This paper concerns a class of DC composite optimization problems which, as an extension of convex composite optimization problems and DC programs with nonsmooth components, often arises in robust factorization models of low-rank matrix recovery. For this class of nonconvex and nonsmooth problems, we propose an inexact linearized proximal algorithm (iLPA) by computing in each step an inexact minimizer of a strongly convex majorization constructed with a partial linearization of their objective functions at the current iterate, and establish the convergence of the generated iterate sequence under the Kurdyka-\L\"ojasiewicz (KL) property of a potential function. In particular, by leveraging the composite structure, we provide a verifiable condition for the potential function to have the KL property of exponent $1/2$ at the limit point, so for the iterate sequence to have a local R-linear convergence rate. Finally, we apply the proposed iLPA to a robust factorization model for matrix completions with outliers and non-uniform sampling, and numerical comparison with the Polyak subgradient method confirms its superiority in terms of computing time and quality of solutions.

We consider the problem of nonlinear stochastic optimal control. This problem is thought to be fundamentally intractable owing to Bellman's infamous "curse of dimensionality". We present a result that shows that repeatedly solving an open-loop deterministic problem from the current state, similar to Model Predictive Control (MPC), results in a feedback policy that is $O(\epsilon^4)$ near to the true global stochastic optimal policy. Furthermore, empirical results show that solving the Stochastic Dynamic Programming (DP) problem is highly susceptible to noise, even when tractable, and in practice, the MPC-type feedback law offers superior performance even for stochastic systems.

The availability of representative datasets is an essential prerequisite for many successful artificial intelligence and machine learning models. However, in real life applications these models often encounter scenarios that are inadequately represented in the data used for training. There are various reasons for the absence of sufficient data, ranging from time and cost constraints to ethical considerations. As a consequence, the reliable usage of these models, especially in safety-critical applications, is still a tremendous challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches. Knowledge augmented machine learning approaches offer the possibility of compensating for deficiencies, errors, or ambiguities in the data, thus increasing the generalization capability of the applied models. Even more, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-driven models with existing knowledge. The identified approaches are structured according to the categories knowledge integration, extraction and conformity. In particular, we address the application of the presented methods in the field of autonomous driving.

We study accelerated optimization methods in the Gaussian phase retrieval problem. In this setting, we prove that gradient methods with Polyak or Nesterov momentum have similar implicit regularization to gradient descent. This implicit regularization ensures that the algorithms remain in a nice region, where the cost function is strongly convex and smooth despite being nonconvex in general. This ensures that these accelerated methods achieve faster rates of convergence than gradient descent. Experimental evidence demonstrates that the accelerated methods converge faster than gradient descent in practice.

This paper presents an integrated algorithmic framework for minimising product delivery costs in e-commerce (known as the cost-to-serve or C2S). One of the major challenges in e-commerce is the large volume of spatio-temporally diverse orders from multiple customers, each of which has to be fulfilled from one of several warehouses using a fleet of vehicles. This results in two levels of decision-making: (i) selection of a fulfillment node for each order (including the option of deferral to a future time), and then (ii) routing of vehicles (each of which can carry multiple orders originating from the same warehouse). We propose an approach that combines graph neural networks and reinforcement learning to train the node selection and vehicle routing agents. We include real-world constraints such as warehouse inventory capacity, vehicle characteristics such as travel times, service times, carrying capacity, and customer constraints including time windows for delivery. The complexity of this problem arises from the fact that outcomes (rewards) are driven both by the fulfillment node mapping as well as the routing algorithms, and are spatio-temporally distributed. Our experiments show that this algorithmic pipeline outperforms pure heuristic policies.

We propose and analyze an efficient algorithm for solving the joint sparse recovery problem using a new regularization-based method, named orthogonally weighted $\ell_{2,1}$ ($\mathit{ow}\ell_{2,1}$), which is specifically designed to take into account the rank of the solution matrix. This method has applications in feature extraction, matrix column selection, and dictionary learning, and it is distinct from commonly used $\ell_{2,1}$ regularization and other existing regularization-based approaches because it can exploit the full rank of the row-sparse solution matrix, a key feature in many applications. We provide a proof of the method's rank-awareness, establish the existence of solutions to the proposed optimization problem, and develop an efficient algorithm for solving it, whose convergence is analyzed. We also present numerical experiments to illustrate the theory and demonstrate the effectiveness of our method on real-life problems.

