In this context, BS lacks two important properties essential for offline RL: It does not account for the aforementioned uncertainty, and its greedy left-right search approach often results in sequences with minimal variations, failing to explore potentially better alternatives. To address these limitations, we propose Portfolio Beam Search (PBS), a simple-yet-effective alternative to BS that balances exploration and exploitation within a Transformer model during decoding. We draw inspiration from financial economics and apply these principles to develop an uncertainty-aware diversification mechanism, which we integrate into a sequential decoding algorithm at inference time. We empirically demonstrate the effectiveness of PBS on the D4RL locomotion benchmark, where it achieves higher returns and significantly reduces outcome variability.

Infectious diseases pose major public health challenges to society, highlighting the importance of designing effective policies to reduce economic loss and mortality. In this paper, we propose a framework for sequential decision-making under uncertainty to design fairness-aware disease mitigation policies that incorporate various measures of unfairness. Specifically, our approach learns equitable vaccination and lockdown strategies based on a stochastic multi-group SIR model. To address the challenges of solving the resulting sequential decision-making problem, we adopt the path integral control algorithm as an efficient solution scheme. Through a case study, we demonstrate that our approach effectively improves fairness compared to conventional methods and provides valuable insights for policymakers.

We present a novel method for Deep Reinforcement Learning (DRL), incorporating the convex property of the value function over the belief space in Partially Observable Markov Decision Processes (POMDPs). We introduce hard- and soft-enforced convexity as two different approaches, and compare their performance against standard DRL on two well-known POMDP environments, namely the Tiger and FieldVisionRockSample problems. Our findings show that including the convexity feature can substantially increase performance of the agents, as well as increase robustness over the hyperparameter space, especially when testing on out-of-distribution domains. The source code for this work can be found at https://github.com/Dakout/Convex_DRL.

Integrated communication and control serves as a critical ingredient in Multi-Agent Reinforcement Learning. However, partial observability limitations will impair collaboration effectiveness, and a potential solution is to establish consensus through well-calibrated latent variables obtained from neighboring agents. Nevertheless, the rigid transmission of less informative content can still result in redundant information exchanges. Therefore, we propose a Consensus-Driven Event-Based Graph Information Bottleneck (CDE-GIB) method, which integrates the communication graph and information flow through a GIB regularizer to extract more concise message representations while avoiding the high computational complexity of inner-loop operations. To further minimize the communication volume required for establishing consensus during interactions, we also develop a variable-threshold event-triggering mechanism. By simultaneously considering historical data and current observations, this mechanism capably evaluates the importance of information to determine whether an event should be triggered. Experimental results demonstrate that our proposed method outperforms existing state-of-the-art methods in terms of both efficiency and adaptability.

In this paper, we study a reinforcement learning (RL) setting where a deployed policy impacts multiple stakeholders in different ways. Each stakeholder is associated with a unique reward function, and the goal is to train a policy that adequately aggregates their preferences. This setting, which is often modeled using multi-objective reinforcement learning (MORL), arises in many RL applications, such as fair resource allocation in healthcare [32], cloud computing [27, 18] and communication networks [36, 7]. Recently, with the rise of large language models (LLMs), reinforcement learning from human feedback (RLHF) techniques that reflect the preferences of heterogeneous individuals have also been explored [6, 38, 26]. Preference aggregation in such scenarios is often achieved by choosing a social welfare function, which takes the utilities of multiple stakeholders as input and outputs a scalar value representing the overall welfare [37, 9, 32, 13, 38, 26, 6]. However, selecting the appropriate social welfare function is a nontrivial task, as each function embodies a different notion of social welfare and can lead to vastly different outcomes for the involved stakeholders. In this work, we focus on a class of social welfare functions known as generalized p-means, a widely used class of social welfare functions in algorithmic fairness and social choice theory.

