Inferring the graph structure from observed data is a key task in graph machine learning to capture the intrinsic relationship between data entities. While significant advancements have been made in learning the structure of homogeneous graphs, many real-world graphs exhibit heterogeneous patterns where nodes and edges have multiple types. This paper fills this gap by introducing the first approach for heterogeneous graph structure learning (HGSL). To this end, we first propose a novel statistical model for the data-generating process (DGP) of heterogeneous graph data, namely hidden Markov networks for heterogeneous graphs (H2MN). Then we formalize HGSL as a maximum a-posterior estimation problem parameterized by such DGP and derive an alternating optimization method to obtain a solution together with a theoretical justification of the optimization conditions. Finally, we conduct extensive experiments on both synthetic and real-world datasets to demonstrate that our proposed method excels in learning structure on heterogeneous graphs in terms of edge type identification and edge weight recovery.

Message Passing Neural Networks (MPNNs) are a class of Graph Neural Networks (GNNs) that leverage the graph topology to propagate messages across increasingly larger neighborhoods. The message-passing scheme leads to two distinct challenges: over-smoothing and over-squashing. DropEdge and its variants - DropNode, DropAgg and DropGNN - have successfully addressed the over-smoothing problem, their impact on over-squashing remains largely unexplored. This represents a critical gap in the literature as failure to mitigate over-squashing would make these methods unsuitable for longrange tasks. In this work, we take the first step towards closing this gap by studying the aforementioned algorithms in the context of over-squashing. We present novel theoretical results that characterize the negative effects of DropEdge on sensitivity between distant nodes, suggesting its unsuitability for long-range tasks. Our findings are easily extended to its variants, allowing us to build a comprehensive understanding of how they affect over-squashing. We evaluate these methods using real-world datasets, demonstrating their detrimental effects. Specifically, we show that while DropEdge-variants improve test-time performance in short-range tasks, they deteriorate performance in long-range ones. Our theory explains these results as follows: random edge-dropping lowers the effective receptive field of GNNs, which although beneficial for short-range tasks, misaligns the models on long-range ones. This forces the models to overfit to short-range artefacts in the training set, resulting in poor generalization. Our conclusions highlight the need to re-evaluate various methods designed for training deep GNNs, with a renewed focus on modelling long-range interactions. Graph-structured data is ubiquitous - it is found in social media platforms, online retail platforms, molecular structures, transportation networks, and even computer systems.

Reinforcement Learning (RL) problems are being considered under increasingly more complex structures. While tabular and linear models have been thoroughly explored, the analytical study of RL under nonlinear function approximation, especially kernel-based models, has recently gained traction for their strong representational capacity and theoretical tractability. In this context, we examine the question of statistical efficiency in kernel-based RL within the reward-free RL framework, specifically asking: how many samples are required to design a near-optimal policy? Existing work addresses this question under restrictive assumptions about the class of kernel functions. We first explore this question by assuming a generative model, then relax this assumption at the cost of increasing the sample complexity by a factor of H, the length of the episode. We tackle this fundamental problem using a broad class of kernels and a simpler algorithm compared to prior work. Our approach derives new confidence intervals for kernel ridge regression, specific to our RL setting, which may be of broader applicability. We further validate our theoretical findings through simulations.

One of the open challenges in Reinforcement Learning is the hard exploration problem in sparse reward environments. Various types of intrinsic rewards have been proposed to address this challenge by pushing towards diversity. This diversity might be imposed at different levels, favouring the agent to explore different states, policies or behaviours (State, Policy and Skill level diversity, respectively). However, the impact of diversity on the agent's behaviour remains unclear. In this work, we aim to fill this gap by studying the effect of different levels of diversity imposed by intrinsic rewards on the exploration patterns of RL agents. We select four intrinsic rewards (State Count, Intrinsic Curiosity Module (ICM), Maximum Entropy, and Diversity is all you need (DIAYN)), each pushing for a different diversity level. We conduct an empirical study on MiniGrid environment to compare their impact on exploration considering various metrics related to the agent's exploration, namely: episodic return, observation coverage, agent's position coverage, policy entropy, and timeframes to reach the sparse reward. The main outcome of the study is that State Count leads to the best exploration performance in the case of low-dimensional observations. However, in the case of RGB observations, the performance of State Count is highly degraded mostly due to representation learning challenges. Conversely, Maximum Entropy is less impacted, resulting in a more robust exploration, despite being not always optimal. Lastly, our empirical study revealed that learning diverse skills with DIAYN, often linked to improved robustness and generalisation, does not promote exploration in MiniGrid environments. This is because: i) learning the skill space itself can be challenging, and ii) exploration within the skill space prioritises differentiating between behaviours rather than achieving uniform state visitation.

