The small size, high dexterity, and intrinsic compliance of continuum robots (CRs) make them well suited for constrained environments. Solving the inverse kinematics (IK), that is finding robot joint configurations that satisfy desired position or pose queries, is a fundamental challenge in motion planning, control, and calibration for any robot structure. For CRs, the need to avoid obstacles in tightly confined workspaces greatly complicates the search for feasible IK solutions. Without an accurate initialization or multiple re-starts, existing algorithms often fail to find a solution. We present CIDGIKc (Convex Iteration for Distance-Geometric Inverse Kinematics for Continuum Robots), an algorithm that solves these nonconvex feasibility problems with a sequence of semidefinite programs whose objectives are designed to encourage low-rank minimizers. CIDGIKc is enabled by a novel distance-geometric parameterization of constant curvature segment geometry for CRs with extensible segments. The resulting IK formulation involves only quadratic expressions and can efficiently incorporate a large number of collision avoidance constraints. Our experimental results demonstrate >98% solve success rates within complex, highly cluttered environments which existing algorithms cannot account for.

The existing model compression methods via structured pruning typically require complicated multi-stage procedures. Each individual stage necessitates numerous engineering efforts and domain-knowledge from the end-users which prevent their wider applications onto broader scenarios. We propose the second generation of Only-Train-Once (OTOv2), which first automatically trains and compresses a general DNN only once from scratch to produce a more compact model with competitive performance without fine-tuning. OTOv2 is automatic and pluggable into various deep learning applications, and requires almost minimal engineering efforts from the users. Methodologically, OTOv2 proposes two major improvements: (i) Autonomy: automatically exploits the dependency of general DNNs, partitions the trainable variables into Zero-Invariant Groups (ZIGs), and constructs the compressed model; and (ii) Dual Half-Space Projected Gradient (DHSPG): a novel optimizer to more reliably solve structured-sparsity problems. Numerically, we demonstrate the generality and autonomy of OTOv2 on a variety of model architectures such as VGG, ResNet, CARN, ConvNeXt, DenseNet and StackedUnets, the majority of which cannot be handled by other methods without extensive handcrafting efforts. Together with benchmark datasets including CIFAR10/100, DIV2K, Fashion-MNIST, SVNH and ImageNet, its effectiveness is validated by performing competitively or even better than the state-of-the-arts. The source code is available at https://github.com/tianyic/only_train_once.

We focus on analyzing the classical stochastic projected gradient methods under a general dependent data sampling scheme for constrained smooth nonconvex optimization. We show the worst-case rate of convergence $\tilde{O}(t^{-1/4})$ and complexity $\tilde{O}(\varepsilon^{-4})$ for achieving an $\varepsilon$-near stationary point in terms of the norm of the gradient of Moreau envelope and gradient mapping. While classical convergence guarantee requires i.i.d. data sampling from the target distribution, we only require a mild mixing condition of the conditional distribution, which holds for a wide class of Markov chain sampling algorithms. This improves the existing complexity for the constrained smooth nonconvex optimization with dependent data from $\tilde{O}(\varepsilon^{-8})$ to $\tilde{O}(\varepsilon^{-4})$ with a significantly simpler analysis. We illustrate the generality of our approach by deriving convergence results with dependent data for stochastic proximal gradient methods, adaptive stochastic gradient algorithm AdaGrad and stochastic gradient algorithm with heavy ball momentum. As an application, we obtain first online nonnegative matrix factorization algorithms for dependent data based on stochastic projected gradient methods with adaptive step sizes and optimal rate of convergence.

In this paper, an efficient motion planning approach with grid-based generalized Voronoi diagrams (G$ \mathbf{^2} $VD) is newly proposed for mobile robots. Different from existing approaches, the novelty of this work is twofold: 1) a new state lattice-based path searching approach is proposed, in which the search space is reduced to a Voronoi corridor to further improve the search efficiency, along with a Voronoi potential field constructed to make the searched path keep a reasonable distance from obstacles to provide sufficient optimization margin for the subsequent path smoothing; 2) an efficient quadratic programming-based path smoothing approach is presented, wherein the clearance to obstacles is considered in the form of the penalty of the deviation from the safe reference path to improve the path clearance of hard-constrained path smoothing approaches. We validate the efficiency and smoothness of our approach in various challenging simulation scenarios and outdoor environments. It is shown that the computational efficiency is improved by 17.1% in the path searching stage, and path smoothing with the proposed approach is 25.3 times faster than an advanced sparse-banded structure-based path smoothing approach.

