Predicting future observations plays a central role in machine learning, biology, economics, and many other fields. It lies at the heart of organizational principles such as the variational free energy principle and has even been shown -- based on the second law of thermodynamics -- to be necessary for reaching the fundamental energetic limits of sequential information processing. While the usefulness of the predictive paradigm is undisputed, complex adaptive systems that interact with their environment are more than just predictive machines: they have the power to act upon their environment and cause change. In this work, we develop a framework to analyze the thermodynamics of information processing in percept-action loops -- a model of agent-environment interaction -- allowing us to investigate the thermodynamic implications of actions and percepts on equal footing. To this end, we introduce the concept of work capacity -- the maximum rate at which an agent can expect to extract work from its environment. Our results reveal that neither of two previously established design principles for work-efficient agents -- maximizing predictive power and forgetting past actions -- remains optimal in environments where actions have observable consequences. Instead, a trade-off emerges: work-efficient agents must balance prediction and forgetting, as remembering past actions can reduce the available free energy. This highlights a fundamental departure from the thermodynamics of passive observation, suggesting that prediction and energy efficiency may be at odds in active learning systems.

Considerable progress has been made in the recent literature studies to tackle the Algorithms Selection and Parametrization (ASP) problem, which is diversified in multiple meta-learning setups. Yet there is a lack of surveys and comparative evaluations that critically analyze, summarize and assess the performance of existing methods. In this paper, we provide an overview of the state of the art in this continuously evolving field. The survey sheds light on the motivational reasons for pursuing classifiers selection through meta-learning. In this regard, Automated Machine Learning (AutoML) is usually treated as an ASP problem under the umbrella of the democratization of machine learning. Accordingly, AutoML makes machine learning techniques accessible to domain scientists who are interested in applying advanced analytics but lack the required expertise. It can ease the task of manually selecting ML algorithms and tuning related hyperparameters. We comprehensively discuss the different phases of classifiers selection based on a generic framework that is formed as an outcome of reviewing prior works. Subsequently, we propose a benchmark knowledge base of 4 millions previously learned models and present extensive comparative evaluations of the prominent methods for classifiers selection based on 08 classification algorithms and 400 benchmark datasets. The comparative study quantitatively assesses the performance of algorithms selection methods along while emphasizing the strengths and limitations of existing studies.

Recent research has shown that representation learning models may accidentally memorize their training data. For example, the déjà vu method shows that for certain representation learning models and training images, it is sometimes possible to correctly predict the foreground label given only the representation of the background - better than through dataset-level correlations. However, their measurement method requires training two models - one to estimate dataset-level correlations and the other to estimate memorization. This multiple model setup becomes infeasible for large open-source models. In this work, we propose alternative simple methods to estimate dataset-level correlations, and show that these can be used to approximate an off-the-shelf model's memorization ability without any retraining. This enables, for the first time, the measurement of memorization in pre-trained open-source image representation and vision-language representation models. Our results show that different ways of measuring memorization yield very similar aggregate results. We also find that open-source models typically have lower aggregate memorization than similar models trained on a subset of the data. The code is available both for vision and vision language models.

In the field of legged robot motion control, reinforcement learning (RL) holds great promise but faces two major challenges: high computational cost for training individual robots and poor generalization of trained models. To address these problems, this paper proposes a novel framework called Prior Transfer Reinforcement Learning (PTRL), which improves both training efficiency and model transferability across different robots. Drawing inspiration from model transfer techniques in deep learning, PTRL introduces a fine-tuning mechanism that selectively freezes layers of the policy network during transfer, making it the first to apply such a method in RL. The framework consists of three stages: pre-training on a source robot using the Proximal Policy Optimization (PPO) algorithm, transferring the learned policy to a target robot, and fine-tuning with partial network freezing. Extensive experiments on various robot platforms confirm that this approach significantly reduces training time while maintaining or even improving performance. Moreover, the study quantitatively analyzes how the ratio of frozen layers affects transfer results, providing valuable insights into optimizing the process. The experimental outcomes show that PTRL achieves better walking control performance and demonstrates strong generalization and adaptability, offering a promising solution for efficient and scalable RL-based control of legged robots.