Recently, Zhuang, Roth, \& Sudhakar [1] proposed a method that allows simultaneous computation of the rigid transformations from world frame to robot base frame and from hand frame to camera frame. Their method attempts to solve a homogeneous matrix equation of the form AX=ZB. They use quaternions to derive explicit linear solutions for X and Z. In this short paper, we present two new solutions that attempt to solve the homogeneous matrix equation mentioned above: (i) a closed-form method which uses quaternion algebra and a positive quadratic error function associated with this representation and (ii) a method based on non-linear constrained minimization and which simultaneously solves for rotations and translations. These results may be useful to other problems that can be formulated in the same mathematical form. We perform a sensitivity analysis for both our two methods and the linear method developed by Zhuang et al. This analysis allows the comparison of the three methods. In the light of this comparison the non-linear optimization method, which solves for rotations and translations simultaneously, seems to be the most stable one with respect to noise and to measurement errors.

Artificial Intelligence (AI) systems such as autonomous vehicles, facial recognition, and speech recognition systems are increasingly integrated into our daily lives. However, despite their utility, these AI systems are vulnerable to a wide range of attacks such as adversarial, backdoor, data poisoning, membership inference, model inversion, and model stealing attacks. In particular, numerous attacks are designed to target a particular model or system, yet their effects can spread to additional targets, referred to as transferable attacks. Although considerable efforts have been directed toward developing transferable attacks, a holistic understanding of the advancements in transferable attacks remains elusive. In this paper, we comprehensively explore learning-based attacks from the perspective of transferability, particularly within the context of cyber-physical security. We delve into different domains -- the image, text, graph, audio, and video domains -- to highlight the ubiquitous and pervasive nature of transferable attacks. This paper categorizes and reviews the architecture of existing attacks from various viewpoints: data, process, model, and system. We further examine the implications of transferable attacks in practical scenarios such as autonomous driving, speech recognition, and large language models (LLMs). Additionally, we outline the potential research directions to encourage efforts in exploring the landscape of transferable attacks. This survey offers a holistic understanding of the prevailing transferable attacks and their impacts across different domains.

We note that decoupled weight decay regularization is a particular case of weight norm control where the target norm of weights is set to 0. Any optimization method (e.g., Adam) which uses decoupled weight decay regularization (respectively, AdamW) can be viewed as a particular case of a more general algorithm with weight norm control (respectively, AdamWN). We argue that setting the target norm of weights to 0 can be suboptimal and other target norm values can be considered. For instance, any training run where AdamW achieves a particular norm of weights can be challenged by AdamWN scheduled to achieve a comparable norm of weights. We discuss various implications of introducing weight norm control instead of weight decay. They introduced AdamW algorithm where Adam's loss-based update is decoupled from weight decay.

Eight percent of global carbon dioxide emissions can be attributed to the production of cement, the main component of concrete, which is also the dominant source of CO2 emissions in the construction of data centers. The discovery of lower-carbon concrete formulae is therefore of high significance for sustainability. However, experimenting with new concrete formulae is time consuming and labor intensive, as one usually has to wait to record the concrete's 28-day compressive strength, a quantity whose measurement can by its definition not be accelerated. This provides an opportunity for experimental design methodology like Bayesian Optimization (BO) to accelerate the search for strong and sustainable concrete formulae. Herein, we 1) propose modeling steps that make concrete strength amenable to be predicted accurately by a Gaussian process model with relatively few measurements, 2) formulate the search for sustainable concrete as a multi-objective optimization problem, and 3) leverage the proposed model to carry out multi-objective BO with real-world strength measurements of the algorithmically proposed mixes. Our experimental results show improved trade-offs between the mixtures' global warming potential (GWP) and their associated compressive strengths, compared to mixes based on current industry practices. Our methods are open-sourced at github.com/facebookresearch/SustainableConcrete.