In this paper, we study the binary classification problem on $[0,1]^d$ under the Tsybakov noise condition (with exponent $s \in [0,\infty]$) and the compositional assumption. This assumption requires the conditional class probability function of the data distribution to be the composition of $q+1$ vector-valued multivariate functions, where each component function is either a maximum value function or a Hölder-$β$ smooth function that depends only on $d_*$ of its input variables. Notably, $d_*$ can be significantly smaller than the input dimension $d$. We prove that, under these conditions, the optimal convergence rate for the excess 0-1 risk of classifiers is $$ \left( \frac{1}{n} \right)^{\frac{β\cdot(1\wedgeβ)^q}{{\frac{d_*}{s+1}+(1+\frac{1}{s+1})\cdotβ\cdot(1\wedgeβ)^q}}}\;\;\;, $$ which is independent of the input dimension $d$. Additionally, we demonstrate that ReLU deep neural networks (DNNs) trained with hinge loss can achieve this optimal convergence rate up to a logarithmic factor. This result provides theoretical justification for the excellent performance of ReLU DNNs in practical classification tasks, particularly in high-dimensional settings. The technique used to establish these results extends the oracle inequality presented in our previous work. The generalized approach is of independent interest.

We study the problem of clustering $T$ trajectories of length $H$, each generated by one of $K$ unknown ergodic Markov chains over a finite state space of size $S$. The goal is to accurately group trajectories according to their underlying generative model. We begin by deriving an instance-dependent, high-probability lower bound on the clustering error rate, governed by the weighted KL divergence between the transition kernels of the chains. We then present a novel two-stage clustering algorithm. In Stage~I, we apply spectral clustering using a new injective Euclidean embedding for ergodic Markov chains -- a contribution of independent interest that enables sharp concentration results. Stage~II refines the initial clusters via a single step of likelihood-based reassignment. Our method achieves a near-optimal clustering error with high probability, under the conditions $H = \tildeΩ(γ_{\mathrm{ps}}^{-1} (S^2 \vee π_{\min}^{-1}))$ and $TH = \tildeΩ(γ_{\mathrm{ps}}^{-1} S^2 )$, where $π_{\min}$ is the minimum stationary probability of a state across the $K$ chains and $γ_{\mathrm{ps}}$ is the minimum pseudo-spectral gap. These requirements provide significant improvements, if not at least comparable, to the state-of-the-art guarantee (Kausik et al., 2023), and moreover, our algorithm offers a key practical advantage: unlike existing approach, it requires no prior knowledge of model-specific quantities (e.g., separation between kernels or visitation probabilities). We conclude by discussing the inherent gap between our upper and lower bounds, providing insights into the unique structure of this clustering problem.

Graph-based learning provides a powerful framework for modeling complex relational structures; however, its application within the domain of wireless security remains significantly underexplored. In this work, we introduce the first application of graph-based learning for jamming source localization, addressing the imminent threat of jamming attacks in wireless networks. Unlike geometric optimization techniques that struggle under environmental uncertainties and dense interference, we reformulate the localization as an inductive graph regression task. Our approach integrates structured node representations that encode local and global signal aggregation, ensuring spatial coherence and adaptive signal fusion. To enhance robustness, we incorporate an attention-based \ac{GNN} that adaptively refines neighborhood influence and introduces a confidence-guided estimation mechanism that dynamically balances learned predictions with domain-informed priors. We evaluate our approach under complex \ac{RF} environments with various sampling densities, network topologies, jammer characteristics, and signal propagation conditions, conducting comprehensive ablation studies on graph construction, feature selection, and pooling strategies. Results demonstrate that our novel graph-based learning framework significantly outperforms established localization baselines, particularly in challenging scenarios with sparse and obfuscated signal information. Our code is available at https://github.com/tiiuae/gnn-jamming-source-localization.

Recent work has shown that, under certain assumptions, zero-shot reinforcement learning (RL) methods can generalise to any unseen task in an environment after reward-free pre-training. Access to Markov states is one such assumption, yet, in many real-world applications, the Markov state is only partially observable . Here, we explore how the performance of standard zero-shot RL methods degrades when subjected to partially observability, and show that, as in single-task RL, memory-based architectures are an effective remedy. We evaluate our memory-based zero-shot RL methods in domains where the states, rewards and a change in dynamics are partially observed, and show improved performance over memory-free baselines.

The Susceptible-Infected-Susceptible (SIS) model is a widely used model for the spread of information and infectious diseases, particularly non-immunizing ones, on a graph. Given a highly contagious disease, a natural question is how to best vaccinate individuals to minimize the disease's extinction time. While previous works showed that the problem of optimal vaccination is closely linked to the NP-hard Spectral Radius Minimization (SRM) problem, they assumed that the graph is known, which is often not the case in practice. In this work, we consider the problem of minimizing the extinction time of an outbreak modeled by an SIS model where the graph on which the disease spreads is unknown and only the infection states of the vertices are observed. To this end, we split the problem into two: learning the graph and determining effective vaccination strategies. We propose a novel inclusion-exclusion-based learning algorithm and, unlike previous approaches, establish its sample complexity for graph recovery. We then detail an optimal algorithm for the SRM problem and prove that its running time is polynomial in the number of vertices for graphs with bounded treewidth. This is complemented by an efficient and effective polynomial-time greedy heuristic for any graph. Finally, we present experiments on synthetic and real-world data that numerically validate our learning and vaccination algorithms.