A common approach is to apply a spectral algorithm to initialize the parameters of interest, and then run a locally convergent nonconvex optimization algorithm; alternatively, one could even run the nonconvex algorithm from a random initialization. These nonconvex optimization algorithms have been extensively analyzed under Gaussian assumptions on the covariates (see, e.g. Balakrishnan et al. (2017); Klusowski et al. (2019); Chen et al. (2019); Kwon and Caramanis (2020)), and it is known that they can exhibit favorable behavior globally in some settings. In many tasks such as ranking (Bradley and Terry, 1952), crowd-labeling (Dawid and Skene, 1979) and web search (Chen et al., 2013), however, measurements are taken as pairwise comparisons between entities, which renders the covariates inherently discrete. These designs or covariates are far from Gaussian, and it is natural to ask how standard nonconvex optimization algorithms now perform. Motivated by this question, we study how the celebrated expectation-maximization (EM) algorithm behaves when estimating a mixture of symmetric linear regressions under the pairwise comparison design.

In federated learning, data heterogeneity is a critical challenge. A straightforward solution is to shuffle the clients' data to homogenize the distribution. However, this may violate data access rights, and how and when shuffling can accelerate the convergence of a federated optimization algorithm is not theoretically well understood. In this paper, we establish a precise and quantifiable correspondence between data heterogeneity and parameters in the convergence rate when a fraction of data is shuffled across clients. We prove that shuffling can quadratically reduce the gradient dissimilarity with respect to the shuffling percentage, accelerating convergence. Inspired by the theory, we propose a practical approach that addresses the data access rights issue by shuffling locally generated synthetic data. The experimental results show that shuffling synthetic data improves the performance of multiple existing federated learning algorithms by a large margin.

In this paper, we focus on non-conservative obstacle avoidance between robots with control affine dynamics with strictly convex and polytopic shapes. The core challenge for this obstacle avoidance problem is that the minimum distance between strictly convex regions or polytopes is generally implicit and non-smooth, such that distance constraints cannot be enforced directly in the optimization problem. To handle this challenge, we employ non-smooth control barrier functions to reformulate the avoidance problem in the dual space, with the positivity of the minimum distance between robots equivalently expressed using a quadratic program. Our approach is proven to guarantee system safety. We theoretically analyze the smoothness properties of the minimum distance quadratic program and its KKT conditions. We validate our approach by demonstrating computationally-efficient obstacle avoidance for multi-agent robotic systems with strictly convex and polytopic shapes. To our best knowledge, this is the first time a real-time QP problem can be formulated for general non-conservative avoidance between strictly convex shapes and polytopes.

Causal effect estimation has been studied by many researchers when only observational data is available. Sound and complete algorithms have been developed for pointwise estimation of identifiable causal queries. For non-identifiable causal queries, researchers developed polynomial programs to estimate tight bounds on causal effect. However, these are computationally difficult to optimize for variables with large support sizes. In this paper, we analyze the effect of "weak confounding" on causal estimands. More specifically, under the assumption that the unobserved confounders that render a query non-identifiable have small entropy, we propose an efficient linear program to derive the upper and lower bounds of the causal effect. We show that our bounds are consistent in the sense that as the entropy of unobserved confounders goes to zero, the gap between the upper and lower bound vanishes. Finally, we conduct synthetic and real data simulations to compare our bounds with the bounds obtained by the existing work that cannot incorporate such entropy constraints and show that our bounds are tighter for the setting with weak confounders.

While a large amount of work has focused on designing adversarial attacks against image classifiers, only a few methods exist to attack semantic segmentation models. We show that attacking segmentation models presents task-specific challenges, for which we propose novel solutions. Our final evaluation protocol outperforms existing methods, and shows that those can overestimate the robustness of the models. Additionally, so far adversarial training, the most successful way for obtaining robust image classifiers, could not be successfully applied to semantic segmentation. We argue that this is because the task to be learned is more challenging, and requires significantly higher computational effort than for image classification. As a remedy, we show that by taking advantage of recent advances in robust ImageNet classifiers, one can train adversarially robust segmentation models at limited computational cost by fine-tuning robust backbones.

In this work, we propose a built-in Deep Learning Physics Optimization (DLPO) framework to set up a shape optimization study of the Duisburg Test Case (DTC) container vessel. We present two different applications: (1) sensitivity analysis to detect the most promising generic basis hull shapes, and (2) multi-objective optimization to quantify the trade-off between optimal hull forms. DLPO framework allows for the evaluation of design iterations automatically in an end-to-end manner. We achieved these results by coupling Extrality's Deep Learning Physics (DLP) model to a CAD engine and an optimizer. Our proposed DLP model is trained on full 3D volume data coming from RANS simulations, and it can provide accurate and high-quality 3D flow predictions in real-time, which makes it a good evaluator to perform optimization of new container vessel designs w.r.t the hydrodynamic efficiency. In particular, it is able to recover the forces acting on the vessel by integration on the hull surface with a mean relative error of 3.84\% \pm 2.179\% on the total resistance. Each iteration takes only 20 seconds, thus leading to a drastic saving of time and engineering efforts, while delivering valuable insight into the performance of the vessel, including RANS-like detailed flow information. We conclude that DLPO framework is a promising tool to accelerate the ship design process and lead to more efficient ships with better hydrodynamic performance.