Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large errors in the solutions. We specify conditions under which approximations are well behaved in the sense of minimizers, stationary points, and level-sets and this leads to a framework of consistent approximations. The framework is developed for a broad class of composite problems, which are neither convex nor smooth. We demonstrate the framework using examples from stochastic optimization, neural-network based machine learning, distributionally robust optimization, penalty and augmented Lagrangian methods, interior-point methods, homotopy methods, smoothing methods, extended nonlinear programming, difference-of-convex programming, and multi-objective optimization. An enhanced proximal method illustrates the algorithmic possibilities.

Fusing artificial intelligence with mathematical optimization will dramatically increase the "brainpower" for the task at hand, whether it's optimizing flight patterns or bringing energy and food to underserved areas. That's the word from the academic researchers who are part of a new interdisciplinary institute that aims to integrate the two fields. The National AI Institute for Advances in Optimization (AI4OPT) is led by a multidisciplinary team from six U.S. universities, including computer science and civil, environmental, electrical, and computer engineering professors. The combined methods will foster no less than a "paradigm shift" in optimization, said Pascal Van Hentenryck, professor of industrial and systems engineering at Georgia Tech and institute lead. According to Hentenryck, tackling problems at the scale and complexity faced by society today requires a fusion of optimization and machine learning, with the two technologies working hand-in-hand.

This paper formulates a general cross validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as Trend Filtering and Dyadic CART. The resulting cross validated versions are then shown to attain nearly the same rates of convergence as are known for the optimally tuned analogues. There did not exist any previous theoretical analyses of cross validated versions of Trend Filtering or Dyadic CART. To illustrate the generality of the framework we also propose and study cross validated versions of two fundamental estimators; lasso for high dimensional linear regression and singular value thresholding for matrix estimation. Our general framework is inspired by the ideas in Chatterjee and Jafarov (2015) and is potentially applicable to a wide range of estimation methods which use tuning parameters.

Tether-net launched from a chaser spacecraft provides a promising method to capture and dispose of large space debris in orbit. This tether-net system is subject to several sources of uncertainty in sensing and actuation that affect the performance of its net launch and closing control. Earlier reliability-based optimization approaches to design control actions however remain challenging and computationally prohibitive to generalize over varying launch scenarios and target (debris) state relative to the chaser. To search for a general and reliable control policy, this paper presents a reinforcement learning framework that integrates a proximal policy optimization (PPO2) approach with net dynamics simulations. The latter allows evaluating the episodes of net-based target capture, and estimate the capture quality index that serves as the reward feedback to PPO2. Here, the learned policy is designed to model the timing of the net closing action based on the state of the moving net and the target, under any given launch scenario. A stochastic state transition model is considered in order to incorporate synthetic uncertainties in state estimation and launch actuation. Along with notable reward improvement during training, the trained policy demonstrates capture performance (over a wide range of launch/target scenarios) that is close to that obtained with reliability-based optimization run over an individual scenario.

We present a personal mobility device for lower-body impaired users through a light-weighted exoskeleton on wheels. On its core, a novel passive exoskeleton provides postural transition leveraging natural body postures with support to the trunk on sit-to-stand and stand-to-sit (STS) transitions by a single gas spring as an energy storage unit. We propose a direction-dependent coupling of knees and hip joints through a double-pulley wire system, transferring energy from the torso motion towards balancing the moment load at the knee joint actuator. Herewith, the exoskeleton maximizes energy transfer and the naturalness of the user's movement. We introduce an embodied user interface for hands-free navigation through a torso pressure sensing with minimal trunk rotations, resulting on average $19^{\circ} \pm 13^{\circ}$ on six unimpaired users. We evaluated the design for STS assistance on 11 unimpaired users observing motions and muscle activity during the transitions. Results comparing assisted and unassisted STS transitions validated a significant reduction (up to $68\%$ $p<0.01$) at the involved muscle groups. Moreover, we showed it feasible through natural torso leaning movements of $+12^{\circ}\pm 6.5^{\circ}$ and $- 13.7^{\circ} \pm 6.1^{\circ}$ for standing and sitting, respectively. Passive postural transition assistance warrants further work on increasing its applicability and broadening the user population.

