The choice of the underlying probability measure is crucial in measuring risk or other objectives, but it presents a challenge for decision-makers (DMs) to find an expressive yet tractable reference measure. One simple option is to use the empirical measure on a sample dataset, but this choice is prone to model misspecification due to small sample sizes or blurred observations. Additionally, time-series data can pose further difficulties for modeling, creating another source of misspecification. This paper aims to provide a robust framework for risk evaluation with temporal data. Since Knight (1921) clarified the subtle difference between risk and model uncertainty (misspecification), several methodologies have been developed to incorporate robustness.

Abstract: The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for solving PDE-constrained topology optimization problems. Our approach is based on and extends the popular solution algorithm of Amstutz and Andrä (A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, 216, 2006). To do so, we introduce a new perspective on the commonly used evolution equation for the level-set method, which allows us to derive our quasi-Newton methods for topology optimization.

Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function is unnormalized and contains isolated modes. We tackle this difficulty by fitting an invertible transformation mapping, called a transport map, between a reference probability measure and the target distribution, so that sampling from the target distribution can be achieved by pushing forward a reference sample through the transport map. We theoretically analyze the limitations of existing transport-based sampling methods using the Wasserstein gradient flow theory, and propose a new method called TemperFlow that addresses the multimodality issue. TemperFlow adaptively learns a sequence of tempered distributions to progressively approach the target distribution, and we prove that it overcomes the limitations of existing methods. Various experiments demonstrate the superior performance of this novel sampler compared to traditional methods, and we show its applications in modern deep learning tasks such as image generation. The programming code for the numerical experiments is available at https://github.com/yixuan/temperflow.

Network pruning is a widely used technique to reduce computation cost and model size for deep neural networks. However, the typical three-stage pipeline significantly increases the overall training time. In this paper, we develop a systematic weight-pruning optimization approach based on Surrogate Lagrangian relaxation, which is tailored to overcome difficulties caused by the discrete nature of the weight-pruning problem. We prove that our method ensures fast convergence of the model compression problem, and the convergence of the SLR is accelerated by using quadratic penalties. Model parameters obtained by SLR during the training phase are much closer to their optimal values as compared to those obtained by other state-of-the-art methods. We evaluate our method on image classification tasks using CIFAR-10 and ImageNet with state-of-the-art MLP-Mixer, Swin Transformer, and VGG-16, ResNet-18, ResNet-50 and ResNet-110, MobileNetV2. We also evaluate object detection and segmentation tasks on COCO, KITTI benchmark, and TuSimple lane detection dataset using a variety of models. Experimental results demonstrate that our SLR-based weight-pruning optimization approach achieves a higher compression rate than state-of-the-art methods under the same accuracy requirement and also can achieve higher accuracy under the same compression rate requirement. Under classification tasks, our SLR approach converges to the desired accuracy $3\times$ faster on both of the datasets. Under object detection and segmentation tasks, SLR also converges $2\times$ faster to the desired accuracy. Further, our SLR achieves high model accuracy even at the hard-pruning stage without retraining, which reduces the traditional three-stage pruning into a two-stage process. Given a limited budget of retraining epochs, our approach quickly recovers the model's accuracy.

Neural network (NN) classifiers are vulnerable to adversarial attacks. Although the existing gradient-based attacks achieve state-of-the-art performance in feed-forward NNs and image recognition tasks, they do not perform as well on time series classification with recurrent neural network (RNN) models. This is because the cyclical structure of RNN prevents direct model differentiation and the visual sensitivity of time series data to perturbations challenges the traditional local optimization objective of the adversarial attack. In this paper, a black-box method called TSFool is proposed to efficiently craft highly-imperceptible adversarial time series for RNN classifiers. We propose a novel global optimization objective named Camouflage Coefficient to consider the imperceptibility of adversarial samples from the perspective of class distribution, and accordingly refine the adversarial attack as a multi-objective optimization problem to enhance the perturbation quality. To get rid of the dependence on gradient information, we also propose a new idea that introduces a representation model for RNN to capture deeply embedded vulnerable samples having otherness between their features and latent manifold, based on which the optimization solution can be heuristically approximated. Experiments on 10 UCR datasets are conducted to confirm that TSFool averagely outperforms existing methods with a 46.3% higher attack success rate, 87.4% smaller perturbation and 25.6% better Camouflage Coefficient at a similar time cost.

We define very large multi-objective optimization problems to be multiobjective optimization problems in which the number of decision variables is greater than 100,000 dimensions. This is an important class of problems as many real-world problems require optimizing hundreds of thousands of variables. Existing evolutionary optimization methods fall short of such requirements when dealing with problems at this very large scale. Inspired by the success of existing recommender systems to handle very large-scale items with limited historical interactions, in this paper we propose a method termed Very large-scale Multiobjective Optimization through Recommender Systems (VMORS). The idea of the proposed method is to transform the defined such very large-scale problems into a problem that can be tackled by a recommender system. In the framework, the solutions are regarded as users, and the different evolution directions are items waiting for the recommendation. We use Thompson sampling to recommend the most suitable items (evolutionary directions) for different users (solutions), in order to locate the optimal solution to a multiobjective optimization problem in a very large search space within acceptable time. We test our proposed method on different problems from 100,000 to 500,000 dimensions, and experimental results show that our method not only shows good performance but also significant improvement over existing methods.

