Quantization Avoids Saddle Points in Distributed Optimization
This addresses a fundamental issue in distributed systems like deep learning and sensor networks, offering a method to improve optimization accuracy while reducing communication costs, though it appears incremental as it builds on existing quantization techniques.
The paper tackles the problem of avoiding convergence to saddle points in distributed nonconvex optimization, which degrades accuracy, by proposing a stochastic quantization scheme that enables saddle-point avoidance and reduces communication overhead, with numerical experiments confirming its effectiveness on benchmark datasets.
Distributed nonconvex optimization underpins key functionalities of numerous distributed systems, ranging from power systems, smart buildings, cooperative robots, vehicle networks to sensor networks. Recently, it has also merged as a promising solution to handle the enormous growth in data and model sizes in deep learning. A fundamental problem in distributed nonconvex optimization is avoiding convergence to saddle points, which significantly degrade optimization accuracy. We discover that the process of quantization, which is necessary for all digital communications, can be exploited to enable saddle-point avoidance. More specifically, we propose a stochastic quantization scheme and prove that it can effectively escape saddle points and ensure convergence to a second-order stationary point in distributed nonconvex optimization. With an easily adjustable quantization granularity, the approach allows a user to control the number of bits sent per iteration and, hence, to aggressively reduce the communication overhead. Numerical experimental results using distributed optimization and learning problems on benchmark datasets confirm the effectiveness of the approach.