We introduce the Overcooked Generalisation Challenge (OGC) - the first benchmark to study agents' zero-shot cooperation abilities when faced with novel partners and levels in the Overcooked-AI environment. This perspective starkly contrasts a large body of previous work that has trained and evaluated cooperating agents only on the same level, failing to capture generalisation abilities required for real-world human-AI cooperation. Our challenge interfaces with state-of-the-art dual curriculum design (DCD) methods to generate auto-curricula for training general agents in Overcooked. It is the first cooperative multi-agent environment specially designed for DCD methods and, consequently, the first benchmarked with state-of-the-art methods. It is fully GPU-accelerated, built on the DCD benchmark suite minimax, and freely available under an open-source license: https://git.hcics.simtech.uni-stuttgart.de/public-projects/OGC. We show that current DCD algorithms struggle to produce useful policies in this novel challenge, even if combined with recent network architectures that were designed for scalability and generalisability. The OGC pushes the boundaries of real-world human-AI cooperation by enabling the research community to study the impact of generalisation on cooperating agents.

Test-time augmentation (TTA) is a well-known technique employed during the testing phase of computer vision tasks. It involves aggregating multiple augmented versions of input data. Combining predictions using a simple average formulation is a common and straightforward approach after performing TTA. This paper introduces a novel framework for optimizing TTA, called BayTTA (Bayesian-based TTA), which is based on Bayesian Model Averaging (BMA). First, we generate a model list associated with different variations of the input data created through TTA. Then, we use BMA to combine model predictions weighted by their respective posterior probabilities. Such an approach allows one to take into account model uncertainty, and thus to enhance the predictive performance of the related machine learning or deep learning model. We evaluate the performance of BayTTA on various public data, including three medical image datasets comprising skin cancer, breast cancer, and chest X-ray images and two well-known gene editing datasets, CRISPOR and GUIDE-seq. Our experimental results indicate that BayTTA can be effectively integrated into state-of-the-art deep learning models used in medical image analysis as well as into some popular pre-trained CNN models such as VGG-16, MobileNetV2, DenseNet201, ResNet152V2, and InceptionRes-NetV2, leading to the enhancement in their accuracy and robustness performance.

In this paper, we present a guide to the foundations of learning Dynamic Bayesian Networks (DBNs) from data in the form of multiple samples of trajectories for some length of time. We present the formalism for a generic as well as a set of common types of DBNs for particular variable distributions. We present the analytical form of the models, with a comprehensive discussion on the interdependence between structure and weights in a DBN model and their implications for learning. Next, we give a broad overview of learning methods and describe and categorize them based on the most important statistical features, and how they treat the interplay between learning structure and weights. We give the analytical form of the likelihood and Bayesian score functions, emphasizing the distinction from the static case. We discuss functions used in optimization to enforce structural requirements. We briefly discuss more complex extensions and representations. Finally we present a set of comparisons in different settings for various distinct but representative algorithms across the variants.

We consider the problem of privacy protection in Reinforcement Learning (RL) algorithms that operate over population processes, a practical but understudied setting that includes, for example, the control of epidemics in large populations of dynamically interacting individuals. In this setting, the RL algorithm interacts with the population over $T$ time steps by receiving population-level statistics as state and performing actions which can affect the entire population at each time step. An individual's data can be collected across multiple interactions and their privacy must be protected at all times. We clarify the Bayesian semantics of Differential Privacy (DP) in the presence of correlated data in population processes through a Pufferfish Privacy analysis. We then give a meta algorithm that can take any RL algorithm as input and make it differentially private. This is achieved by taking an approach that uses DP mechanisms to privatize the state and reward signal at each time step before the RL algorithm receives them as input. Our main theoretical result shows that the value-function approximation error when applying standard RL algorithms directly to the privatized states shrinks quickly as the population size and privacy budget increase. This highlights that reasonable privacy-utility trade-offs are possible for differentially private RL algorithms in population processes. Our theoretical findings are validated by experiments performed on a simulated epidemic control problem over large population sizes.

Specifying a prior distribution is an essential part of solving Bayesian inverse problems. The prior encodes a belief on the nature of the solution and this regularizes the problem. In this article we completely characterize a Gaussian prior that encodes the belief that the solution is a structured tensor. We first define the notion of (A,b)-constrained tensors and show that they describe a large variety of different structures such as Hankel, circulant, triangular, symmetric, and so on. Then we completely characterize the Gaussian probability distribution of such tensors by specifying its mean vector and covariance matrix. Furthermore, explicit expressions are proved for the covariance matrix of tensors whose entries are invariant under a permutation. These results unlock a whole new class of priors for Bayesian inverse problems. We illustrate how new kernel functions can be designed and efficiently computed and apply our results on two particular Bayesian inverse problems: completing a Hankel matrix from a few noisy measurements and learning an image classifier of handwritten digits. The effectiveness of the proposed priors is demonstrated for both problems. All applications have been implemented as reactive Pluto notebooks in Julia.