Integrating Global Navigation Satellite Systems (GNSS) in Simultaneous Localization and Mapping (SLAM) systems draws increasing attention to a global and continuous localization solution. Nonetheless, in dense urban environments, GNSS-based SLAM systems will suffer from the Non-Line-Of-Sight (NLOS) measurements, which might lead to a sharp deterioration in localization results. In this paper, we propose to detect the sky area from the up-looking camera to improve GNSS measurement reliability for more accurate position estimation. We present Sky-GVINS: a sky-aware GNSS-Visual-Inertial system based on a recent work called GVINS. Specifically, we adopt a global threshold method to segment the sky regions and non-sky regions in the fish-eye sky-pointing image and then project satellites to the image using the geometric relationship between satellites and the camera. After that, we reject satellites in non-sky regions to eliminate NLOS signals. We investigated various segmentation algorithms for sky detection and found that the Otsu algorithm reported the highest classification rate and computational efficiency, despite the algorithm's simplicity and ease of implementation. To evaluate the effectiveness of Sky-GVINS, we built a ground robot and conducted extensive real-world experiments on campus. Experimental results show that our method improves localization accuracy in both open areas and dense urban environments compared to the baseline method. Finally, we also conduct a detailed analysis and point out possible further directions for future research. For detailed information, visit our project website at https://github.com/SJTU-ViSYS/Sky-GVINS.

Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end, leveraging recent work in risk-aware verification, we provide two algorithms to (1) probabilistically bound the optimality gaps of solutions reported by novel percentile optimization techniques, and (2) probabilistically bound the maximum optimality gap reported by percentile approaches for repetitive applications, e.g. Model Predictive Control (MPC). Notably, our results work for a large class of optimization problems. We showcase the efficacy and repeatability of our results on a few, benchmark non-convex optimization problems and the utility of our results for controls in a Nonlinear MPC setting.

Nonsmooth composite optimization with orthogonality constraints has a broad spectrum of applications in statistical learning and data science. However, this problem is generally challenging to solve due to its non-convex and non-smooth nature. Existing solutions are limited by one or more of the following restrictions: (i) they are full gradient methods that require high computational costs in each iteration; (ii) they are not capable of solving general nonsmooth composite problems; (iii) they are infeasible methods and can only achieve the feasibility of the solution at the limit point; (iv) they lack rigorous convergence guarantees; (v) they only obtain weak optimality of critical points. In this paper, we propose \textit{\textbf{OBCD}}, a new Block Coordinate Descent method for solving general nonsmooth composite problems under Orthogonality constraints. \textit{\textbf{OBCD}} is a feasible method with low computation complexity footprints. In each iteration, our algorithm updates $k$ rows of the solution matrix ($k\geq2$ is a parameter) to preserve the constraints. Then, it solves a small-sized nonsmooth composite optimization problem under orthogonality constraints either exactly or approximately. We demonstrate that any exact block-$k$ stationary point is always an approximate block-$k$ stationary point, which is equivalent to the critical stationary point. We are particularly interested in the case where $k=2$ as the resulting subproblem reduces to a one-dimensional nonconvex problem. We propose a breakpoint searching method and a fifth-order iterative method to solve this problem efficiently and effectively. We also propose two novel greedy strategies to find a good working set to further accelerate the convergence of \textit{\textbf{OBCD}}. Finally, we have conducted extensive experiments on several tasks to demonstrate the superiority of our approach.

Mobility-on-demand (MoD) systems consist of a fleet of shared vehicles that can be hailed for one-way point-to-point trips. The total distance driven by the vehicles and the fleet size can be reduced by employing ridesharing, i.e., by assigning multiple passengers to one vehicle. However, finding the optimal passenger-vehicle assignment in an MoD system is a hard combinatorial problem. In this work, we demonstrate how the VGA method, a recently proposed systematic method for ridesharing, can be used to compute the optimal passenger-vehicle assignments and corresponding vehicle routes in a massive-scale MoD system. In contrast to existing works, we solve all passenger-vehicle assignment problems to optimality, regularly dealing with instances containing thousands of vehicles and passengers. Moreover, to examine the impact of using optimal ridesharing assignments, we compare the performance of an MoD system that uses optimal assignments against an MoD system that uses assignments computed using insertion heuristic and against an MoD system that uses no ridesharing. We found that the system that uses optimal ridesharing assignments subject to the maximum travel delay of 4 minutes reduces the vehicle distance driven by 57 % compared to an MoD system without ridesharing. Furthermore, we found that the optimal assignments result in a 20 % reduction in vehicle distance driven and 5 % lower average passenger travel delay compared to a system that uses insertion heuristic.