We propose a novel reinforcement learning framework for post training large language models that does not rely on human in the loop feedback. Instead, our approach uses cross attention signals within the model itself to derive a self supervised reward, thereby guiding iterative fine tuning of the model policy. By analyzing how the model attends to the input prompt during generation, we construct measures of prompt coverage, focus, and coherence. We then use these measures to rank or score candidate responses, providing a reward signal that encourages the model to produce well aligned, on topic text. In empirical comparisons against standard policy gradient methods and RL fine tuning with synthetic preference models, our method shows significant gains in prompt relevance and consistency over a non RL baseline. While it does not yet match the performance of fully human supervised RLHF systems, it highlights an important direction for scaling alignment with minimal human labeling. We provide a detailed analysis, discuss potential limitations, and outline future work for combining cross-attention based signals with smaller amounts of human feedback.

We consider linear two-time-scale stochastic approximation algorithms driven by martingale noise. Recent applications in machine learning motivate the need to understand finite-time error rates, but conventional stochastic approximation analysis focus on either asymptotic convergence in distribution or finite-time bounds that are far from optimal. Prior work on asymptotic central limit theorems (CLTs) suggest that two-time-scale algorithms may be able to achieve $1/\sqrt{n}$ error in expectation, with a constant given by the expected norm of the limiting Gaussian vector. However, the best known finite-time rates are much slower. We derive the first non-asymptotic central limit theorem with respect to the Wasserstein-1 distance for two-time-scale stochastic approximation with Polyak-Ruppert averaging. As a corollary, we show that expected error achieved by Polyak-Ruppert averaging decays at rate $1/\sqrt{n}$, which significantly improves on the rates of convergence in prior works.

Reinforcement Learning (RL) has become a critical tool for optimization challenges within automation, leading to significant advancements in several areas. This review article examines the current landscape of RL within automation, with a particular focus on its roles in manufacturing, energy systems, and robotics. It discusses state-of-the-art methods, major challenges, and upcoming avenues of research within each sector, highlighting RL's capacity to solve intricate optimization challenges. The paper reviews the advantages and constraints of RL-driven optimization methods in automation. It points out prevalent challenges encountered in RL optimization, including issues related to sample efficiency and scalability; safety and robustness; interpretability and trustworthiness; transfer learning and meta-learning; and real-world deployment and integration. It further explores prospective strategies and future research pathways to navigate these challenges. Additionally, the survey includes a comprehensive list of relevant research papers, making it an indispensable guide for scholars and practitioners keen on exploring this domain.

While a number of existing approaches for building foundation model agents rely on prompting or fine-tuning with human demonstrations, it is not sufficient in dynamic environments (e.g., mobile device control). On-policy reinforcement learning (RL) should address these limitations, but collecting actual rollouts in an environment is often undesirable in truly open-ended agentic problems such as mobile device control or interacting with humans, where each unit of interaction is associated with a cost. In such scenarios, a method for policy learning that can utilize off-policy experience by learning a trained action-value function is much more effective. In this paper, we develop an approach, called Digi-Q, to train VLM-based action-value Q-functions which are then used to extract the agent policy. We study our approach in the mobile device control setting. Digi-Q trains the Q-function using offline temporal-difference (TD) learning, on top of frozen, intermediate-layer features of a VLM. Compared to fine-tuning the whole VLM, this approach saves us compute and enhances scalability. To make the VLM features amenable for representing the Q-function, we need to employ an initial phase of fine-tuning to amplify coverage over actionable information needed for value function. Once trained, we use this Q-function via a Best-of-N policy extraction operator that imitates the best action out of multiple candidate actions from the current policy as ranked by the value function, enabling policy improvement without environment interaction. Digi-Q outperforms several prior methods on user-scale device control tasks in Android-in-the-Wild, attaining 21.2% improvement over prior best-performing method. In some cases, our Digi-Q approach already matches state-of-the-art RL methods that require interaction. The project is open-sourced at https://github.com/DigiRL-agent/digiq