Time and Location Aware Mobile Data Pricing

Mobile users' correlated mobility and data consumption patterns often lead to severe cellular network congestion in peak hours and hot spots. This paper presents an optimal design of time and location aware mobile data pricing, which incentivizes users to smooth traffic and reduce network congestion. We derive the optimal pricing scheme through analyzing a two-stage decision process, where the operator determines the time and location aware prices by minimizing his total cost in Stage I, and each mobile user schedules his mobile traffic by maximizing his payoff (i.e., utility minus payment) in Stage II. We formulate the two-stage decision problem as a bilevel optimization problem, and propose a derivative-free algorithm to solve the problem for any increasing concave user utility functions. We further develop low complexity algorithms for the commonly used logarithmic and linear utility functions. The optimal pricing scheme ensures a win-win situation for the operator and users. Simulations show that the operator can reduce the cost by up to 97.52% in the logarithmic utility case and 98.70% in the linear utility case, and users can increase their payoff by up to 79.69% and 106.10% for the two types of utilities, respectively, comparing with a time and location independent pricing benchmark. Our study suggests that the operator should provide price discounts at less crowded time slots and locations, and the discounts need to be significant when the operator's cost of provisioning excessive traffic is high or users' willingness to delay traffic is low.Comment: This manuscript serves as the online technical report of the article accepted by IEEE Transactions on Mobile Computin

The N-K Problem in Power Grids: New Models, Formulations and Numerical Experiments (extended version)

Given a power grid modeled by a network together with equations describing the power flows, power generation and consumption, and the laws of physics, the so-called N-k problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. The case where k is small is of practical interest. We present theoretical and computational results involving a mixed-integer model and a continuous nonlinear model related to this question.Comment: 40 pages 3 figure

Advancing Model Pruning via Bi-level Optimization

The deployment constraints in practical applications necessitate the pruning of large-scale deep learning models, i.e., promoting their weight sparsity. As illustrated by the Lottery Ticket Hypothesis (LTH), pruning also has the potential of improving their generalization ability. At the core of LTH, iterative magnitude pruning (IMP) is the predominant pruning method to successfully find 'winning tickets'. Yet, the computation cost of IMP grows prohibitively as the targeted pruning ratio increases. To reduce the computation overhead, various efficient 'one-shot' pruning methods have been developed, but these schemes are usually unable to find winning tickets as good as IMP. This raises the question of how to close the gap between pruning accuracy and pruning efficiency? To tackle it, we pursue the algorithmic advancement of model pruning. Specifically, we formulate the pruning problem from a fresh and novel viewpoint, bi-level optimization (BLO). We show that the BLO interpretation provides a technically-grounded optimization base for an efficient implementation of the pruning-retraining learning paradigm used in IMP. We also show that the proposed bi-level optimization-oriented pruning method (termed BiP) is a special class of BLO problems with a bi-linear problem structure. By leveraging such bi-linearity, we theoretically show that BiP can be solved as easily as first-order optimization, thus inheriting the computation efficiency. Through extensive experiments on both structured and unstructured pruning with 5 model architectures and 4 data sets, we demonstrate that BiP can find better winning tickets than IMP in most cases, and is computationally as efficient as the one-shot pruning schemes, demonstrating 2-7 times speedup over IMP for the same level of model accuracy and sparsity.Comment: Thirty-sixth Conference on Neural Information Processing Systems (NeurIPS 2022

Optimal selection of the regularization function in a generalized total variation model. Part II: Algorithm, its analysis and numerical tests

Based on the generalized total variation model and its analysis pursued in part I (WIAS Preprint no. 2235), in this paper a continuous, i.e., infinite dimensional, projected gradient algorithm and its convergence analysis are presented. The method computes a stationary point of a regularized bilevel optimization problem for simultaneously recovering the image as well as determining a spatially distributed regularization weight. Further, its numerical realization is discussed and results obtained for image denoising and deblurring as well as Fourier and wavelet inpainting are reported on

Contingency ranking with respect to overloads in very large power systems taking into account uncertainty, preventive, and corrective actions

peer reviewedThis paper deals with day-ahead security management with respect to a postulated set of contingencies, while taking into account uncertainties about the next day generation/load scenario. In order to help the system operator in decision making under uncertainty, we aim at ranking these contingencies into four clusters according to the type of control actions needed to cover the worst uncertainty pattern of each contingency with respect to branch overload. To this end we use a fixed point algorithm that loops over two main modules: a discrete bi-level program (BLV) that computes the worst-case scenario, and a special kind of security constrained optimal power flow (SCOPF) which computes optimal preventive/corrective actions to cover the worst-case. We rely on a DC grid model, as the large number of binary variables, the large size of the problem, and the stringent computational requirements preclude the use of existing mixed integer nonlinear programming (MINLP) solvers. Consequently we solve the SCOPF using a mixed integer linear programming (MILP) solver while the BLV is decomposed into a series of MILPs. We provide numerical results with our approach on a very large European system model with 9241 buses and 5126 contingencies

Constrained Design of Deep Iris Networks

Despite the promise of recent deep neural networks in the iris recognition setting, there are vital properties of the classic IrisCode which are almost unable to be achieved with current deep iris networks: the compactness of model and the small number of computing operations (FLOPs). This paper re-models the iris network design process as a constrained optimization problem which takes model size and computation into account as learning criteria. On one hand, this allows us to fully automate the network design process to search for the best iris network confined to the computation and model compactness constraints. On the other hand, it allows us to investigate the optimality of the classic IrisCode and recent iris networks. It also allows us to learn an optimal iris network and demonstrate state-of-the-art performance with less computation and memory requirements