Multi-agent reinforcement learning (MARL) has shown promise for adaptive traffic signal control (ATSC), enabling multiple intersections to coordinate signal timings in real time. However, in large-scale settings, MARL faces constraints due to extensive data sharing and communication requirements. Federated learning (FL) mitigates these challenges by training shared models without directly exchanging raw data, yet traditional FL methods such as FedAvg struggle with highly heterogeneous intersections. Different intersections exhibit varying traffic patterns, demands, and road structures, so performing FedAvg across all agents is inefficient. To address this gap, we propose Hierarchical Federated Reinforcement Learning (HFRL) for ATSC. HFRL employs clustering-based or optimization-based techniques to dynamically group intersections and perform FedAvg independently within groups of intersections with similar characteristics, enabling more effective coordination and scalability than standard FedAvg. Our experiments on synthetic and real-world traffic networks demonstrate that HFRL not only outperforms both decentralized and standard federated RL approaches but also identifies suitable grouping patterns based on network structure or traffic demand, resulting in a more robust framework for distributed, heterogeneous systems.

We study Reinforcement Learning (RL) in environments with large state spaces, where function approximation is required for sample-efficient learning. Departing from a long history of prior work, we consider the weakest possible form of function approximation, called agnostic policy learning, where the learner seeks to find the best policy in a given class $\Pi$, with no guarantee that $\Pi$ contains an optimal policy for the underlying task. Although it is known that sample-efficient agnostic policy learning is not possible in the standard online RL setting without further assumptions, we investigate the extent to which this can be overcome with stronger forms of access to the environment. Specifically, we show that: 1. Agnostic policy learning remains statistically intractable when given access to a local simulator, from which one can reset to any previously seen state. This result holds even when the policy class is realizable, and stands in contrast to a positive result of [MFR24] showing that value-based learning under realizability is tractable with local simulator access. 2. Agnostic policy learning remains statistically intractable when given online access to a reset distribution with good coverage properties over the state space (the so-called $\mu$-reset setting). We also study stronger forms of function approximation for policy learning, showing that PSDP [BKSN03] and CPI [KL02] provably fail in the absence of policy completeness. 3. On a positive note, agnostic policy learning is statistically tractable for Block MDPs with access to both of the above reset models. We establish this via a new algorithm that carefully constructs a policy emulator: a tabular MDP with a small state space that approximates the value functions of all policies $\pi \in \Pi$. These values are approximated without any explicit value function class.

Abstract--In this paper, we analyze the performance of the estimation of Laplacian matrices under general observatio n models. Laplacian matrix estimation involves structural c on-straints, including symmetry and null-space properties, a long with matrix sparsity. By exploiting a linear reparametriza tion that enforces the structural constraints, we derive closed -form matrix expressions for the Cram er-Rao Bound (CRB) specifically tailored to Laplacian matrix estimation. We further extend the derivation to the sparsity-constrained case, introduc ing two oracle CRBs that incorporate prior information of the suppo rt set, i.e. the locations of the nonzero entries in the Laplaci an matrix. We examine the properties and order relations betwe en the bounds, and provide the associated Slepian-Bangs formu la for the Gaussian case. We demonstrate the use of the new CRBs in three representative applications: (i) topology identi fication in power systems, (ii) graph filter identification in diffuse d models, and (iii) precision matrix estimation in Gaussian M arkov random fields under Laplacian constraints. The CRBs are eval - uated and compared with the mean-squared-errors (MSEs) of the constrained maximum likelihood estimator (CMLE), whic h integrates both equality and inequality constraints along with sparsity constraints, and of the oracle CMLE, which knows the locations of the nonzero entries of the Laplacian matrix . We perform this analysis for the applications of power syste m topology identification and graphical LASSO, and demonstra te that the MSEs of the estimators converge to the CRB and oracle CRB, given a sufficient number of measurements. Graph-structured data and signals arise in numerous applications, including power systems, communications, finance, social networks, and biological networks, for analysis and inference of networks [ 2 ], [ 3 ]. In this context, the Laplacian matrix, which captures node connectivity and edge weights, serves as a fundamental tool for clustering [ 4 ], modeling graph diffusion processes [ 5 ], [ 6 ], topology inference [ 6 ]-[ 12 ], anomaly detection [ 13 ], graph-based filtering [ 14 ]-[ 18 ], and analyzing smoothness on graphs [ 19 ]. M. Halihal and T. Routtenberg are with the School of Electric al and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel, e-mail: moradha@post.bgu.ac.il, tirzar@b gu.ac.il.

