Although actor-critic methods have been successful in practice, their theoretical analyses have several limitations. Specifically, existing theoretical work either sidesteps the exploration problem by making strong assumptions or analyzes impractical methods with complicated algorithmic modifications. Moreover, the actor-critic methods analyzed for linear MDPs often employ natural policy gradient and construct "implicit" policies without explicit parameterization. Such policies are computationally expensive to sample from, making the environment interactions inefficient. To that end, we focus on the finite-horizon linear MDPs and propose an optimistic actor-critic framework that uses parametric log-linear policies. In particular, we introduce a tractable $\textit{logit-matching}$ regression objective for the actor. For the critic, we use approximate Thompson sampling via Langevin Monte Carlo to obtain optimistic value estimates. We prove that the resulting algorithm achieves $\widetilde{\mathcal{O}}(ε^{-4})$ and $\widetilde{\mathcal{O}}(ε^{-2})$ sample complexity in the on-policy and off-policy setting, respectively. Our results match prior theoretical work in achieving the state-of-the-art sample complexity, while our algorithm is more aligned with practice.

Michael Pollan: 'Consciousness is really under siege' A psychedelic experience set author Michael Pollan on a quest to understand consciousness in his new book A World Appears. Michael Pollan: "Psychedelics have a way of smudging the windshield of experience" Author Michael Pollan has tackled plants, food and psychedelics in bestselling books including The Omnivore's Dilemma and How to Change Your Mind . Now, he has taken on the thorny problem of consciousness. In his latest book, Pollan charts the work of scientists and philosophers, weaving in literary perspectives along the way. He spoke to New Scientist about the value of writing a book where you know less at the end than before you started.

Cross-validation (CV) is commonly used to estimate predictive risk when independent test data are unavailable. Its validity depends on the assumption that validation tasks are sampled from the same distribution as prediction tasks encountered during deployment. In spatial prediction and other settings with structured data, this assumption is frequently violated, leading to biased estimates of deployment risk. We propose Target-Weighted CV (TWCV), an estimator of deployment risk that accounts for discrepancies between validation and deployment task distributions, thus accounting for (1) covariate shift and (2) task-difficulty shift. We characterize prediction tasks by descriptors such as covariates and spatial configuration. TWCV assigns weights to validation losses such that the weighted empirical distribution of validation tasks matches the corresponding distribution over a target domain. The weights are obtained via calibration weighting, yielding an importance-weighted estimator that targets deployment risk. Since TWCV requires adequate coverage of the deployment distribution's support, we combine it with spatially buffered resampling that diversifies the task difficulty distribution. In a simulation study, conventional as well as spatial estimators exhibit substantial bias depending on sampling, whereas buffered TWCV remains approximately unbiased across scenarios. A case study in environmental pollution mapping further confirms that discrepancies between validation and deployment task distributions can affect performance assessment, and that buffered TWCV better reflects the prediction task over the target domain. These results establish task distribution mismatch as a primary source of CV bias in spatial prediction and show that calibration weighting combined with a suitable validation task generator provides a viable approach to estimating predictive risk under dataset shift.

We propose a simple detection mechanism for the Gumbel watermarking scheme proposed by Aaronson (2022). The new mechanism is proven to be near-optimal in a problem-dependent sense among all model-agnostic watermarking schemes under the assumption that the next-token distribution is sampled i.i.d.

We present mlr3mbo, a comprehensive and modular toolbox for Bayesian optimization in R. mlr3mbo supports single- and multi-objective optimization, multi-point proposals, batch and asynchronous parallelization, input and output transformations, and robust error handling. While it can be used for many standard Bayesian optimization variants in applied settings, researchers can also construct custom BO algorithms from its flexible building blocks. In addition to an introduction to the software, its design principles, and its building blocks, the paper presents two extensive empirical evaluations of the software on the surrogate-based benchmark suite YAHPO Gym. To identify robust default configurations for both numeric and mixed-hierarchical optimization regimes, and to gain further insights into the respective impacts of individual settings, we run a coordinate descent search over the mlr3mbo configuration space and analyze its results. Furthermore, we demonstrate that mlr3mbo achieves state-of-the-art performance by benchmarking it against a wide range of optimizers, including HEBO, SMAC3, Ax, and Optuna.

