Formal verification techniques play a pivotal role in ensuring the safety of complex cyber-physical systems. To transfer model-based verification results to the real world, we require that the measurements of the target system lie in the set of reachable outputs of the corresponding model, a property we refer to as reachset conformance. This paper is on automatically identifying those reachset-conformant models. While state-of-the-art reachset-conformant identification methods focus on linear state-space models, we generalize these methods to nonlinear state-space models and linear and nonlinear input-output models. Furthermore, our identification framework adapts to different levels of prior knowledge on the system dynamics. In particular, we identify the set of model uncertainties for white-box models, the parameters and the set of model uncertainties for gray-box models, and entire reachset-conformant black-box models from data. For the black-box identification, we propose a new genetic programming variant, which we call conformant genetic programming. The robustness and efficacy of our framework are demonstrated in extensive numerical experiments using simulated and real-world data.

Our main contribution is the introduction of the map of elections framework. A map of elections consists of three main elements: (1) a dataset of elections (i.e., collections of ordinal votes over given sets of candidates), (2) a way of measuring similarities between these elections, and (3) a representation of the elections in the 2D Euclidean space as points, so that the more similar two elections are, the closer are their points. In our maps, we mostly focus on datasets of synthetic elections, but we also show an example of a map over real-life ones. To measure similarities, we would have preferred to use, e.g., the isomorphic swap distance, but this is infeasible due to its high computational complexity. Hence, we propose polynomial-time computable positionwise distance and use it instead. Regarding the representations in 2D Euclidean space, we mostly use the Kamada-Kawai algorithm, but we also show two alternatives. We develop the necessary theoretical results to form our maps and argue experimentally that they are accurate and credible. Further, we show how coloring the elections in a map according to various criteria helps in analyzing results of a number of experiments. In particular, we show colorings according to the scores of winning candidates or committees, running times of ILP-based winner determination algorithms, and approximation ratios achieved by particular algorithms.

Existing studies have shown that Graph Neural Networks (GNNs) are vulnerable to adversarial attacks. Even though Graph Transformers (GTs) surpassed Message-Passing GNNs on several benchmarks, their adversarial robustness properties are unexplored. However, attacking GTs is challenging due to their Positional Encodings (PEs) and special attention mechanisms which can be difficult to differentiate. We overcome these challenges by targeting three representative architectures based on (1) random-walk PEs, (2) pair-wise-shortest-path PEs, and (3) spectral PEs - and propose the first adaptive attacks for GTs. We leverage our attacks to evaluate robustness to (a) structure perturbations on node classification; and (b) node injection attacks for (fake-news) graph classification. Our evaluation reveals that they can be catastrophically fragile and underlines our work's importance and the necessity for adaptive attacks.

The integrated inertial system, typically integrating an IMU and an exteroceptive sensor such as radar, LiDAR, and camera, has been widely accepted and applied in modern robotic applications for ego-motion estimation, motion control, or autonomous exploration. To improve system accuracy, robustness, and further usability, both multiple and various sensors are generally resiliently integrated, which benefits the system performance regarding failure tolerance, perception capability, and environment compatibility. For such systems, accurate and consistent spatiotemporal calibration is required to maintain a unique spatiotemporal framework for multi-sensor fusion. Considering most existing calibration methods (i) are generally oriented to specific integrated inertial systems, (ii) often only focus on spatial determination, (iii) usually require artificial targets, lacking convenience and usability, we propose iKalibr: a unified targetless spatiotemporal calibration framework for resilient integrated inertial systems, which overcomes the above issues, and enables both accurate and consistent calibration. Altogether four commonly employed sensors are supported in iKalibr currently, namely IMU, radar, LiDAR, and camera. The proposed method starts with a rigorous and efficient dynamic initialization, where all parameters in the estimator would be accurately recovered. Following that, several continuous-time-based batch optimizations would be carried out to refine initialized parameters to global optimal ones. Sufficient real-world experiments were conducted to verify the feasibility and evaluate the calibration performance of iKalibr. The results demonstrate that iKalibr can achieve accurate resilient spatiotemporal calibration. We open-source our implementations at (https://github.com/Unsigned-Long/iKalibr) to benefit the research community.

Most interesting problems in robotics (e.g., locomotion and manipulation) are realized through intermittent contact with the environment. Due to the perception and modeling errors, assuming an exact time for establishing contact with the environment is unrealistic. On the other hand, handling uncertainties in contact timing is notoriously difficult as it gives rise to either handling uncertain complementarity systems or solving combinatorial optimization problems at run-time. This work presents a novel optimal control formulation to find robust control policies under contact timing uncertainties. Our main novelty lies in casting the stochastic problem to a deterministic optimization over the uncertainty set that ensures robustness criterion satisfaction of candidate pre-contact states and optimizes for contact-relevant objectives. This way, we only need to solve a manageable standard nonlinear programming problem without complementarity constraints or combinatorial explosion. Our simulation results on multiple simplified locomotion and manipulation tasks demonstrate the robustness of our uncertainty-aware formulation compared to the nominal optimal control formulation.

