With the electrification of transportation, the rising uptake of electric vehicles (EVs) might stress distribution networks significantly, leaving their performance degraded and stability jeopardized. To accommodate these new loads cost-effectively, modern power grids require coordinated or ``smart'' charging strategies capable of optimizing EV charging scheduling in a scalable and efficient fashion. With this in view, the present work focuses on reservation management programs for large-scale, networked EV charging stations. We formulate a time-coupled binary optimization problem that maximizes EV users' total welfare gain while accounting for the network's available power capacity and stations' occupancy limits. To tackle the problem at scale while retaining high solution quality, a data-driven optimization framework combining techniques from the fields of Deep Learning and Approximation Algorithms is introduced. The framework's key ingredient is a novel input-output processing scheme for neural networks that allows direct extrapolation to problem sizes substantially larger than those included in the training set. Extensive numerical simulations based on synthetic and real-world data traces verify the effectiveness and superiority of the presented approach over two representative scheduling algorithms. Lastly, we round up the contributions by listing several immediate extensions to the proposed framework and outlining the prospects for further exploration.

Differentiable optimization has received a significant amount of attention due to its foundational role in the domain of machine learning based on neural networks. The existing methods leverages the optimality conditions and implicit function theorem to obtain the Jacobian matrix of the output, which increases the computational cost and limits the application of differentiable optimization. In addition, some non-differentiable constraints lead to more challenges when using prior differentiable optimization layers. This paper proposes a differentiable layer, named Differentiable Frank-Wolfe Layer (DFWLayer), by rolling out the Frank-Wolfe method, a well-known optimization algorithm which can solve constrained optimization problems without projections and Hessian matrix computations, thus leading to a efficient way of dealing with large-scale problems. Theoretically, we establish a bound on the suboptimality gap of the DFWLayer in the context of l1-norm constraints. Experimental assessments demonstrate that the DFWLayer not only attains competitive accuracy in solutions and gradients but also consistently adheres to constraints. Moreover, it surpasses the baselines in both forward and backward computational speeds.

Since wearable linkage mechanisms could control the moment transmission from actuator(s) to wearers, they can help ensure that even low-cost wearable systems provide advanced functionality tailored to users' needs. For example, if a hip mechanism transforms an input torque into a spatially-varying moment, a wearer can get effective assistance both in the sagittal and frontal planes during walking, even with an affordable single-actuator system. However, due to the combinatorial nature of the linkage mechanism design space, the topologies of such nonlinear-moment-generating mechanisms are challenging to determine, even with significant computational resources and numerical data. Furthermore, on-premise production development and interactive design are nearly impossible in conventional synthesis approaches. Here, we propose an innovative autonomous computational approach for synthesizing such wearable robot mechanisms, eliminating the need for exhaustive searches or numerous data sets. Our method transforms the synthesis problem into a gradient-based optimization problem with sophisticated objective and constraint functions while ensuring the desired degree of freedom, range of motion, and force transmission characteristics. To generate arbitrary mechanism topologies and dimensions, we employed a unified ground model. By applying the proposed method for the design of hip joint mechanisms, the topologies and dimensions of non-series-type hip joint mechanisms were obtained. Biomechanical simulations validated its multi-moment assistance capability, and its wearability was verified via prototype fabrication. The proposed design strategy can open a new way to design various wearable robot mechanisms, such as shoulders, knees, and ankles.

As the complexity of learning tasks surges, modern machine learning encounters a new constrained learning paradigm characterized by more intricate and data-driven function constraints. Prominent applications include Neyman-Pearson classification (NPC) and fairness classification, which entail specific risk constraints that render standard projection-based training algorithms unsuitable. Gradient boosting machines (GBMs) are among the most popular algorithms for supervised learning; however, they are generally limited to unconstrained settings. In this paper, we adapt the GBM for constrained learning tasks within the framework of Bregman proximal algorithms. We introduce a new Bregman primal-dual method with a global optimality guarantee when the learning objective and constraint functions are convex. In cases of nonconvex functions, we demonstrate how our algorithm remains effective under a Bregman proximal point framework. Distinct from existing constrained learning algorithms, ours possess a unique advantage in their ability to seamlessly integrate with publicly available GBM implementations such as XGBoost (Chen and Guestrin, 2016) and LightGBM (Ke et al., 2017), exclusively relying on their public interfaces. We provide substantial experimental evidence to showcase the effectiveness of the Bregman algorithm framework. While our primary focus is on NPC and fairness ML, our framework holds significant potential for a broader range of constrained learning applications. The source code is currently freely available at https://github.com/zhenweilin/ConstrainedGBM}{https://github.com/zhenweilin/ConstrainedGBM.

Nowadays, machine learning systems tend to incorporate an increasing number of hyperparameters with the purpose of improving the overall performance of learning tasks and achieving a higher flexibility. Then, optimizing such high-dimensional hyperparameters becomes a crucial step for devising efficient and fully parameter-free machine learning systems. In recent years, bilevel approaches to hyperparameter optimization have become very popular as an effective way to estimate high-dimensional hyperparameters [1, 2, 3, 6, 10, 16, 18]. On the other hand, in many circumstances binary hyperparameters are included in the model to allow the pruning of the irrelevant variables or the discovery of sparsity structures. Interesting examples are given by the pruning of large-scale deep learning models [22], the identification of the group-sparsity structures in regression problems [8, 20], and learning the discrete structure of a graph neural networks [7]. For these cases the usual optimization approach is that of relaxing the respective parameter over the unit interval [0, 1], solve the continuous optimization problem, and then rounding the solution so to get a binary output. This is essentially a heuristic, which overcomes the challenge of dealing with integer variables, but does not offer any theoretical guarantee. The aim of the present work is that of providing a more principled way of approaching mixed-binary hyperparameter optimization.