Offensive Robot Cybersecurity introduces a groundbreaking approach by advocating for offensive security methods empowered by means of automation. It emphasizes the necessity of understanding attackers' tactics and identifying vulnerabilities in advance to develop effective defenses, thereby improving robots' security posture. This thesis leverages a decade of robotics experience, employing Machine Learning and Game Theory to streamline the vulnerability identification and exploitation process. Intrinsically, the thesis uncovers a profound connection between robotic architecture and cybersecurity, highlighting that the design and creation aspect of robotics deeply intertwines with its protection against attacks. This duality -- whereby the architecture that shapes robot behavior and capabilities also necessitates a defense mechanism through offensive and defensive cybersecurity strategies -- creates a unique equilibrium. Approaching cybersecurity with a dual perspective of defense and attack, rooted in an understanding of systems architecture, has been pivotal. Through comprehensive analysis, including ethical considerations, the development of security tools, and executing cyber attacks on robot software, hardware, and industry deployments, this thesis proposes a novel architecture for cybersecurity cognitive engines. These engines, powered by advanced game theory and machine learning, pave the way for autonomous offensive cybersecurity strategies for robots, marking a significant shift towards self-defending robotic systems. This research not only underscores the importance of offensive measures in enhancing robot cybersecurity but also sets the stage for future advancements where robots are not just resilient to cyber threats but are equipped to autonomously safeguard themselves.

Recent advancements in reinforcement learning (RL) have led to significant progress in humanoid robot locomotion, simplifying the design and training of motion policies in simulation. However, the numerous implementation details make transferring these policies to real-world robots a challenging task. To address this, we have developed a comprehensive code framework that covers the entire process from training to deployment, incorporating common RL training methods, domain randomization, reward function design, and solutions for handling parallel structures. This library is made available as a community resource, with detailed descriptions of its design and experimental results. We validate the framework on the Booster T1 robot, demonstrating that the trained policies seamlessly transfer to the physical platform, enabling capabilities such as omnidirectional walking, disturbance resistance, and terrain adaptability. We hope this work provides a convenient tool for the robotics community, accelerating the development of humanoid robots. The code can be found in https://github.com/BoosterRobotics/booster_gym.

Real-time identification and quantification of greenhouse-gas emissions under transient atmospheric conditions is a critical challenge in environmental monitoring. We introduce a spatio-temporal inversion framework that embeds a deep-learning surrogate of computational fluid dynamics (CFD) within a sequential Monte Carlo algorithm to perform Bayesian inference of both emission rate and source location in dynamic flow fields. By substituting costly numerical solvers with a multilayer perceptron trained on high-fidelity CFD outputs, our surrogate captures spatial heterogeneity and temporal evolution of gas dispersion, while delivering near-real-time predictions. Validation on the Chilbolton methane release dataset demonstrates comparable accuracy to full CFD solvers and Gaussian plume models, yet achieves orders-of-magnitude faster runtimes. Further experiments under simulated obstructed-flow scenarios confirm robustness in complex environments. This work reconciles physical fidelity with computational feasibility, offering a scalable solution for industrial emissions monitoring and other time-sensitive spatio-temporal inversion tasks in environmental and scientific modeling.

Humans interpret the world around them in terms of cause and effect and communicate their understanding of the world to each other in causal terms. These causal aspects of human cognition are thought to underlie humans' ability to generalize and learn efficiently in new domains, an area where current machine learning systems are weak. Building human-like causal competency into machine learning systems may facilitate the construction of effective and interpretable AI. Indeed, the machine learning community has been importing ideas on causality formalized by the Structural Causal Model (SCM) framework, which provides a rigorous formal language for many aspects of causality and has led to significant advances. However, the SCM framework fails to capture some salient aspects of human causal cognition and has likewise not yet led to advances in machine learning in certain critical areas where humans excel. We contend that the problem of causality in the ``human niche'' -- for a social, autonomous, and goal-driven agent sensing and acting in the world in which humans live -- is quite different from the kind of causality captured by SCMs. For example, everyday objects come in similar types that have similar causal properties, and so humans readily generalize knowledge of one type of object (cups) to another related type (bowls) by drawing causal analogies between objects with similar properties, but such analogies are at best awkward to express in SCMs. We explore how such causal capabilities are adaptive in, and motivated by, the human niche. By better appreciating properties of human causal cognition and, crucially, how those properties are adaptive in the niche in which humans live, we hope that future work at the intersection of machine learning and causality will leverage more human-like inductive biases to create more capable, controllable, and interpretable systems.

We present the Gaussian process dynamical mixture model (GPDMM) and show its utility in single-example learning of human motion data. The Gaussian process dynamical model (GPDM) is a form of the Gaussian process latent variable model (GPLVM), but optimized with a hidden Markov model dynamical prior. The GPDMM combines multiple GPDMs in a probabilistic mixture-of-experts framework, utilizing embedded geometric features to allow for diverse sequences to be encoded in a single latent space, enabling the categorization and generation of each sequence class. GPDMs and our mixture model are particularly advantageous in addressing the challenges of modeling human movement in scenarios where data is limited and model interpretability is vital, such as in patient-specific medical applications like prosthesis control. We score the GPDMM on classification accuracy and generative ability in single-example learning, showcase model variations, and benchmark it against LSTMs, VAEs, and transformers.