CoolMomentum: A Method for Stochastic Optimization by Langevin Dynamics with Simulated Annealing
This work addresses optimization challenges in deep learning for researchers and practitioners, but it is incremental as it builds on existing momentum and annealing techniques.
The paper tackled the problem of global optimization in non-convex deep learning by proposing CoolMomentum, a method that integrates Langevin dynamics with simulated annealing into momentum optimization, and demonstrated its effectiveness by achieving high accuracies on ResNet-20 with CIFAR-10 and EfficientNet-B0 with ImageNet.
Deep learning applications require global optimization of non-convex objective functions, which have multiple local minima. The same problem is often found in physical simulations and may be resolved by the methods of Langevin dynamics with Simulated Annealing, which is a well-established approach for minimization of many-particle potentials. This analogy provides useful insights for non-convex stochastic optimization in machine learning. Here we find that integration of the discretized Langevin equation gives a coordinate updating rule equivalent to the famous Momentum optimization algorithm. As a main result, we show that a gradual decrease of the momentum coefficient from the initial value close to unity until zero is equivalent to application of Simulated Annealing or slow cooling, in physical terms. Making use of this novel approach, we propose CoolMomentum -- a new stochastic optimization method. Applying Coolmomentum to optimization of Resnet-20 on Cifar-10 dataset and Efficientnet-B0 on Imagenet, we demonstrate that it is able to achieve high accuracies.