Classical policy search algorithms for robotics typically require performing extensive explorations, which are time-consuming and expensive to implement with real physical platforms. To facilitate the efficient learning of robot manipulation skills, in this work, we propose a new approach comprised of three modules: (1) learning of general prior knowledge with random explorations in simulation, including state representations, dynamic models, and the constrained action space of the task; (2) extraction of a state alignment-based reward function from a single demonstration video; (3) real-time optimization of the imitation policy under systematic safety constraints with sampling-based model predictive control. This solution results in an efficient one-shot imitation-from-video strategy that simplifies the learning and execution of robot skills in real applications. Specifically, we learn priors in a scene of a task family and then deploy the policy in a novel scene immediately following a single demonstration, preventing time-consuming and risky explorations in the environment. As we do not make a strong assumption of dynamic consistency between the scenes, learning priors can be conducted in simulation to avoid collecting data in real-world circumstances. We evaluate the effectiveness of our approach in the context of contact-rich fabric manipulation, which is a common scenario in industrial and domestic tasks. Detailed numerical simulations and real-world hardware experiments reveal that our method can achieve rapid skill acquisition for challenging manipulation tasks.

The Frank-Wolfe (FW) method is a popular approach for solving optimization problems with structured constraints that arise in machine learning applications. In recent years, stochastic versions of FW have gained popularity, motivated by large datasets for which the computation of the full gradient is prohibitively expensive. In this paper, we present two new variants of the FW algorithms for stochastic finite-sum minimization. Our algorithms have the best convergence guarantees of existing stochastic FW approaches for both convex and non-convex objective functions. Our methods do not have the issue of permanently collecting large batches, which is common to many stochastic projection-free approaches. Moreover, our second approach does not require either large batches or full deterministic gradients, which is a typical weakness of many techniques for finite-sum problems. The faster theoretical rates of our approaches are confirmed experimentally.

In this paper, we introduce Optimal Classification Forests, a new family of classifiers that takes advantage of an optimal ensemble of decision trees to derive accurate and interpretable classifiers. We propose a novel mathematical optimization-based methodology in which a given number of trees are simultaneously constructed, each of them providing a predicted class for the observations in the feature space. The classification rule is derived by assigning to each observation its most frequently predicted class among the trees in the forest. We provide a mixed integer linear programming formulation for the problem. We report the results of our computational experiments, from which we conclude that our proposed method has equal or superior performance compared with state-of-the-art tree-based classification methods. More importantly, it achieves high prediction accuracy with, for example, orders of magnitude fewer trees than random forests. We also present three real-world case studies showing that our methodology has very interesting implications in terms of interpretability.

Precise and real-time localization of unmanned aerial vehicles (UAVs) or robots in GNSS denied indoor environments are critically important for various logistics and surveillance applications. Vision-based simultaneously locating and mapping (VSLAM) are key solutions but suffer location drifts in texture-less, man-made indoor environments. Line features are rich in man-made environments which can be exploited to improve the localization robustness, but existing point-line based VSLAM methods still lack accuracy and efficiency for the representation of lines introducing unnecessary degrees of freedoms. In this paper, we propose Inverse Depth Line Localization(IDLL), which models each extracted line feature using two inverse depth variables exploiting the fact that the projected pixel coordinates on the image plane are rather accurate, which partially restrict the lines. This freedom-reduced representation of lines enables easier line determination and faster convergence of bundle adjustment in each step, therefore achieves more accurate and more efficient frame-to-frame registration and frame-to-map registration using both point and line visual features. We redesign the whole front-end and back-end modules of VSLAM using this line model. IDLL is extensively evaluated in multiple perceptually-challenging datasets. The results show it is more accurate, robust, and needs lower computational overhead than the current state-of-the-art of feature-based VSLAM methods.

Decentralized minimax optimization has been actively studied in the past few years due to its application in a wide range of machine learning models. However, the current theoretical understanding of its convergence rate is far from satisfactory since existing works only focus on the nonconvex-strongly-concave problem. This motivates us to study decentralized minimax optimization algorithms for the nonconvex-nonconcave problem. To this end, we develop two novel decentralized stochastic variance-reduced gradient descent ascent algorithms for the finite-sum nonconvex-nonconcave problem that satisfies the Polyak-{\L}ojasiewicz (PL) condition. In particular, our theoretical analyses demonstrate how to conduct local updates and perform communication to achieve the linear convergence rate. To the best of our knowledge, this is the first work achieving linear convergence rates for decentralized nonconvex-nonconcave problems. Finally, we verify the performance of our algorithms on both synthetic and real-world datasets. The experimental results confirm the efficacy of our algorithms.