Learning invariant representations is an important requirement when training machine learning models that are driven by spurious correlations in the datasets. These spurious correlations, between input samples and the target labels, wrongly direct the neural network predictions resulting in poor performance on certain groups, especially the minority groups. Robust training against these spurious correlations requires the knowledge of group membership for every sample. Such a requirement is impractical in situations where the data labeling efforts for minority or rare groups are significantly laborious or where the individuals comprising the dataset choose to conceal sensitive information. On the other hand, the presence of such data collection efforts results in datasets that contain partially labeled group information. Recent works have tackled the fully unsupervised scenario where no labels for groups are available. Thus, we aim to fill the missing gap in the literature by tackling a more realistic setting that can leverage partially available sensitive or group information during training. First, we construct a constraint set and derive a high probability bound for the group assignment to belong to the set. Second, we propose an algorithm that optimizes for the worst-off group assignments from the constraint set. Through experiments on image and tabular datasets, we show improvements in the minority group's performance while preserving overall aggregate accuracy across groups.

Federated learning often suffers from unstable and slow convergence due to heterogeneous characteristics of participating clients. Such tendency is aggravated when the client participation ratio is low since the information collected from the clients at each round is prone to be more inconsistent. To tackle the challenge, we propose a novel federated learning framework, which improves the stability of the server-side aggregation step, which is achieved by sending the clients an accelerated model estimated with the global gradient to guide the local gradient updates. Our algorithm naturally aggregates and conveys the global update information to participants with no additional communication cost and does not require to store the past models in the clients. We also regularize local update to further reduce the bias and improve the stability of local updates. We perform comprehensive empirical studies on real data under various settings and demonstrate the remarkable performance of the proposed method in terms of accuracy and communication-efficiency compared to the state-of-the-art methods, especially with low client participation rates. Our code is available at https://github.com/ ninigapa0/FedAGM

Hottopixx, proposed by Bittorf et al. at NIPS 2012, is an algorithm for solving nonnegative matrix factorization (NMF) problems under the separability assumption. Separable NMFs have important applications, such as topic extraction from documents and unmixing of hyperspectral images. In such applications, the robustness of the algorithm to noise is the key to the success. Hottopixx has been shown to be robust to noise, and its robustness can be further enhanced through postprocessing. However, there is a drawback. Hottopixx and its postprocessing require us to estimate the noise level involved in the matrix we want to factorize before running, since they use it as part of the input data. The noise-level estimation is not an easy task. In this paper, we overcome this drawback. We present a refinement of Hottopixx and its postprocessing that runs without prior knowledge of the noise level. We show that the refinement has almost the same robustness to noise as the original algorithm.

This paper explores the environmental impact of the super-linear growth trends for AI from a holistic perspective, spanning Data, Algorithms, and System Hardware. We characterize the carbon footprint of AI computing by examining the model development cycle across industry-scale machine learning use cases and, at the same time, considering the life cycle of system hardware. Taking a step further, we capture the operational and manufacturing carbon footprint of AI computing and present an end-to-end analysis for what and how hardware-software design and at-scale optimization can help reduce the overall carbon footprint of AI. Based on the industry experience and lessons learned, we share the key challenges and chart out important development directions across the many dimensions of AI. We hope the key messages and insights presented in this paper can inspire the community to advance the field of AI in an environmentally-responsible manner.

In this paper, we propose a novel nonconvex approach to robust principal component analysis for HSI denoising, which focuses on simultaneously developing more accurate approximations to both rank and column-wise sparsity for the low-rank and sparse components, respectively. In particular, the new method adopts the log-determinant rank approximation and a novel $\ell_{2,\log}$ norm, to restrict the local low-rank or column-wisely sparse properties for the component matrices, respectively. For the $\ell_{2,\log}$-regularized shrinkage problem, we develop an efficient, closed-form solution, which is named $\ell_{2,\log}$-shrinkage operator. The new regularization and the corresponding operator can be generally used in other problems that require column-wise sparsity. Moreover, we impose the spatial-spectral total variation regularization in the log-based nonconvex RPCA model, which enhances the global piece-wise smoothness and spectral consistency from the spatial and spectral views in the recovered HSI. Extensive experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method in denoising HSIs.