Neural networks (NNs) are known to be vulnerable against adversarial perturbations, and thus there is a line of work aiming to provide robustness certification for NNs, such as randomized smoothing, which samples smoothing noises from a certain distribution to certify the robustness for a smoothed classifier. However, as shown by previous work, the certified robust radius in randomized smoothing suffers from scaling to large datasets ("curse of dimensionality"). To overcome this hurdle, we propose a Double Sampling Randomized Smoothing (DSRS) framework, which exploits the sampled probability from an additional smoothing distribution to tighten the robustness certification of the previous smoothed classifier. Theoretically, under mild assumptions, we prove that DSRS can certify $\Theta(\sqrt d)$ robust radius under $\ell_2$ norm where $d$ is the input dimension, implying that DSRS may be able to break the curse of dimensionality of randomized smoothing. We instantiate DSRS for a generalized family of Gaussian smoothing and propose an efficient and sound computing method based on customized dual optimization considering sampling error. Extensive experiments on MNIST, CIFAR-10, and ImageNet verify our theory and show that DSRS certifies larger robust radii than existing baselines consistently under different settings. Code is available at https://github.com/llylly/DSRS.

Multi-task learning (MTL) aims at solving multiple related tasks simultaneously and has experienced rapid growth in recent years. However, MTL models often suffer from performance degeneration with negative transfer due to learning several tasks simultaneously. Some related work attributed the source of the problem is the conflicting gradients. In this case, it is needed to select useful gradient updates for all tasks carefully. To this end, we propose a novel optimization approach for MTL, named GDOD, which manipulates gradients of each task using an orthogonal basis decomposed from the span of all task gradients. GDOD decomposes gradients into task-shared and task-conflict components explicitly and adopts a general update rule for avoiding interference across all task gradients. This allows guiding the update directions depending on the task-shared components. Moreover, we prove the convergence of GDOD theoretically under both convex and non-convex assumptions. Experiment results on several multi-task datasets not only demonstrate the significant improvement of GDOD performed to existing MTL models but also prove that our algorithm outperforms state-of-the-art optimization methods in terms of AUC and Logloss metrics.

Pin fins are imperative in the cooling of turbine blades. The designs of pin fins, therefore, have seen significant research in the past. With the developments in metal additive manufacturing, novel design approaches toward complex geometries are now feasible. To that end, this article presents a Bayesian optimization approach for designing inline pins that can achieve low pressure loss. The pin-fin shape is defined using featurized (parametrized) piecewise cubic splines in 2D. The complexity of the shape is dependent on the number of splines used for the analysis. From a method development perspective, the study is performed using three splines. Owing to this piece-wise modeling, a unique pin fin design is defined using five features. After specifying the design, a computational fluid dynamics-based model is developed that computes the pressure drop during the flow. Bayesian optimization is carried out on a Gaussian processes-based surrogate to obtain an optimal combination of pin-fin features to minimize the pressure drop. The results show that the optimization tends to approach an aerodynamic design leading to low pressure drop corroborating with the existing knowledge. Furthermore, multiple iterations of optimizations are conducted with varying degree of input data. The results reveal that a convergence to similar optimal design is achieved with a minimum of just twenty five initial design-of-experiments data points for the surrogate. Sensitivity analysis shows that the distance between the rows of the pin fins is the most dominant feature influencing the pressure drop. In summary, the newly developed automated framework demonstrates remarkable capabilities in designing pin fins with superior performance characteristics.

This work revisits the joint beamforming (BF) and antenna selection (AS) problem, as well as its robust beamforming (RBF) version under imperfect channel state information (CSI). Such problems arise due to various reasons, e.g., the costly nature of the radio frequency (RF) chains and energy/resource-saving considerations. The joint (R)BF\&AS problem is a mixed integer and nonlinear program, and thus finding {\it optimal solutions} is often costly, if not outright impossible. The vast majority of the prior works tackled these problems using techniques such as continuous approximations, greedy methods, and supervised machine learning -- yet these approaches do not ensure optimality or even feasibility of the solutions. The main contribution of this work is threefold. First, an effective {\it branch and bound} (B\&B) framework for solving the problems of interest is proposed. Leveraging existing BF and RBF solvers, it is shown that the B\&B framework guarantees global optimality of the considered problems. Second, to expedite the potentially costly B\&B algorithm, a machine learning (ML)-based scheme is proposed to help skip intermediate states of the B\&B search tree. The learning model features a {\it graph neural network} (GNN)-based design that is resilient to a commonly encountered challenge in wireless communications, namely, the change of problem size (e.g., the number of users) across the training and test stages. Third, comprehensive performance characterizations are presented, showing that the GNN-based method retains the global optimality of B\&B with provably reduced complexity, under reasonable conditions. Numerical simulations also show that the ML-based acceleration can often achieve an order-of-magnitude speedup relative to B\&B.