Cell transmission models enable the quantification of the motion of traffic participants on a high level of aggregation. This provides computational advantages in comparison to microscopic traffic models that capture the motion of traffic participants in great detail. This gain in computational efficiency is sometimes disadvantageously associated with lower granularity, which complicates the representation of complex traffic modules and interactions of traffic participants. In this paper, we propose a rigorous framework for cell transmission models that incorporates three important features: a) The cells are identified with the nodes of a graph. We introduce a precise notation for the directions of the traffic participants within each cell. This allows the construction of cell transmission models for general traffic networks.

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem. Several iterative methods have been developed for tackling this class of problems. Alas, their convergence guarantees are either asymptotic for the upper-level objective, or the convergence rates are slow and sub-optimal. To address this issue, in this paper, we introduce a novel bilevel optimization method that locally approximates the solution set of the lower-level problem via a cutting plane, and then runs a conditional gradient update to decrease the upper-level objective. When the upper-level objective is convex, we show that our method requires ${\mathcal{O}}(\max\{1/\epsilon_f,1/\epsilon_g\})$ iterations to find a solution that is $\epsilon_f$-optimal for the upper-level objective and $\epsilon_g$-optimal for the lower-level objective. Moreover, when the upper-level objective is non-convex, our method requires ${\mathcal{O}}(\max\{1/\epsilon_f^2,1/(\epsilon_f\epsilon_g)\})$ iterations to find an $(\epsilon_f,\epsilon_g)$-optimal solution. We also prove stronger convergence guarantees under the H\"olderian error bound assumption on the lower-level problem. To the best of our knowledge, our method achieves the best-known iteration complexity for the considered class of bilevel problems.

Finding saddle points of dynamical systems is an important problem in practical applications such as the study of rare events of molecular systems. Gentlest ascent dynamics (GAD) is one of a number of algorithms in existence that attempt to find saddle points in dynamical systems. It works by deriving a new dynamical system in which saddle points of the original system become stable equilibria. GAD has been recently generalized to the study of dynamical systems on manifolds (differential algebraic equations) described by equality constraints and given in an extrinsic formulation. In this paper, we present an extension of GAD to manifolds defined by point-clouds, formulated using the intrinsic viewpoint. These point-clouds are adaptively sampled during an iterative process that drives the system from the initial conformation (typically in the neighborhood of a stable equilibrium) to a saddle point. Our method requires the reactant (initial conformation), does not require the explicit constraint equations to be specified, and is purely data-driven.

This paper proposes a vehicular edge federated learning (VEFL) solution, where an edge server leverages highly mobile connected vehicles' (CVs') onboard central processing units (CPUs) and local datasets to train a global model. Convergence analysis reveals that the VEFL training loss depends on the successful receptions of the CVs' trained models over the intermittent vehicle-to-infrastructure (V2I) wireless links. Owing to high mobility, in the full device participation case (FDPC), the edge server aggregates client model parameters based on a weighted combination according to the CVs' dataset sizes and sojourn periods, while it selects a subset of CVs in the partial device participation case (PDPC). We then devise joint VEFL and radio access technology (RAT) parameters optimization problems under delay, energy and cost constraints to maximize the probability of successful reception of the locally trained models. Considering that the optimization problem is NP-hard, we decompose it into a VEFL parameter optimization sub-problem, given the estimated worst-case sojourn period, delay and energy expense, and an online RAT parameter optimization sub-problem. Finally, extensive simulations are conducted to validate the effectiveness of the proposed solutions with a practical 5G new radio (5G-NR) RAT under a realistic microscopic mobility model.

Recent advances have extended the scope of Bayesian optimization (BO) to expensive-to-evaluate black-box functions with dozens of dimensions, aspiring to unlock impactful applications, for example, in the life sciences, neural architecture search, and robotics. However, a closer examination reveals that the state-of-the-art methods for high-dimensional Bayesian optimization (HDBO) suffer from degrading performance as the number of dimensions increases or even risk failure if certain unverifiable assumptions are not met. This paper proposes BAxUS that leverages a novel family of nested random subspaces to adapt the space it optimizes over to the problem. This ensures high performance while removing the risk of failure, which we assert via theoretical guarantees. A comprehensive evaluation demonstrates that BAxUS achieves better results than the state-of-the-art methods for a broad set of applications.