Optimal Complexity in Non-Convex Decentralized Learning over Time-Varying Networks

Decentralized optimization with time-varying networks is an emerging paradigm in machine learning. It saves remarkable communication overhead in large-scale deep training and is more robust in wireless scenarios especially when nodes are moving. Federated learning can also be regarded as decentralized optimization with time-varying communication patterns alternating between global averaging and local updates. While numerous studies exist to clarify its theoretical limits and develop efficient algorithms, it remains unclear what the optimal complexity is for non-convex decentralized stochastic optimization over time-varying networks. The main difficulties lie in how to gauge the effectiveness when transmitting messages between two nodes via time-varying communications, and how to establish the lower bound when the network size is fixed (which is a prerequisite in stochastic optimization). This paper resolves these challenges and establish the first lower bound complexity. We also develop a new decentralized algorithm to nearly attain the lower bound, showing the tightness of the lower bound and the optimality of our algorithm.Comment: Accepted by 14th Annual Workshop on Optimization for Machine Learning. arXiv admin note: text overlap with arXiv:2210.0786

Momentum Benefits Non-IID Federated Learning Simply and Provably

Federated learning is a powerful paradigm for large-scale machine learning, but it faces significant challenges due to unreliable network connections, slow communication, and substantial data heterogeneity across clients. FedAvg and SCAFFOLD are two fundamental algorithms to address these challenges. In particular, FedAvg employs multiple local updates before communicating with a central server, while SCAFFOLD maintains a control variable on each client to compensate for "client drift" in its local updates. Various methods have been proposed in literature to enhance the convergence of these two algorithms, but they either make impractical adjustments to algorithmic structure, or rely on the assumption of bounded data heterogeneity. This paper explores the utilization of momentum to enhance the performance of FedAvg and SCAFFOLD. When all clients participate in the training process, we demonstrate that incorporating momentum allows FedAvg to converge without relying on the assumption of bounded data heterogeneity even using a constant local learning rate. This is a novel result since existing analyses for FedAvg require bounded data heterogeneity even with diminishing local learning rates. In the case of partial client participation, we show that momentum enables SCAFFOLD to converge provably faster without imposing any additional assumptions. Furthermore, we use momentum to develop new variance-reduced extensions of FedAvg and SCAFFOLD, which exhibit state-of-the-art convergence rates. Our experimental results support all theoretical findings

Optimization of ultrasonic-assisted extraction procedure of capsaicinoids from Chili peppers using orthogonal array experimental design

In this present study, the optimal conditions of ultrasonic-assisted extraction (UAE) of capsaicinoids from hot Chili peppers were determined for large scale preparation. First, single factor experiments were performed to optimize the extraction procedure of capsaicinoids, and initial optimized results were: ratio of solvent to mass of 6 to 10 ml/g, extraction temperature of 25 to 35°C, and extraction time of 0 to 30 min. Then, an orthogonal array experimental design (L9(34)) was used to further optimize the extraction procedure. The results of F-test and P-value indicated that the effect order on extraction yield of capsaicinoids from high to low was ratio of solvent to mass, extraction time, and extraction temperature. The maximum extraction yield of capsaicinoids was obtained at ratio of solvent to mass of 10 ml/g, extraction time of 40 min, and extraction temperature of 25°C. Under these conditions, the extraction yields of capsaicinoids were 2.35 ± 0.042 and 3.92 ± 0.089 mg/g for conventional and UAE methods, respectively.Keywords: Chili pepper, ultrasonic-assisted extraction, capsaicinoids, orthogonal array design, single factor experiment