Multi-Agent Search and Rescue (MASAR) plays a vital role in disaster response, exploration, and reconnaissance. However, dynamic and unknown environments pose significant challenges due to target unpredictability and environmental uncertainty. To tackle these issues, we propose PILOC, a framework that operates without global prior knowledge, leveraging local perception and communication. It introduces a pheromone inverse guidance mechanism to enable efficient coordination and dynamic target localization. PILOC promotes decentralized cooperation through local communication, significantly reducing reliance on global channels. Unlike conventional heuristics, the pheromone mechanism is embedded into the observation space of Deep Reinforcement Learning (DRL), supporting indirect agent coordination based on environmental cues. We further integrate this strategy into a DRL-based multi-agent architecture and conduct extensive experiments. Results show that combining local communication with pheromone-based guidance significantly boosts search efficiency, adaptability, and system robustness. Compared to existing methods, PILOC performs better under dynamic and communication-constrained scenarios, offering promising directions for future MASAR applications.

We show that mixtures comprised of multicomponent systems typically are much more structurally complex than the sum of their parts; sometimes, infinitely more complex. We contrast this with the more familiar notion of statistical mixtures, demonstrating how statistical mixtures miss key aspects of emergent hierarchical organization. This leads us to identify a new kind of structural complexity inherent in multicomponent systems and to draw out broad consequences for system ergodicity.

Efficient exploration is a well known problem in deep reinforcement learning and this problem is exacerbated in multi-agent reinforcement learning due the intrinsic complexities of such algorithms. There are several approaches to efficiently explore an environment to learn to solve tasks by multi-agent operating in that environment, of which, the idea of expert exploration is investigated in this work. More specifically, this work investigates the application of large-language models as expert planners for efficient exploration in planning based tasks for multiple agents.

Invariant prediction [Peters et al., 2016] analyzes feature/outcome data from multiple environments to identify invariant features - those with a stable predictive relationship to the outcome. Such features support generalization to new environments and help reveal causal mechanisms. Previous methods have primarily tackled this problem through hypothesis testing or regularized optimization. Here we develop Bayesian Invariant Prediction (BIP), a probabilistic model for invariant prediction. BIP encodes the indices of invariant features as a latent variable and recover them by posterior inference. Under the assumptions of Peters et al. [2016], the BIP posterior targets the true invariant features. We prove that the posterior is consistent and that greater environment heterogeneity leads to faster posterior contraction. To handle many features, we design an efficient variational approximation called VI-BIP. In simulations and real data, we find that BIP and VI-BIP are more accurate and scalable than existing methods for invariant prediction.

stCEG is an R package which allows a user to fully specify a Chain Event Graph (CEG) model from data and to produce interactive plots. It includes functions for the user to visualise spatial variables they wish to include in the model. There is also a web-based graphical user interface (GUI) provided, increasing ease of use for those without knowledge of R. We demonstrate stCEG using a dataset of homicides in London, which is included in the package. stCEG is the first software package for CEGs that allows for full model customisation.

Gaussian processes (GPs) are widely used as surrogate models for complicated functions in scientific and engineering applications. In many cases, prior knowledge about the function to be approximated, such as monotonicity, is available and can be leveraged to improve model fidelity. Incorporating such constraints into GP models enhances predictive accuracy and reduces uncertainty, but remains a computationally challenging task for high-dimensional problems. In this work, we present a novel virtual point-based framework for building constrained GP models under monotonicity constraints, based on regularized linear randomize-then-optimize (RLRTO), which enables efficient sampling from a constrained posterior distribution by means of solving randomized optimization problems. We also enhance two existing virtual point-based approaches by replacing Gibbs sampling with the No U-Turn Sampler (NUTS) for improved efficiency. A Python implementation of these methods is provided and can be easily applied to a wide range of problems. This implementation is then used to validate the approaches on approximating a range of synthetic functions, demonstrating comparable predictive performance between all considered methods and significant improvements in computational efficiency with the two NUTS methods and especially with the RLRTO method. The framework is further applied to construct surrogate models for systems of differential equations.

Prediction uncertainty quantification is a key research topic in recent years scientific and business problems. In insurance industries (\cite{parodi2023pricing}), assessing the range of possible claim costs for individual drivers improves premium pricing accuracy. It also enables insurers to manage risk more effectively by accounting for uncertainty in accident likelihood and severity. In the presence of covariates, a variety of regression-type models are often used for modeling insurance claims, ranging from relatively simple generalized linear models (GLMs) to regularized GLMs to gradient boosting models (GBMs). Conformal predictive inference has arisen as a popular distribution-free approach for quantifying predictive uncertainty under relatively weak assumptions of exchangeability, and has been well studied under the classic linear regression setting. In this work, we propose new non-conformity measures for GLMs and GBMs with GLM-type loss. Using regularized Tweedie GLM regression and LightGBM with Tweedie loss, we demonstrate conformal prediction performance with these non-conformity measures in insurance claims data. Our simulation results favor the use of locally weighted Pearson residuals for LightGBM over other methods considered, as the resulting intervals maintained the nominal coverage with the smallest average width.

Closed-loop learning is the process of repeatedly estimating a model from data generated from the model itself. It is receiving great attention due to the possibility that large neural network models may, in the future, be primarily trained with data generated by artificial neural networks themselves. We study this process for models that belong to exponential families, deriving equations of motions that govern the dynamics of the parameters. We show that maximum likelihood estimation of the parameters endows sufficient statistics with the martingale property and that as a result the process converges to absorbing states that amplify initial biases present in the data. However, we show that this outcome may be prevented if the data contains at least one data point generated from a ground truth model, by relying on maximum a posteriori estimation or by introducing regularisation.

A common class of algorithms for informative path planning (IPP) follows boustrophedon ("as the ox turns") patterns, which aim to achieve uniform area coverage. However, IPP is often applied in scenarios where anomalies, such as plant diseases, pollution, or hurricane damage, appear in clusters. In such cases, prioritizing the exploration of anomalous regions over uniform coverage is beneficial. This work introduces a class of algorithms referred to as bounomōdes ("as the ox grazes"), which alternates between uniform boustrophedon sampling and targeted exploration of detected anomaly clusters. While uniform sampling can be designed using geometric principles, close exploration of clusters depends on the spatial distribution of anomalies and must be learned. In our implementation, the close exploration behavior is learned using deep reinforcement learning algorithms. Experimental evaluations demonstrate that the proposed approach outperforms several established baselines.

For reinforcement learning agents to be deployed in high-risk settings, they must achieve a high level of robustness to unfamiliar scenarios. One approach for improving robustness is unsupervised environment design (UED), a suite of methods that aim to maximise an agent's generalisability by training it on a wide variety of environment configurations. In this work, we study UED from an optimisation perspective, providing stronger theoretical guarantees for practical settings than prior work. Whereas previous methods relied on guarantees if they reach convergence, our framework employs a nonconvex-strongly-concave objective for which we provide a provably convergent algorithm in the zero-sum setting. We empirically verify the efficacy of our method, outperforming prior methods on two of three environments with varying difficulties.