Federated Multi-Level Optimization over Decentralized Networks

Multi-level optimization has gained increasing attention in recent years, as it provides a powerful framework for solving complex optimization problems that arise in many fields, such as meta-learning, multi-player games, reinforcement learning, and nested composition optimization. In this paper, we study the problem of distributed multi-level optimization over a network, where agents can only communicate with their immediate neighbors. This setting is motivated by the need for distributed optimization in large-scale systems, where centralized optimization may not be practical or feasible. To address this problem, we propose a novel gossip-based distributed multi-level optimization algorithm that enables networked agents to solve optimization problems at different levels in a single timescale and share information through network propagation. Our algorithm achieves optimal sample complexity, scaling linearly with the network size, and demonstrates state-of-the-art performance on various applications, including hyper-parameter tuning, decentralized reinforcement learning, and risk-averse optimization.Comment: arXiv admin note: substantial text overlap with arXiv:2206.1087

Multi-Level Stochastic Gradient Methods for Nested Composition Optimization

Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level expectations. In this paper, we consider the multi-level compositional optimization problem that involves compositions of multi-level component functions and nested expectations over a random path. It finds applications in risk-averse optimization and sequential planning. We propose a class of multi-level stochastic gradient methods that are motivated from the method of multi-timescale stochastic approximation. First we propose a basic $T$-level stochastic compositional gradient algorithm, establish its almost sure convergence and obtain an $n$-iteration error bound $O (n^{-1/2^T})$. Then we develop accelerated multi-level stochastic gradient methods by using an extrapolation-interpolation scheme to take advantage of the smoothness of individual component functions. When all component functions are smooth, we show that the convergence rate improves to $O(n^{-4/(7+T)})$ for general objectives and $O (n^{-4/(3+T)})$ for strongly convex objectives. We also provide almost sure convergence and rate of convergence results for nonconvex problems. The proposed methods and theoretical results are validated using numerical experiments

Towards Large-scale Single-shot Millimeter-wave Imaging for Low-cost Security Inspection

Millimeter-wave (MMW) imaging is emerging as a promising technique for safe security inspection. It achieves a delicate balance between imaging resolution, penetrability and human safety, resulting in higher resolution compared to low-frequency microwave, stronger penetrability compared to visible light, and stronger safety compared to X ray. Despite of recent advance in the last decades, the high cost of requisite large-scale antenna array hinders widespread adoption of MMW imaging in practice. To tackle this challenge, we report a large-scale single-shot MMW imaging framework using sparse antenna array, achieving low-cost but high-fidelity security inspection under an interpretable learning scheme. We first collected extensive full-sampled MMW echoes to study the statistical ranking of each element in the large-scale array. These elements are then sampled based on the ranking, building the experimentally optimal sparse sampling strategy that reduces the cost of antenna array by up to one order of magnitude. Additionally, we derived an untrained interpretable learning scheme, which realizes robust and accurate image reconstruction from sparsely sampled echoes. Last, we developed a neural network for automatic object detection, and experimentally demonstrated successful detection of concealed centimeter-sized targets using 10% sparse array, whereas all the other contemporary approaches failed at the same sample sampling ratio. The performance of the reported technique presents higher than 50% superiority over the existing MMW imaging schemes on various metrics including precision, recall, and mAP50. With such strong detection ability and order-of-magnitude cost reduction, we anticipate that this technique provides a practical way for large-scale single-shot MMW imaging, and could advocate its further practical applications

Optimality Conditions and Algorithms for Top-K Arm Identification

We consider the top-k arm identification problem for multi-armed bandits with rewards belonging to a one-parameter canonical exponential family. The objective is to select the set of k arms with the highest mean rewards by sequential allocation of sampling efforts. We propose a unified optimal allocation problem that identifies the complexity measures of this problem under the fixed-confidence, fixed-budget settings, and the posterior convergence rate from the Bayesian perspective. We provide the first characterization of its optimality. We provide the first provably optimal algorithm in the fixed-confidence setting for k>1. We also propose an efficient heuristic algorithm for the top-k arm identification problem. Extensive numerical experiments demonstrate superior performance compare to existing methods in all three settings

Through-the-Wall Micro-Doppler De-Wiring Technique via Cycle-Consistent Adversarial Network

The radar penetrating technique has aroused a keen interest in the research community, due to its superior abilities for through-the-wall indoor human motion monitoring. Micro-Doppler signatures in this situation play a significant role in recognition and classification for human activities. However, the live wire buried in the wall introduces additive clutters to the spectrograms. Such degraded spectrograms drastically affect the performance of behind-the-wall human activity detection. In this paper, an ultra-wideband (UWB) radar system is utilized in the through-the-wall scenario to get the feature enhanced micro-Doppler signature called range-max time-frequency representation (R-max TFR). Then, a recently introduced Cycle-Consistent Generative Adversarial Network (Cycle GAN) is employed to realize the end-to-end de-wiring task. Cycle GAN can learn the mapping between spectrograms with and without the live wire effect. To minimize the wiring clutters, a loss function called identity loss is introduced in this work. Finally, the proposed de-wiring approach is evaluated through classification. The results show that the proposed Cycle GAN architecture outperforms other state-of-art de-wiring methods

Through-the-Wall Micro-Doppler De-Wiring Technique via Cycle-Consistent Adversarial Network

The radar penetrating technique has aroused a keen interest in the research community, due to its superior abilities for through-the-wall indoor human motion monitoring. Micro-Doppler signatures in this situation play a significant role in recognition and classification for human activities. However, the live wire buried in the wall introduces additive clutters to the spectrograms. Such degraded spectrograms drastically affect the performance of behind-the-wall human activity detection. In this paper, an ultra-wideband (UWB) radar system is utilized in the through-the-wall scenario to get the feature enhanced micro-Doppler signature called range-max time-frequency representation (R-max TFR). Then, a recently introduced Cycle-Consistent Generative Adversarial Network (Cycle GAN) is employed to realize the end-to-end de-wiring task. Cycle GAN can learn the mapping between spectrograms with and without the live wire effect. To minimize the wiring clutters, a loss function called identity loss is introduced in this work. Finally, the proposed de-wiring approach is evaluated through classification. The results show that the proposed Cycle GAN architecture outperforms other state-of-art de-wiring methods