Department of Decision Sciences, Bocconi Institute for Data Science and Analytics, Bocconi University, Milan Abstract Accurate tuning of hyperparameters is crucial to ensure that models can generalise effectively across different settings. We construct a variational approximation to a hierarchical Bayes procedure, and derive upper bounds for the contraction rate of the variational posterior in an abstract setting. The theory is applied to various Gaussian process priors and variational classes, resulting in minimax optimal rates. Our theoretical results are accompanied with numerical analysis both on synthetic and real world data sets. Keywords: variational inference, Bayesian model selection, Gaussian processes, nonparametric regression, adaptation, posterior contraction rates 1 Introduction A core challenge in Bayesian statistics is scalability, i.e. the computation of the posterior for large sample sizes. Variational Bayes approximation is a standard approach to speed up inference. Variational posteriors are random probability measures that minimise the Kullback-Leibler divergence between a suitable class of distributions and the otherwise hard to compute posterior. Typically, the variational class of distributions over which the optimisation takes place does not contain the original posterior, hence the variational procedure can be viewed as a projection onto this class. The projected variational distribution then approximates the posterior. During the approximation procedure one inevitably loses information and hence it is important to characterize the accuracy of the approach. Despite the wide use of variational approximations, their theoretical underpinning started to emerge only recently, see for instance Alquier and Ridgway (2020); Yang et al. (2020); Zhang and Gao (2020a); Ray and Szab o (2022). In a Bayesian procedure, the choice of prior reflects the presumed properties of the unknown parameter. In comparison to regular parametric models, where in view of the Bernstein-von Mises theorem the posterior is asymptotically normal, the prior plays a crucial role in the asymptotic behaviour of the posterior. In fact, the large-sample behaviour of the posterior typically depends intricately on the choice of prior hyperparam-eters, so it is vital that these are tuned correctly. The two classical approaches are hierarchical and empirical Bayes methods.

Complex systems with intricate causal dependencies challenge accurate prediction. Effective modeling requires precise physical process representation, integration of interdependent factors, and incorporation of multi-resolution observational data. These systems manifest in both static scenarios with instantaneous causal chains and temporal scenarios with evolving dynamics, complicating modeling efforts. Current methods struggle to simultaneously handle varying resolutions, capture physical relationships, model causal dependencies, and incorporate temporal dynamics, especially with inconsistently sampled data from diverse sources. We introduce Temporal-SVGDM: Score-based Variational Graphical Diffusion Model for Multi-resolution observations. Our framework constructs individual SDEs for each variable at its native resolution, then couples these SDEs through a causal score mechanism where parent nodes inform child nodes' evolution. This enables unified modeling of both immediate causal effects in static scenarios and evolving dependencies in temporal scenarios. In temporal models, state representations are processed through a sequence prediction model to predict future states based on historical patterns and causal relationships. Experiments on real-world datasets demonstrate improved prediction accuracy and causal understanding compared to existing methods, with robust performance under varying levels of background knowledge. Our model exhibits graceful degradation across different disaster types, successfully handling both static earthquake scenarios and temporal hurricane and wildfire scenarios, while maintaining superior performance even with limited data.

Increasing test-time computation has emerged as a promising direction for improving language model performance, particularly in scenarios where model finetuning is impractical or impossible due to computational constraints or private model weights. However, existing test-time search methods using a reward model (RM) often degrade in quality as compute scales, due to the over-optimization of what are inherently imperfect reward proxies. We introduce QAlign, a new test-time alignment approach. As we scale test-time compute, QAlign converges to sampling from the optimal aligned distribution for each individual prompt. By adopting recent advances in Markov chain Monte Carlo for text generation, our method enables better-aligned outputs without modifying the underlying model or even requiring logit access. We demonstrate the effectiveness of QAlign on mathematical reasoning benchmarks (GSM8K and GSM-Symbolic) using a task-specific RM, showing consistent improvements over existing test-time compute methods like best-of-n and majority voting. Furthermore, when applied with more realistic RMs trained on the Tulu 3 preference dataset, QAlign outperforms direct preference optimization (DPO), best-of-n, majority voting, and weighted majority voting on a diverse range of datasets (GSM8K, MATH500, IFEval, MMLU-Redux, and TruthfulQA). A practical solution to aligning language models at test time using additional computation without degradation, our approach expands the limits of the capability that can be obtained from off-the-shelf language models without further training.