In standard reinforcement learning settings, agents typically assume immediate feedback about the effects of their actions after taking them. However, in practice, this assumption may not hold true due to physical constraints and can significantly impact the performance of learning algorithms. In this paper, we address observation delays in partially observable environments. We propose leveraging world models, which have shown success in integrating past observations and learning dynamics, to handle observation delays. By reducing delayed POMDPs to delayed MDPs with world models, our methods can effectively handle partial observability, where existing approaches achieve sub-optimal performance or degrade quickly as observability decreases. Experiments suggest that one of our methods can outperform a naive model-based approach by up to 250%. Moreover, we evaluate our methods on visual delayed environments, for the first time showcasing delay-aware reinforcement learning continuous control with visual observations.

We study the error introduced by entropy regularization in infinite-horizon discrete discounted Markov decision processes. We show that this error decreases exponentially in the inverse regularization strength both in a weighted KL-divergence and in value with a problemspecific exponent. We provide a lower bound matching our upper bound up to a polynomial term. Our proof relies on the correspondence of the solutions of entropy-regularized Markov decision processes with gradient flows of the unregularized reward with respect to a Riemannian metric common in natural policy gradient methods. This correspondence allows us to identify the limit of the gradient flow as the generalized maximum entropy optimal policy, thereby characterizing the implicit bias of this particular gradient flow which corresponds to a time-continuous version of the natural policy gradient method. We use our improved error estimates to show that for entropyregularized natural policy gradient methods the overall error decays exponentially in the square root of the number of iterations improving existing sublinear guarantees.

In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and engineering applications. The computational challenges we address with the proposed methodology are: (i) the need for repeated evaluations of expensive forward models; (ii) the potential existence of multiple modes; and (iii) the fact that gradient of, or adjoint solver for, the forward model might not be feasible. While existing Bayesian inference methods meet some of these challenges individually, we propose a framework that tackles all three systematically. Our approach builds upon the Fisher-Rao gradient flow in probability space, yielding a dynamical system for probability densities that converges towards the target distribution at a uniform exponential rate. This rapid convergence is advantageous for the computational burden outlined in (i). We apply Gaussian mixture approximations with operator splitting techniques to simulate the flow numerically; the resulting approximation can capture multiple modes thus addressing (ii). Furthermore, we employ the Kalman methodology to facilitate a derivative-free update of these Gaussian components and their respective weights, addressing the issue in (iii). The proposed methodology results in an efficient derivative-free sampler flexible enough to handle multi-modal distributions: Gaussian Mixture Kalman Inversion (GMKI). The effectiveness of GMKI is demonstrated both theoretically and numerically in several experiments with multimodal target distributions, including proof-of-concept and two-dimensional examples, as well as a large-scale application: recovering the Navier-Stokes initial condition from solution data at positive times.

When studying ecosystems, hierarchical trees are often used to organize entities based on proximity criteria, such as the taxonomy in microbiology, social classes in geography, or product types in retail businesses, offering valuable insights into entity relationships. Despite their significance, current count-data models do not leverage this structured information. In particular, the widely used Poisson log-normal (PLN) model, known for its ability to model interactions between entities from count data, lacks the possibility to incorporate such hierarchical tree structures, limiting its applicability in domains characterized by such complexities. To address this matter, we introduce the PLN-Tree model as an extension of the PLN model, specifically designed for modeling hierarchical count data. By integrating structured variational inference techniques, we propose an adapted training procedure and establish identifiability results, enhancisng both theoretical foundations and practical interpretability. Additionally, we extend our framework to classification tasks as a preprocessing pipeline, showcasing its versatility. Experimental evaluations on synthetic datasets as well as real-world microbiome data demonstrate the superior performance of the PLN-Tree model in capturing hierarchical dependencies and providing valuable insights into complex data structures, showing the practical interest of knowledge graphs like the taxonomy in ecosystems modeling.

Causal discovery in time series is a rapidly evolving field with a wide variety of applications in other areas such as climate science and neuroscience. Traditional approaches assume a stationary causal graph, which can be adapted to nonstationary time series with time-dependent effects or heterogeneous noise. In this work we address nonstationarity via regime-dependent causal structures. We first establish identifiability for high-order Markov Switching Models, which provide the foundations for identifiable regime-dependent causal discovery. Our empirical studies demonstrate the scalability of our proposed approach for high-order regime-dependent structure estimation, and we illustrate its applicability on brain activity data.