The Credit Assignment Problem (CAP) refers to the longstanding challenge of Reinforcement Learning (RL) agents to associate actions with their long-term consequences. Solving the CAP is a crucial step towards the successful deployment of RL in the real world since most decision problems provide feedback that is noisy, delayed, and with little or no information about the causes. These conditions make it hard to distinguish serendipitous outcomes from those caused by informed decision-making. However, the mathematical nature of credit and the CAP remains poorly understood and defined. In this survey, we review the state of the art of Temporal Credit Assignment (CA) in deep RL. We propose a unifying formalism for credit that enables equitable comparisons of state of the art algorithms and improves our understanding of the trade-offs between the various methods. We cast the CAP as the problem of learning the influence of an action over an outcome from a finite amount of experience. We discuss the challenges posed by delayed effects, transpositions, and a lack of action influence, and analyse how existing methods aim to address them. Finally, we survey the protocols to evaluate a credit assignment method, and suggest ways to diagnoses the sources of struggle for different credit assignment methods. Overall, this survey provides an overview of the field for new-entry practitioners and researchers, it offers a coherent perspective for scholars looking to expedite the starting stages of a new study on the CAP, and it suggests potential directions for future research

We propose Grab-UCB, a graph-kernel multi-arms bandit algorithm to learn online the optimal source placement in large scale networks, such that the reward obtained from a priori unknown network processes is maximized. The uncertainty calls for online learning, which suffers however from the curse of dimensionality. To achieve sample efficiency, we describe the network processes with an adaptive graph dictionary model, which typically leads to sparse spectral representations. This enables a data-efficient learning framework, whose learning rate scales with the dimension of the spectral representation model instead of the one of the network. We then propose Grab-UCB, an online sequential decision strategy that learns the parameters of the spectral representation while optimizing the action strategy. We derive the performance guarantees that depend on network parameters, which further influence the learning curve of the sequential decision strategy We introduce a computationally simplified solving method, Grab-arm-Light, an algorithm that walks along the edges of the polytope representing the objective function. Simulations results show that the proposed online learning algorithm outperforms baseline offline methods that typically separate the learning phase from the testing one. The results confirm the theoretical findings, and further highlight the gain of the proposed online learning strategy in terms of cumulative regret, sample efficiency and computational complexity.

This work introduces MiDi, a novel diffusion model for jointly generating molecular graphs and their corresponding 3D arrangement of atoms. Unlike existing methods that rely on predefined rules to determine molecular bonds based on the 3D conformation, MiDi offers an end-to-end differentiable approach that streamlines the molecule generation process. Our experimental results demonstrate the effectiveness of this approach. On the challenging GEOM-DRUGS dataset, MiDi generates 92% of stable molecules, against 6% for the previous EDM model that uses interatomic distances for bond prediction, and 40% using EDM followed by an algorithm that directly optimize bond orders for validity. Our code is available at github.com/cvignac/MiDi.

We provide an information-theoretic analysis of the generalization ability of Gibbs-based transfer learning algorithms by focusing on two popular transfer learning approaches, $\alpha$-weighted-ERM and two-stage-ERM. Our key result is an exact characterization of the generalization behaviour using the conditional symmetrized KL information between the output hypothesis and the target training samples given the source samples. Our results can also be applied to provide novel distribution-free generalization error upper bounds on these two aforementioned Gibbs algorithms. Our approach is versatile, as it also characterizes the generalization errors and excess risks of these two Gibbs algorithms in the asymptotic regime, where they converge to the $\alpha$-weighted-ERM and two-stage-ERM, respectively. Based on our theoretical results, we show that the benefits of transfer learning can be viewed as a bias-variance trade-off, with the bias induced by the source distribution and the variance induced by the lack of target samples. We believe this viewpoint can guide the choice of transfer learning algorithms in practice.

Bounding the generalization error of a supervised learning algorithm is one of the most important problems in learning theory, and various approaches have been developed. However, existing bounds are often loose and lack of guarantees. As a result, they may fail to characterize the exact generalization ability of a learning algorithm. Our main contribution is an exact characterization of the expected generalization error of the well-known Gibbs algorithm in terms of symmetrized KL information between the input training samples and the output hypothesis. Such a result can be applied to tighten existing expected generalization error bound. Our analysis provides more insight on the fundamental role the symmetrized KL information plays in controlling the generalization error of the Gibbs algorithm.

Generalization error bounds are critical to understanding the performance of machine learning models. In this work, building upon a new bound of the expected value of an arbitrary function of the population and empirical risk of a learning algorithm, we offer a more refined analysis of the generalization behaviour of a machine learning models based on a characterization of (bounds) to their generalization error moments. We discuss how the proposed bounds -- which also encompass new bounds to the expected generalization error -- relate to existing bounds in the literature. We also discuss how the proposed generalization error moment bounds can be used to construct new generalization error high-probability bounds.