Mostly Beneficial Clustering: Aggregating Data for Operational Decision Making

With increasingly volatile market conditions and rapid product innovations, operational decision-making for large-scale systems entails solving thousands of problems with limited data. Data aggregation is proposed to combine the data across problems to improve the decisions obtained by solving those problems individually. We propose a novel cluster-based shrunken-SAA approach that can exploit the cluster structure among problems when implementing the data aggregation approaches. We prove that, as the number of problems grows, leveraging the known cluster structure among problems yields additional benefits over the data aggregation approaches that neglect such structure. When the cluster structure is unknown, we show that unveiling the cluster structure, even at the cost of a few data points, can be beneficial, especially when the distance between clusters of problems is substantial. Our proposed approach can be extended to general cost functions under mild conditions. When the number of problems gets large, the optimality gap of our proposed approach decreases exponentially in the distance between the clusters. We explore the performance of the proposed approach through the application of managing newsvendor systems via numerical experiments. We investigate the impacts of distance metrics between problem instances on the performance of the cluster-based Shrunken-SAA approach with synthetic data. We further validate our proposed approach with real data and highlight the advantages of cluster-based data aggregation, especially in the small-data large-scale regime, compared to the existing approaches.

Design, Dynamics, and Dissipation of a Torsional-Magnetic Spring Mechanism

We present an analytical and experimental study of torsional magnetic mechanism where the restoring torque is due to magnetic field interactions between rotating and fixed permanent magnets. The oscillator consists of a ball bearing-supported permanent magnet, called the rotor, placed between two fixed permanent magnets called the stators. Perturbing the rotor from its equilibrium angle induces a restoring magnetic torque whose effect is modeled as a torsional spring. This restoring effect is accompanied by dissipation mechanisms arising from structural viscoelasticity, air and electromagnetic damping, as well as friction in the ball bearings. To investigate the system dynamics, we constructed an experimental setup capable of mechanical, electrical and magnetic measurements. For various rotor-stator gaps in this setup, we validated an analytical model that assumes viscous and dry (Coulomb) damping during the rotor free response. Moreover, we forced the rotor by a neighboring electromagnetic coil into high amplitude oscillations. We observed unusual resonator nonlinearity: at large rotor-stator gaps, the oscillations are softening; at reduced gaps, the oscillations stiffen-then-soften. The developed reduced-order models capture the nonlinear effects of the rotor-to-stator and the rotor-to-coil distances. These magnetic oscillators are promising in low-frequency electromagnetic signal transmission and in designing magneto-elastic metamaterials with tailorable nonlinearity.

Reminding the Incremental Language Model via Data-Free Self-Distillation

Incremental language learning with pseudo-data can alleviate catastrophic forgetting in neural networks. However, to obtain better performance, former methods have higher demands for pseudo-data of the previous tasks. The performance dramatically decreases when fewer pseudo-data are employed. In addition, the distribution of pseudo-data gradually deviates from the real data with the sequential learning of different tasks. The deviation will be greater with more tasks learned, which results in more serious catastrophic forgetting. To address these issues, we propose reminding incremental language model via data-free self-distillation (DFSD), which includes self-distillation based on the Earth Mover's Distance and hidden data augmentation. By estimating the knowledge distribution in all layers of GPT-2 and transforming it from teacher model to student model, the Self-distillation based on the Earth Mover's Distance can significantly reduce the demand for pseudo-data. Hidden data augmentation can greatly alleviate the catastrophic forgetting caused by deviations via modeling the generation of pseudo-data as a hidden data augmentation process, where each sample is a mixture of all trained task data. The experimental results demonstrate that our DFSD can exceed the previous state-of-the-art methods even if the maximum decrease in pseudo-data is 90%.

RAN Slicing in Multi-MVNO Environment under Dynamic Channel Conditions

With the increasing diversity in the requirement of wireless services with guaranteed quality of service(QoS), radio access network(RAN) slicing becomes an important aspect in implementation of next generation wireless systems(5G). RAN slicing involves division of network resources into many logical segments where each segment has specific QoS and can serve users of mobile virtual network operator(MVNO) with these requirements. This allows the Network Operator(NO) to provide service to multiple MVNOs each with different service requirements. Efficient allocation of the available resources to slices becomes vital in determining number of users and therefore, number of MVNOs that a NO can support. In this work, we study the problem of Modulation and Coding Scheme(MCS) aware RAN slicing(MaRS) in the context of a wireless system having MVNOs which have users with minimum data rate requirement. Channel Quality Indicator(CQI) report sent from each user in the network determines the MCS selected, which in turn determines the achievable data rate. But the channel conditions might not remain the same for the entire duration of user being served. For this reason, we consider the channel conditions to be dynamic where the choice of MCS level varies at each time instant. We model the MaRS problem as a Non-Linear Programming problem and show that it is NP-Hard. Next, we propose a solution based on greedy algorithm paradigm. We then develop an upper performance bound for this problem and finally evaluate the performance of proposed solution by comparing against the upper bound under various channel and network configurations.