Aligning human-interpretable concepts with the internal representations learned by modern machine learning systems remains a central challenge for interpretable AI. We introduce a geometric framework for comparing supervised human concepts with unsupervised intermediate representations extracted from foundation model embeddings. Motivated by the role of conceptual leaps in scientific discovery, we formalise the notion of concept frustration: a contradiction that arises when an unobserved concept induces relationships between known concepts that cannot be made consistent within an existing ontology. We develop task-aligned similarity measures that detect concept frustration between supervised concept-based models and unsupervised representations derived from foundation models, and show that the phenomenon is detectable in task-aligned geometry while conventional Euclidean comparisons fail. Under a linear-Gaussian generative model we derive a closed-form expression for Bayes-optimal concept-based classifier accuracy, decomposing predictive signal into known-known, known-unknown and unknown-unknown contributions and identifying analytically where frustration affects performance. Experiments on synthetic data and real language and vision tasks demonstrate that frustration can be detected in foundation model representations and that incorporating a frustrating concept into an interpretable model reorganises the geometry of learned concept representations, to better align human and machine reasoning. These results suggest a principled framework for diagnosing incomplete concept ontologies and aligning human and machine conceptual reasoning, with implications for the development and validation of safe interpretable AI for high-risk applications.

The use of transfer learning within Bayesian optimization addresses the disadvantages of the so-called \textit{cold start} problem by using source data to aid in the optimization of a target problem. We present a method that leverages an ensemble of surrogate models using transfer learning and integrates it in a constrained Bayesian optimization framework. We identify challenges particular to aircraft design optimization related to heterogeneous design variables and constraints. We propose the use of a partial-least-squares dimension reduction algorithm to address design space heterogeneity, and a \textit{meta} data surrogate selection method to address constraint heterogeneity. Numerical benchmark problems and an aircraft conceptual design optimization problem are used to demonstrate the proposed methods. Results show significant improvement in convergence in early optimization iterations compared to standard Bayesian optimization, with improved prediction accuracy for both objective and constraint surrogate models.

This paper focuses on the problem of unbounded density ratio estimation -- an understudied yet critical challenge in statistical learning -- and its application to covariate shift adaptation. Much of the existing literature assumes that the density ratio is either uniformly bounded or unbounded but known exactly. These conditions are often violated in practice, creating a gap between theoretical guarantees and real-world applicability. In contrast, this work directly addresses unbounded density ratios and integrates them into importance weighting for effective covariate shift adaptation. We propose a three-step estimation method that leverages unlabeled data from both the source and target distributions: (1) estimating a relative density ratio; (2) applying a truncation operation to control its unboundedness; and (3) transforming the truncated estimate back into the standard density ratio. The estimated density ratio is then employed as importance weights for regression under covariate shift. We establish rigorous, non-asymptotic convergence guarantees for both the proposed density ratio estimator and the resulting regression function estimator, demonstrating optimal or near-optimal convergence rates. Our findings offer new theoretical insights into density ratio estimation and learning under covariate shift, extending classical learning theory to more practical and challenging scenarios.

Aircraft design relies heavily on solving challenging and computationally expensive Multidisciplinary Design Optimization problems. In this context, there has been growing interest in multi-fidelity models for Bayesian optimization to improve the MDO process by balancing computational cost and accuracy through the combination of high- and low-fidelity simulation models, enabling efficient exploration of the design process at a minimal computational effort. In the existing literature, fidelity selection focuses only on the objective function to decide how to integrate multiple fidelity levels, balancing precision and computational cost using variance reduction criteria. In this work, we propose novel multi-fidelity selection strategies. Specifically, we demonstrate how incorporating information from both the objective and the constraints can further reduce computational costs without compromising the optimality of the solution. We validate the proposed multi-fidelity optimization strategy by applying it to four analytical test cases, showcasing its effectiveness. The proposed method is used to efficiently solve a challenging aircraft wing aero-structural design problem. The proposed setting uses a linear vortex lattice method and a finite element method for the aerodynamic and structural analysis respectively. We show that employing our proposed multi-fidelity approach leads to $86\%$ to $200\%$ more constraint compliant solutions given a limited budget compared to the state-of-the-art approach.

Constrained sampling is an important and challenging task in computational statistics, concerned with generating samples from a distribution under certain constraints. There are numerous types of algorithm aimed at this task, ranging from general Markov chain Monte Carlo, to unadjusted Langevin methods. In this article we propose a series of new sampling algorithms based on the latter of these, specifically the kinetic Langevin dynamics. Our series of algorithms are motivated on advanced numerical methods which are splitting order schemes, which include the BU and BAO families of splitting schemes.Their advantage lies in the fact that they have favorable strong order (bias) rates and computationally efficiency. In particular we provide a number of theoretical insights which include a Wasserstein contraction and convergence results. We are able to demonstrate favorable results, such as improved complexity bounds over existing non-splitting methodologies. Our results are verified through numerical experiments on a range of models with constraints, which include a toy example and Bayesian linear regression.