We study a class of non-convex and non-smooth problems with \textit{rank} regularization to promote sparsity in optimal solution. We propose to apply the proximal gradient descent method to solve the problem and accelerate the process with a novel support set projection operation on the singular values of the intermediate update. We show that our algorithms are able to achieve a convergence rate of $O(\frac{1}{t^2})$, which is exactly same as Nesterov's optimal convergence rate for first-order methods on smooth and convex problems. Strict sparsity can be expected and the support set of singular values during each update is monotonically shrinking, which to our best knowledge, is novel in momentum-based algorithms.

Even though data annotation is extremely important for interpretability, research and development of artificial intelligence solutions, most research efforts such as active learning or few-shot learning focus on the sample efficiency problem. This paper studies the neglected complementary problem of getting annotated data given a predictor. For the simple binary classification setting, we present the spectrum ranging from optimal general solutions to practical efficient methods. The problem is framed as the full annotation of a binary classification dataset with the minimal number of yes/no questions when a predictor is available. For the case of general binary questions the solution is found in coding theory, where the optimal questioning strategy is given by the Huffman encoding of the possible labelings. However, this approach is computationally intractable even for small dataset sizes. We propose an alternative practical solution based on several heuristics and lookahead minimization of proxy cost functions. The proposed solution is analysed, compared with optimal solutions and evaluated on several synthetic and real-world datasets. On these datasets, the method allows a significant improvement ($23-86\%$) in annotation efficiency.

In this work, we propose to learn robot geometry as distance fields (RDF), which extend the signed distance field (SDF) of the robot with joint configurations. Unlike existing methods that learn an implicit representation encoding joint space and Euclidean space together, the proposed RDF approach leverages the kinematic chain of the robot, which reduces the dimensionality and complexity of the problem, resulting in more accurate and reliable SDFs. A simple and flexible approach that exploits basis functions to represent SDFs for individual robot links is presented, providing a smoother representation and improved efficiency compared to neural networks. RDF is naturally continuous and differentiable, enabling its direct integration as cost functions in robot tasks. It also allows us to obtain high-precision robot surface points with any desired spatial resolution, with the capability of whole-body manipulation. We verify the effectiveness of our RDF representation by conducting various experiments in both simulations and with the 7-axis Franka Emika robot. We compare our approach against baseline methods and demonstrate its efficiency in dual-arm settings for tasks involving collision avoidance and whole-body manipulation. Project page: https://sites.google.com/view/lrdf/home}{https://sites.google.com/view/lrdf/home

Robots will increasingly operate near humans that introduce uncertainties in the motion planning problem due to their complex nature. Typically, chance constraints are introduced in the planner to optimize performance while guaranteeing probabilistic safety. However, existing methods do not consider the actual probability of collision for the planned trajectory, but rather its marginalization, that is, the independent collision probabilities for each planning step and/or dynamic obstacle, resulting in conservative trajectories. To address this issue, we introduce a novel real-time capable method termed Safe Horizon MPC, that explicitly constrains the joint probability of collision with all obstacles over the duration of the motion plan. This is achieved by reformulating the chance-constrained planning problem using scenario optimization and predictive control. Our method is less conservative than state-of-the-art approaches, applicable to arbitrary probability distributions of the obstacles' trajectories, computationally tractable and scalable. We demonstrate our proposed approach using a mobile robot and an autonomous vehicle in an environment shared with humans.

The current advances in generative AI for learning large neural network models with the capability to produce essays, images, music and even 3D assets from text prompts create opportunities for a manifold of disciplines. In the present paper, we study the potential of deep text-to-3D models in the engineering domain, with focus on the chances and challenges when integrating and interacting with 3D assets in computational simulation-based design optimization. In contrast to traditional design optimization of 3D geometries that often searches for the optimum designs using numerical representations, such as B-Spline surface or deformation parameters in vehicle aerodynamic optimization, natural language challenges the optimization framework by requiring a different interpretation of variation operators while at the same time may ease and motivate the human user interaction. Here, we propose and realize a fully automated evolutionary design optimization framework using Shap-E, a recently published text-to-3D asset network by OpenAI, in the context of aerodynamic vehicle optimization. For representing text prompts in the evolutionary optimization, we evaluate (a) a bag-of-words approach based on prompt templates and Wordnet samples, and (b) a tokenisation approach based on prompt templates and the byte pair encoding method from GPT4. Our main findings from the optimizations indicate that, first, it is important to ensure that the designs generated from prompts are within the object class of application, i.e. diverse and novel designs need to be realistic, and, second, that more research is required to develop methods where the strength of text prompt variations and the resulting variations of the 3D designs share causal relations to some degree to improve the optimization.