Efficient trajectory generation in complex dynamic environments remains an open problem in the unmanned surface vehicle (USV). The perception of the USV is usually interfered with by the swing of the hull and the ambient weather, making it challenging to plan the optimal USV trajectories. In this paper, a cooperative trajectory planning algorithm for the coupled USV-UAV system is proposed to ensure that USV can execute a safe and smooth path in the process of autonomous advance in multi-obstacle maps. Specifically, the unmanned aerial vehicle (UAV) plays the role of a flight sensor, providing real-time global map and obstacle information with a lightweight semantic segmentation network and 3D projection transformation. And then, an initial obstacle avoidance trajectory is generated by a graph-based search method. Concerning the unique under-actuated kinematic characteristics of the USV, a numerical optimization method based on hull dynamic constraints is introduced to make the trajectory easier to be tracked for motion control. Finally, a motion control method based on NMPC with the lowest energy consumption constraint during execution is proposed. Experimental results verify the effectiveness of the whole system, and the generated trajectory is locally optimal for USV with considerable tracking accuracy.

Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $\varepsilon$ additive accuracy with runtime $\widetilde{O}( n^2/\varepsilon)$, where $n$ denotes the dimension of the probability distributions of interest. Our algorithm achieves the state-of-the-art computational guarantees among all first-order methods, while exhibiting favorable numerical performance compared to classical algorithms like Sinkhorn and Greenkhorn. Underlying our algorithm designs are two key elements: (a) converting the original problem into a bilinear minimax problem over probability distributions; (b) exploiting the extragradient idea -- in conjunction with entropy regularization and adaptive learning rates -- to accelerate convergence.

We present Mono-STAR, the first real-time 3D reconstruction system that simultaneously supports semantic fusion, fast motion tracking, non-rigid object deformation, and topological change under a unified framework. The proposed system solves a new optimization problem incorporating optical-flow-based 2D constraints to deal with fast motion and a novel semantic-aware deformation graph (SAD-graph) for handling topology change. We test the proposed system under various challenging scenes and demonstrate that it significantly outperforms existing state-of-the-art methods.

We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods with a provable improvement of the condition number, cutting the gaps between highest eigenvalues, without explicit knowledge of the actual spectrum. We give a stochastic interpretation of this preconditioning in terms of coordinate volume sampling and compare it with other classical approaches, including the Chebyshev polynomials. We show how to incorporate a polynomial preconditioning into the Gradient and Fast Gradient Methods and establish the corresponding global complexity bounds. Finally, we propose a simple adaptive search procedure that automatically chooses the best possible polynomial preconditioning for the Gradient Method, minimizing the objective along a low-dimensional Krylov subspace. Numerical experiments confirm the efficiency of our preconditioning strategies for solving various machine learning problems.

Choosing a good resource configuration for big data analytics applications can be challenging, especially in cloud environments. Automated approaches are desirable as poor decisions can reduce performance and raise costs. The majority of existing automated approaches either build performance models from previous workload executions or conduct iterative resource configuration profiling until a near-optimal solution has been found. In doing so, they only obtain an implicit understanding of the underlying infrastructure, which is difficult to transfer to alternative infrastructures and, thus, profiling and modeling insights are not sustained beyond very specific situations. We present Perona, a novel approach to robust infrastructure fingerprinting for usage in the context of big data analytics. Perona employs common sets and configurations of benchmarking tools for target resources, so that resulting benchmark metrics are directly comparable and ranking is enabled. Insignificant benchmark metrics are discarded by learning a low-dimensional representation of the input metric vector, and previous benchmark executions are taken into consideration for context-awareness as well, allowing to detect resource degradation. We evaluate our approach both on data gathered from our own experiments as well as within related works for resource configuration optimization, demonstrating that Perona captures the characteristics from benchmark runs in a compact manner and produces representations that can be used directly.

We consider the problem of decision-making under uncertainty in an environment with safety constraints. Many business and industrial applications rely on real-time optimization to improve key performance indicators. In the case of unknown characteristics, real-time optimization becomes challenging, particularly because of the satisfaction of safety constraints. We propose the ARTEO algorithm, where we cast multi-armed bandits as a mathematical programming problem subject to safety constraints and learn the unknown characteristics through exploration while optimizing the targets. We quantify the uncertainty in unknown characteristics by using Gaussian processes and incorporate it into the cost function as a contribution which drives exploration. We adaptively control the size of this contribution in accordance with the requirements of the environment. We guarantee the safety of our algorithm with a high probability through confidence bounds constructed under the regularity assumptions of Gaussian processes. We demonstrate the safety and efficiency of our approach with two case studies: optimization of electric motor current and real-time bidding problems. We further evaluate the performance of ARTEO compared to a safe variant of upper confidence bound based algorithms. ARTEO achieves less cumulative regret with accurate and safe decisions.