Ground robots navigating in complex, dynamic environments must compute collision-free trajectories to avoid obstacles safely and efficiently. Nonconvex optimization is a popular method to compute a trajectory in real-time. However, these methods often converge to locally optimal solutions and frequently switch between different local minima, leading to inefficient and unsafe robot motion. In this work, We propose a novel topology-driven trajectory optimization strategy for dynamic environments that plans multiple distinct evasive trajectories to enhance the robot's behavior and efficiency. A global planner iteratively generates trajectories in distinct homotopy classes. These trajectories are then optimized by local planners working in parallel. While each planner shares the same navigation objectives, they are locally constrained to a specific homotopy class, meaning each local planner attempts a different evasive maneuver. The robot then executes the feasible trajectory with the lowest cost in a receding horizon manner. We demonstrate, on a mobile robot navigating among pedestrians, that our approach leads to faster and safer trajectories than existing planners.

While machine learning models are typically trained to solve prediction problems, we might often want to use them for optimization problems. For example, given a dataset of proteins and their corresponding fluorescence levels, we might want to optimize for a new protein with the highest possible fluorescence. This kind of data-driven optimization (DDO) presents a range of challenges beyond those in standard prediction problems, since we need models that successfully predict the performance of new designs that are better than the best designs seen in the training set. It is not clear theoretically when existing approaches can even perform better than the naive approach that simply selects the best design in the dataset. In this paper, we study how structure can enable sample-efficient data-driven optimization. To formalize the notion of structure, we introduce functional graphical models (FGMs) and show theoretically how they can provide for principled data-driven optimization by decomposing the original high-dimensional optimization problem into smaller sub-problems. This allows us to derive much more practical regret bounds for DDO, and the result implies that DDO with FGMs can achieve nearly optimal designs in situations where naive approaches fail due to insufficient coverage of the offline data. We further present a data-driven optimization algorithm that inferes the FGM structure itself, either over the original input variables or a latent variable representation of the inputs.

When deploying machine learning solutions, they must satisfy multiple requirements beyond accuracy, such as fairness, robustness, or safety. These requirements are imposed during training either implicitly, using penalties, or explicitly, using constrained optimization methods based on Lagrangian duality. Either way, specifying requirements is hindered by the presence of compromises and limited prior knowledge about the data. Furthermore, their impact on performance can often only be evaluated by actually solving the learning problem. This paper presents a constrained learning approach that adapts the requirements while simultaneously solving the learning task. To do so, it relaxes the learning constraints in a way that contemplates how much they affect the task at hand by balancing the performance gains obtained from the relaxation against a user-defined cost of that relaxation. We call this approach resilient constrained learning after the term used to describe ecological systems that adapt to disruptions by modifying their operation. We show conditions under which this balance can be achieved and introduce a practical algorithm to compute it, for which we derive approximation and generalization guarantees. We showcase the advantages of this resilient learning method in image classification tasks involving multiple potential invariances and in heterogeneous federated learning.

This paper fundamentally reformulates economic and financial theory to include electronic currencies. The valuation of the electronic currencies will be based on macroeconomic theory and the fundamental equation of monetary policy, not the microeconomic theory of discounted cash flows. The view of electronic currency as a transactional equity associated with tangible assets of a sub-economy will be developed, in contrast to the view of stock as an equity associated mostly with intangible assets of a sub-economy. The view will be developed of the electronic currency management firm as an entity responsible for coordinated monetary (electronic currency supply and value stabilization) and fiscal (investment and operational) policies of a substantial (for liquidity of the electronic currency) sub-economy. The risk model used in the valuations and the decision-making will not be the ubiquitous, yet inappropriate, exponential risk model that leads to discount rates, but will be multi time scale models that capture the true risk. The decision-making will be approached from the perspective of true systems control based on a system response function given by the multi scale risk model and system controllers that utilize the Deep Reinforcement Learning, Generative Pretrained Transformers, and other methods of Artificial Intelligence (DRL/GPT/AI). Finally, the sub-economy will be viewed as a nonlinear complex physical system with both stable equilibriums that are associated with short-term exploitation, and unstable equilibriums that need to be stabilized with active nonlinear control based on the multi scale system response functions and DRL/GPT/AI.

This work presents a novel online model-predictive trajectory planner for robotic manipulators called BoundMPC. This planner allows the collision-free following of Cartesian reference paths in the end-effector's position and orientation, including via-points, within desired asymmetric bounds of the orthogonal path error. The path parameter synchronizes the position and orientation reference paths. The decomposition of the path error into the tangential direction, describing the path progress, and the orthogonal direction, which represents the deviation from the path, is well known for the position from the path-following control in the literature. This paper extends this idea to the orientation by utilizing the Lie theory of rotations. Moreover, the orthogonal error plane is further decomposed into basis directions to define asymmetric Cartesian error bounds easily. Using piecewise linear position and orientation reference paths with via-points is computationally very efficient and allows replanning the pose trajectories during the robot's motion. This feature makes it possible to use this planner for dynamically changing environments and varying goals. The flexibility and performance of BoundMPC are experimentally demonstrated by two scenarios on a 7-DoF Kuka LBR iiwa 14 R820 robot. The first scenario shows the transfer of a larger object from a start to a goal pose through a confined space where the object must be tilted. The second scenario deals with grasping an object from a table where the grasping point changes during the robot's motion, and collisions with other obstacles in the scene must be avoided.

