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.

Motivated by the success of Bayesian optimisation algorithms in the Euclidean space, we propose a novel approach to construct Intrinsic Bayesian optimisation (In-BO) on manifolds with a primary focus on complex constrained domains or irregular-shaped spaces arising as submanifolds of R2, R3 and beyond. Data may be collected in a spatial domain but restricted to a complex or intricately structured region corresponding to a geographic feature, such as lakes. Traditional Bayesian Optimisation (Tra-BO) defined with a Radial basis function (RBF) kernel cannot accommodate these complex constrained conditions. The In-BO uses the Sparse Intrinsic Gaussian Processes (SIn-GP) surrogate model to take into account the geometric structure of the manifold. SInGPs are constructed using the heat kernel of the manifold which is estimated as the transition density of the Brownian Motion on manifolds. The efficiency of In-BO is demonstrated through simulation studies on a U-shaped domain, a Bitten torus, and a real dataset from the Aral sea. Its performance is compared to that of traditional BO, which is defined in Euclidean space.

Ensemble methods can deliver surprising performance gains but also bring significantly higher computational costs, e.g., can be up to 2048X in large-scale ensemble tasks. However, we found that the majority of computations in ensemble methods are redundant. For instance, over 77% of samples in CIFAR-100 dataset can be correctly classified with only a single ResNet-18 model, which indicates that only around 23% of the samples need an ensemble of extra models. To this end, we propose an inference efficient ensemble learning method, to simultaneously optimize for effectiveness and efficiency in ensemble learning. More specifically, we regard ensemble of models as a sequential inference process and learn the optimal halting event for inference on a specific sample. At each timestep of the inference process, a common selector judges if the current ensemble has reached ensemble effectiveness and halt further inference, otherwise filters this challenging sample for the subsequent models to conduct more powerful ensemble. Both the base models and common selector are jointly optimized to dynamically adjust ensemble inference for different samples with various hardness, through the novel optimization goals including sequential ensemble boosting and computation saving. The experiments with different backbones on real-world datasets illustrate our method can bring up to 56\% inference cost reduction while maintaining comparable performance to full ensemble, achieving significantly better ensemble utility than other baselines. Code and supplemental materials are available at https://seqml.github.io/irene.

Optimization of atomic structures presents a challenging problem, due to their highly rough and non-convex energy landscape, with wide applications in the fields of drug design, materials discovery, and mechanics. Here, we present a graph reinforcement learning approach, StriderNET, that learns a policy to displace the atoms towards low energy configurations. We evaluate the performance of StriderNET on three complex atomic systems, namely, binary Lennard-Jones particles, calcium silicate hydrates gel, and disordered silicon. We show that StriderNET outperforms all classical optimization algorithms and enables the discovery of a lower energy minimum. In addition, StriderNET exhibits a higher rate of reaching minima with energies, as confirmed by the average over multiple realizations. Finally, we show that StriderNET exhibits inductivity to unseen system sizes that are an order of magnitude different from the training system.