Given a compact subset of a Banach space, the Chebyshev center problem consists of finding a minimal circumscribing ball containing the set. In this article we establish a numerically tractable algorithm for solving the Chebyshev center problem in the context of optimal learning from a finite set of data points. For a hypothesis space realized as a compact but not necessarily convex subset of a finite-dimensional subspace of some underlying Banach space, this algorithm computes the Chebyshev radius and the Chebyshev center of the hypothesis space, thereby solving the problem of optimal recovery of functions from data. The algorithm itself is based on, and significantly extends, recent results for near-optimal solutions of convex semi-infinite problems by means of targeted sampling, and it is of independent interest. Several examples of numerical computations of Chebyshev centers are included in order to illustrate the effectiveness of the algorithm.

In the negative perceptron problem we are given $n$ data points $({\boldsymbol x}_i,y_i)$, where ${\boldsymbol x}_i$ is a $d$-dimensional vector and $y_i\in\{+1,-1\}$ is a binary label. The data are not linearly separable and hence we content ourselves to find a linear classifier with the largest possible \emph{negative} margin. In other words, we want to find a unit norm vector ${\boldsymbol \theta}$ that maximizes $\min_{i\le n}y_i\langle {\boldsymbol \theta},{\boldsymbol x}_i\rangle$. This is a non-convex optimization problem (it is equivalent to finding a maximum norm vector in a polytope), and we study its typical properties under two random models for the data. We consider the proportional asymptotics in which $n,d\to \infty$ with $n/d\to\delta$, and prove upper and lower bounds on the maximum margin $\kappa_{\text{s}}(\delta)$ or -- equivalently -- on its inverse function $\delta_{\text{s}}(\kappa)$. In other words, $\delta_{\text{s}}(\kappa)$ is the overparametrization threshold: for $n/d\le \delta_{\text{s}}(\kappa)-\varepsilon$ a classifier achieving vanishing training error exists with high probability, while for $n/d\ge \delta_{\text{s}}(\kappa)+\varepsilon$ it does not. Our bounds on $\delta_{\text{s}}(\kappa)$ match to the leading order as $\kappa\to -\infty$. We then analyze a linear programming algorithm to find a solution, and characterize the corresponding threshold $\delta_{\text{lin}}(\kappa)$. We observe a gap between the interpolation threshold $\delta_{\text{s}}(\kappa)$ and the linear programming threshold $\delta_{\text{lin}}(\kappa)$, raising the question of the behavior of other algorithms.

We consider minimizing a smooth function subject to a summation constraint over its variables. By exploiting a connection between the greedy 2-coordinate update for this problem and equality-constrained steepest descent in the 1-norm, we give a convergence rate for greedy selection under a proximal Polyak-Lojasiewicz assumption that is faster than random selection and independent of the problem dimension $n$. We then consider minimizing with both a summation constraint and bound constraints, as arises in the support vector machine dual problem. Existing greedy rules for this setting either guarantee trivial progress only or require $O(n^2)$ time to compute. We show that bound- and summation-constrained steepest descent in the L1-norm guarantees more progress per iteration than previous rules and can be computed in only $O(n \log n)$ time.

North star metrics and online experimentation play a central role in how technology companies improve their products. In many practical settings, however, evaluating experiments based on the north star metric directly can be difficult. The two most significant issues are 1) low sensitivity of the north star metric and 2) differences between the short-term and long-term impact on the north star metric. A common solution is to rely on proxy metrics rather than the north star in experiment evaluation and launch decisions. Existing literature on proxy metrics concentrates mainly on the estimation of the long-term impact from short-term experimental data. In this paper, instead, we focus on the trade-off between the estimation of the long-term impact and the sensitivity in the short term. In particular, we propose the Pareto optimal proxy metrics method, which simultaneously optimizes prediction accuracy and sensitivity. In addition, we give an efficient multi-objective optimization algorithm that outperforms standard methods. We applied our methodology to experiments from a large industrial recommendation system, and found proxy metrics that are eight times more sensitive than the north star and consistently moved in the same direction, increasing the velocity and the quality of the decisions to launch new features.

The development of applications based on artificial intelligence and implemented over wireless networks is increasingly rapidly and is expected to grow dramatically in the future. The resulting demand for the aggregation of large amounts of data has caused serious communication bottlenecks in wireless networks and particularly at the network edge. Over-the-air federated learning (OTA-FL), leveraging the superposition feature of multi-access channels (MACs), enables users at the network edge to share spectrum resources and achieves efficient and low-latency global model aggregation. This paper provides a holistic review of progress in OTA-FL and points to potential future research directions. Specifically, we classify OTA-FL from the perspective of system settings, including single-antenna OTA-FL, multi-antenna OTA-FL, and OTA-FL with the aid of the emerging reconfigurable intelligent surface (RIS) technology, and the contributions of existing works in these areas are summarized. Moreover, we discuss the trust, security and privacy aspects of OTA-FL, and highlight concerns arising from security and privacy. Finally, challenges and potential research directions are discussed to promote the future development of OTA-FL in terms of improving system performance, reliability, and trustworthiness. Specifical challenges to be addressed include model distortion under channel fading, the ineffective OTA aggregation of local models trained on substantially unbalanced data, and the limited accessibility and verifiability of individual local models.