A machine learning model is traditionally considered robust if its prediction remains (almost) constant under input perturbations with small norm. However, real-world tasks like molecular property prediction or point cloud segmentation have inherent equivariances, such as rotation or permutation equivariance. In such tasks, even perturbations with large norm do not necessarily change an input's semantic content. Furthermore, there are perturbations for which a model's prediction explicitly needs to change. For the first time, we propose a sound notion of adversarial robustness that accounts for task equivariance. We then demonstrate that provable robustness can be achieved by (1) choosing a model that matches the task's equivariances (2) certifying traditional adversarial robustness. Certification methods are, however, unavailable for many models, such as those with continuous equivariances. We close this gap by developing the framework of equivariance-preserving randomized smoothing, which enables architecture-agnostic certification. We additionally derive the first architecture-specific graph edit distance certificates, i.e. sound robustness guarantees for isomorphism equivariant tasks like node classification. Overall, a sound notion of robustness is an important prerequisite for future work at the intersection of robust and geometric machine learning.

SOTA multiagent reinforcement algorithms distinguish themselves in many ways from their single-agent equivalences. However, most of them still totally inherit the single-agent exploration-exploitation strategy. Naively inheriting this strategy from single-agent algorithms causes potential collaboration failures, in which the agents blindly follow mainstream behaviors and reject taking minority responsibility. We name this problem the Responsibility Diffusion (RD) as it shares similarities with a same-name social psychology effect. In this work, we start by theoretically analyzing the cause of this RD problem, which can be traced back to the exploration-exploitation dilemma of multiagent systems (especially large-scale multiagent systems). We address this RD problem by proposing a Policy Resonance (PR) approach which modifies the collaborative exploration strategy of agents by refactoring the joint agent policy while keeping individual policies approximately invariant. Next, we show that SOTA algorithms can equip this approach to promote the collaborative performance of agents in complex cooperative tasks. Experiments are performed in multiple test benchmark tasks to illustrate the effectiveness of this approach.

We present a method for sampling-based model predictive control that makes use of a generic physics simulator as the dynamical model. In particular, we propose a Model Predictive Path Integral controller (MPPI), that uses the GPU-parallelizable IsaacGym simulator to compute the forward dynamics of a problem. By doing so, we eliminate the need for explicit encoding of robot dynamics and contacts with objects for MPPI. Since no explicit dynamic modeling is required, our method is easily extendable to different objects and robots and allows one to solve complex navigation and contact-rich tasks. We demonstrate the effectiveness of this method in several simulated and real-world settings, among which mobile navigation with collision avoidance, non-prehensile manipulation, and whole-body control for high-dimensional configuration spaces. This method is a powerful and accessible open-source tool to solve a large variety of contact-rich motion planning tasks.

This work uses game theory as a mathematical framework to address interaction modeling in multi-agent motion forecasting and control. Despite its interpretability, applying game theory to real-world robotics, like automated driving, faces challenges such as unknown game parameters. To tackle these, we establish a connection between differential games, optimal control, and energy-based models, demonstrating how existing approaches can be unified under our proposed Energy-based Potential Game formulation. Building upon this, we introduce a new end-to-end learning application that combines neural networks for game-parameter inference with a differentiable game-theoretic optimization layer, acting as an inductive bias. The analysis provides empirical evidence that the game-theoretic layer adds interpretability and improves the predictive performance of various neural network backbones using two simulations and two real-world driving datasets.

Intelligent drill boom hole-seeking is a promising technology for enhancing drilling efficiency, mitigating potential safety hazards, and relieving human operators. Most existing intelligent drill boom control methods rely on a hierarchical control framework based on inverse kinematics. However, these methods are generally time-consuming due to the computational complexity of inverse kinematics and the inefficiency of the sequential execution of multiple joints. To tackle these challenges, this study proposes an integrated drill boom control method based on Reinforcement Learning (RL). We develop an integrated drill boom control framework that utilizes a parameterized policy to directly generate control inputs for all joints at each time step, taking advantage of joint posture and target hole information. By formulating the hole-seeking task as a Markov decision process, contemporary mainstream RL algorithms can be directly employed to learn a hole-seeking policy, thus eliminating the need for inverse kinematics solutions and promoting cooperative multi-joint control. To enhance the drilling accuracy throughout the entire drilling process, we devise a state representation that combines Denavit-Hartenberg joint information and preview hole-seeking discrepancy data. Simulation results show that the proposed method significantly outperforms traditional methods in terms of hole-seeking accuracy and time efficiency.