Control barrier functions (CBFs) are a powerful tool to enforce safety constraints for nonlinear control systems (Ames et al., 2019), with many successful applications in autonomous driving (Xiao et al., 2021), UAV navigation (Xu and Sreenath, 2018), robot locomotion (Grandia et al., 2021), and safe reinforcement learning (Marvi and Kiumarsi, 2021). For control-affine nonlinear systems, CBFs can be used to construct a convex quadratic programming (QP)-based safety filter that can be deployed online to safeguard against potentially unsafe control commands. The induced safety filter, which we denote as CBF-QP, guarantees that the closed-loop system remains in a safe control invariant set by correcting a reference controller online. While CBFs provide an efficient method to ensure safety, in general, it is difficult to find such functions. As the complexity of both the environment and the dynamics increases, we are faced with the following challenges: (C1) Complex safety specifications: CBFs inherently handle single constraint functions, but complex environments often involve multiple constraints. In this work, we consider specifications that are described by the composition of multiple constraints through Boolean logical operations such as AND, OR, and negation, which can capture complex constraints. Shaoru Chen is with Microsoft Research, 300 Lafayette Street, New York, NY, 10012, USA.

Radio frequency (RF) signals have facilitated the development of non-contact human monitoring tasks, such as vital signs measurement, activity recognition, and user identification. In some specific scenarios, an RF signal analysis framework may prioritize the performance of one task over that of others. In response to this requirement, we employ a multi-objective optimization approach inspired by biological principles to select discriminative features that enhance the accuracy of breathing patterns recognition while simultaneously impeding the identification of individual users. This approach is validated using a novel vital signs dataset consisting of 50 subjects engaged in four distinct breathing patterns. Our findings indicate a remarkable result: a substantial divergence in accuracy between breathing recognition and user identification. As a complementary viewpoint, we present a contrariwise result to maximize user identification accuracy and minimize the system's capacity for breathing activity recognition.

Quantization (Alistarh et al., 2017) is an important (stochastic) compression technique that reduces the volume of transmitted bits during each communication round in distributed model training. Suresh et al. (2022) introduce correlated quantizers and show their advantages over independent counterparts by analyzing distributed SGD communication complexity. We analyze the forefront distributed non-convex optimization algorithm MARINA (Gorbunov et al., 2022) utilizing the proposed correlated quantizers and show that it outperforms the original MARINA and distributed SGD of Suresh et al. (2022) with regard to the communication complexity. We significantly refine the original analysis of MARINA without any additional assumptions using the weighted Hessian variance (Tyurin et al., 2022), and then we expand the theoretical framework of MARINA to accommodate a substantially broader range of potentially correlated and biased compressors, thus dilating the applicability of the method beyond the conventional independent unbiased compressor setup. Extensive experimental results corroborate our theoretical findings.

We assume that a sufficiently large database is available, where a physical property of interest and a number of associated ruling primitive variables or observables are stored. We introduce and test two machine learning approaches to discover possible groups or combinations of primitive variables: The first approach is based on regression models whereas the second on classification models. The variable group (here referred to as the new effective good variable) can be considered as successfully found, when the physical property of interest is characterized by the following effective invariant behaviour: In the first method, invariance of the group implies invariance of the property up to a given accuracy; in the other method, upon partition of the physical property values into two or more classes, invariance of the group implies invariance of the class. For the sake of illustration, the two methods are successfully applied to two popular empirical correlations describing the convective heat transfer phenomenon and to the Newton's law of universal gravitation.

In this work, we present a novel, machine-learning approach for constructing Multiclass Interpretable Scoring Systems (MISS) - a fully data-driven methodology for generating single, sparse, and user-friendly scoring systems for multiclass classification problems. Scoring systems are commonly utilized as decision support models in healthcare, criminal justice, and other domains where interpretability of predictions and ease of use are crucial. Prior methods for data-driven scoring, such as SLIM (Supersparse Linear Integer Model), were limited to binary classification tasks and extensions to multiclass domains were primarily accomplished via one-versus-all-type techniques. The scores produced by our method can be easily transformed into class probabilities via the softmax function. We demonstrate techniques for dimensionality reduction and heuristics that enhance the training efficiency and decrease the optimality gap, a measure that can certify the optimality of the model. Our approach has been extensively evaluated on datasets from various domains, and the results indicate that it is competitive with other machine learning models in terms of classification performance metrics and provides well-calibrated class probabilities.