The advent of Urban Air Mobility (UAM) presents the scope for a transformative shift in the domain of urban transportation. However, its widespread adoption and economic viability depends in part on the ability to optimally schedule the fleet of aircraft across vertiports in a UAM network, under uncertainties attributed to airspace congestion, changing weather conditions, and varying demands. This paper presents a comprehensive optimization formulation of the fleet scheduling problem, while also identifying the need for alternate solution approaches, since directly solving the resulting integer nonlinear programming problem is computationally prohibitive for daily fleet scheduling. Previous work has shown the effectiveness of using (graph) reinforcement learning (RL) approaches to train real-time executable policy models for fleet scheduling. However, such policies can often be brittle on out-of-distribution scenarios or edge cases. Moreover, training performance also deteriorates as the complexity (e.g., number of constraints) of the problem increases. To address these issues, this paper presents an imitation learning approach where the RL-based policy exploits expert demonstrations yielded by solving the exact optimization using a Genetic Algorithm. The policy model comprises Graph Neural Network (GNN) based encoders that embed the space of vertiports and aircraft, Transformer networks to encode demand, passenger fare, and transport cost profiles, and a Multi-head attention (MHA) based decoder. Expert demonstrations are used through the Generative Adversarial Imitation Learning (GAIL) algorithm. Interfaced with a UAM simulation environment involving 8 vertiports and 40 aircrafts, in terms of the daily profits earned reward, the new imitative approach achieves better mean performance and remarkable improvement in the case of unseen worst-case scenarios, compared to pure RL results.

We propose a new uncertainty estimator for gradient-free optimisation of black-box simulators using deep generative surrogate models. Optimisation of these simulators is especially challenging for stochastic simulators and higher dimensions. To address these issues, we utilise a deep generative surrogate approach to model the black box response for the entire parameter space. We then leverage this knowledge to estimate the proposed uncertainty based on the Wasserstein distance - the Wasserstein uncertainty. This approach is employed in a posterior agnostic gradient-free optimisation algorithm that minimises regret over the entire parameter space. A series of tests were conducted to demonstrate that our method is more robust to the shape of both the black box function and the stochastic response of the black box than state-of-the-art methods, such as efficient global optimisation with a deep Gaussian process surrogate.

In this paper, we revisit \textsf{ROOT-SGD}, an innovative method for stochastic optimization to bridge the gap between stochastic optimization and statistical efficiency. The proposed method enhances the performance and reliability of \textsf{ROOT-SGD} by integrating a carefully designed \emph{diminishing stepsize strategy}. This approach addresses key challenges in optimization, providing robust theoretical guarantees and practical benefits. Our analysis demonstrates that \textsf{ROOT-SGD} with diminishing achieves optimal convergence rates while maintaining computational efficiency. By dynamically adjusting the learning rate, \textsf{ROOT-SGD} ensures improved stability and precision throughout the optimization process. The findings of this study offer valuable insights for developing advanced optimization algorithms that are both efficient and statistically robust.

Machine-learning models consist of kernels, which are algorithms applying operations on tensors -- data indexed by a linear combination of natural numbers. Examples of kernels include convolutions, transpositions, and vectorial products. There are many ways to implement a kernel. These implementations form the kernel's optimization space. Kernel scheduling is the problem of finding the best implementation, given an objective function -- typically execution speed. Kernel optimizers such as Ansor, Halide, and AutoTVM solve this problem via search heuristics, which combine two phases: exploration and exploitation. The first step evaluates many different kernel optimization spaces. The latter tries to improve the best implementations by investigating a kernel within the same space. For example, Ansor combines kernel generation through sketches for exploration and leverages an evolutionary algorithm to exploit the best sketches. In this work, we demonstrate the potential to reduce Ansor's search time while enhancing kernel quality by incorporating Droplet Search, an AutoTVM algorithm, into Ansor's exploration phase. The approach involves limiting the number of samples explored by Ansor, selecting the best, and exploiting it with a coordinate descent algorithm. By applying this approach to the first 300 kernels that Ansor generates, we usually obtain better kernels in less time than if we let Ansor analyze 10,000 kernels. This result has been replicated in 20 well-known deep-learning models (AlexNet, ResNet, VGG, DenseNet, etc.) running on four architectures: an AMD Ryzen 7 (x86), an NVIDIA A100 tensor core, an NVIDIA RTX 3080 GPU, and an ARM A64FX. A patch with this combined approach was approved in Ansor in February 2024. As evidence of the generality of this search methodology, a similar patch, achieving equally good results, was submitted to TVM's MetaSchedule in June 2024.

Thanks to recent advancements in accelerating non-linear model predictive control (NMPC), it is now feasible to deploy whole-body NMPC at real-time rates for humanoid robots. However, enforcing inequality constraints in real time for such high-dimensional systems remains challenging due to the need for additional iterations. This paper presents an implementation of whole-body NMPC for legged robots that provides low-accuracy solutions to NMPC with general equality and inequality constraints. Instead of aiming for highly accurate optimal solutions, we leverage the alternating direction method of multipliers to rapidly provide low-accuracy solutions to quadratic programming subproblems. Our extensive simulation results indicate that real robots often cannot benefit from highly accurate solutions due to dynamics discretization errors, inertial modeling errors and delays. We incorporate control barrier functions (CBFs) at the initial timestep of the NMPC for the self-collision constraints, resulting in up to a 26-fold reduction in the number of self-collisions without adding computational burden. The controller is reliably deployed on hardware at 90 Hz for a problem involving 32 timesteps, 2004 variables, and 3768 constraints. The NMPC delivers sufficiently accurate solutions, enabling the MIT Humanoid to plan complex crossed-leg and arm motions that enhance stability when walking and recovering from significant disturbances.