Submodular maximization has found extensive applications in various domains within the field of artificial intelligence, including but not limited to machine learning, computer vision, and natural language processing. With the increasing size of datasets in these domains, there is a pressing need to develop efficient and parallelizable algorithms for submodular maximization. One measure of the parallelizability of a submodular maximization algorithm is its adaptive complexity, which indicates the number of sequential rounds where a polynomial number of queries to the objective function can be executed in parallel. In this paper, we study the problem of non-monotone submodular maximization subject to a knapsack constraint, and propose the first combinatorial algorithm achieving an $(8+\epsilon)$-approximation under $\mathcal{O}(\log n)$ adaptive complexity, which is \textit{optimal} up to a factor of $\mathcal{O}(\log\log n)$. Moreover, we also propose the first algorithm with both provable approximation ratio and sublinear adaptive complexity for the problem of non-monotone submodular maximization subject to a $k$-system constraint. As a by-product, we show that our two algorithms can also be applied to the special case of submodular maximization subject to a cardinality constraint, and achieve performance bounds comparable with those of state-of-the-art algorithms. Finally, the effectiveness of our approach is demonstrated by extensive experiments on real-world applications.

Gradient dominance property is a condition weaker than strong convexity, yet it sufficiently ensures global convergence for first-order methods even in non-convex optimization. This property finds application in various machine learning domains, including matrix decomposition, linear neural networks, and policy-based reinforcement learning (RL). In this paper, we study the stochastic homogeneous second-order descent method (SHSODM) for gradient-dominated optimization with $\alpha \in [1, 2]$ based on a recently proposed homogenization approach. Theoretically, we show that SHSODM achieves a sample complexity of $O(\epsilon^{-7/(2 \alpha) +1})$ for $\alpha \in [1, 3/2)$ and $\tilde{O}(\epsilon^{-2/\alpha})$ for $\alpha \in [3/2, 2]$. We further provide a SHSODM with a variance reduction technique enjoying an improved sample complexity of $O( \epsilon ^{-( 7-3\alpha ) /( 2\alpha )})$ for $\alpha \in [1,3/2)$. Our results match the state-of-the-art sample complexity bounds for stochastic gradient-dominated optimization without \emph{cubic regularization}. Since the homogenization approach only relies on solving extremal eigenvector problems instead of Newton-type systems, our methods gain the advantage of cheaper iterations and robustness in ill-conditioned problems. Numerical experiments on several RL tasks demonstrate the efficiency of SHSODM compared to other off-the-shelf methods.

The conjugate gradient method is a crucial first-order optimization method that generally converges faster than the steepest descent method, and its computational cost is much lower than the second-order methods. However, while various types of conjugate gradient methods have been studied in Euclidean spaces and on Riemannian manifolds, there has little study for those in distributed scenarios. This paper proposes a decentralized Riemannian conjugate gradient descent (DRCGD) method that aims at minimizing a global function over the Stiefel manifold. The optimization problem is distributed among a network of agents, where each agent is associated with a local function, and communication between agents occurs over an undirected connected graph. Since the Stiefel manifold is a non-convex set, a global function is represented as a finite sum of possibly non-convex (but smooth) local functions. The proposed method is free from expensive Riemannian geometric operations such as retractions, exponential maps, and vector transports, thereby reducing the computational complexity required by each agent. To the best of our knowledge, DRCGD is the first decentralized Riemannian conjugate gradient algorithm to achieve global convergence over the Stiefel manifold.

The goal of offline black-box optimization (BBO) is to optimize an expensive black-box function using a fixed dataset of function evaluations. Prior works consider forward approaches that learn surrogates to the black-box function and inverse approaches that directly map function values to corresponding points in the input domain of the black-box function. These approaches are limited by the quality of the offline dataset and the difficulty in learning one-to-many mappings in high dimensions, respectively. We propose Denoising Diffusion Optimization Models (DDOM), a new inverse approach for offline black-box optimization based on diffusion models. Given an offline dataset, DDOM learns a conditional generative model over the domain of the black-box function conditioned on the function values. We investigate several design choices in DDOM, such as re-weighting the dataset to focus on high function values and the use of classifier-free guidance at test-time to enable generalization to function values that can even exceed the dataset maxima. Empirically, we conduct experiments on the Design-Bench benchmark and show that DDOM achieves results competitive with state-of-the-art baselines.

The online advertising management platform has become increasingly popular among e-commerce vendors/advertisers, offering a streamlined approach to reach target customers. Despite its advantages, configuring advertising strategies correctly remains a challenge for online vendors, particularly those with limited resources. Ineffective strategies often result in a surge of unproductive ``just looking'' clicks, leading to disproportionately high advertising expenses comparing to the growth of sales. In this paper, we present a novel profit-maximing strategy for targeting options of online advertising. The proposed model aims to find the optimal set of features to maximize the probability of converting targeted audiences into actual buyers. We address the optimization challenge by reformulating it as a multiple-choice knapsack problem (MCKP). We conduct an empirical study featuring real-world data from Tmall to show that our proposed method can effectively optimize the advertising strategy with budgetary constraints.