Many autonomous systems face safety challenges, requiring robust closed-loop control to handle physical limitations and safety constraints. Real-world systems, like autonomous ships, encounter nonlinear dynamics and environmental disturbances. Reinforcement learning is increasingly used to adapt to complex scenarios, but standard frameworks ensuring safety and stability are lacking. Predictive Safety Filters (PSF) offer a promising solution, ensuring constraint satisfaction in learning-based control without explicit constraint handling. This modular approach allows using arbitrary control policies, with the safety filter optimizing proposed actions to meet physical and safety constraints. We apply this approach to marine navigation, combining RL with PSF on a simulated Cybership II model. The RL agent is trained on path following and collision avpodance, while the PSF monitors and modifies control actions for safety. Results demonstrate the PSF's effectiveness in maintaining safety without hindering the RL agent's learning rate and performance, evaluated against a standard RL agent without PSF.

Formation flight is when multiple objects fly together in a coordination. Various automatic control methods have been used for the autonomous execution of formation flight of aerial vehicles. In this paper, the capacity of the model predictive control (MPC) approach in the autonomous execution of formation flight is examined. The MPC is a controller that capable of performing formation flight, maintaining tracking desired trajectory while avoiding collisions between aerial vehicles, and obstacles faced. Through this approach, aerial vehicle models with six degrees of freedom in a three-dimensional environment are performed formation flight autonomously, mostly in a triangle order. Not only the trajectory for the formation flight can be tracked through the MPC architecture, also the collision avoidance strategies of the aerial vehicles can be performed by this architecture. Simulation studies show that MPC has sufficient capability in both cases. Therefore, it is concluded that this method can deal with constraints, avoid obstacles as well as collisions between aerial vehicles. However, implementation of MPC to aerial vehicles in real time holds challenges.

Flow fields are often partitioned into data blocks for massively parallel computation and analysis based on blockwise relationships. However, most of the previous techniques only consider the first-order dependencies among blocks, which is insufficient in describing complex flow patterns. In this work, we present FlowHON, an approach to construct higher-order networks (HONs) from flow fields. FlowHON captures the inherent higher-order dependencies in flow fields as nodes and estimates the transitions among them as edges. We formulate the HON construction as an optimization problem with three linear transformations. The first two layers correspond to the node generation and the third one corresponds to edge estimation. Our formulation allows the node generation and edge estimation to be solved in a unified framework. With FlowHON, the rich set of traditional graph algorithms can be applied without any modification to analyze flow fields, while leveraging the higher-order information to understand the inherent structure and manage flow data for efficiency. We demonstrate the effectiveness of FlowHON using a series of downstream tasks, including estimating the density of particles during tracing, partitioning flow fields for data management, and understanding flow fields using the node-link diagram representation of networks.

This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined by a logistic function that depends on a single threshold variable and two hyperparameters. Each of these individual models only accounts for a minor portion of the variation in the endogenous variables. But many of them are capable of capturing arbitrary nonlinear conditional mean relations. Conjugate priors enable fast and efficient inference. In simulations, we show that our approach produces accurate point and density forecasts. In a real-data exercise, we forecast US macroeconomic aggregates and consider the nonlinear effects of financial shocks in a large-scale nonlinear VAR.

In order to study the formation mechanism of residents' low-carbon awareness and provide an important basis for traffic managers to guide urban residents to choose low-carbon travel mode, this paper proposes a low-carbon energy-saving travel data feature analysis and mining based on machine learning algorithm. This paper uses data mining technology to analyze the data of low-carbon travel questionnaire, and regards the 15-dimensional problem under the framework of planned behavior theory as the internal cause variable that characterizes residents' low-carbon travel willingness. The author uses K-means clustering algorithm to classify the intensity of residents' low-carbon travel willingness, and applies the results as the explanatory variables to the random forest model to explore the mechanism of residents' social attribute characteristics, travel characteristics, etc. on their low-carbon travel willingness. The experimental results show that based on the Silhouette index test and t-SNE dimensionality reduction, residents' low-carbon travel willingness can be divided into three categories: strong, neutral, and not strong; Based on the importance index, the four most significant factors are the occupation, residence, family composition and commuting time of residents. Conclusion: This method provides policy recommendations for the development and management of urban traffic low-carbon from multiple perspectives.