Stochastic Optimization is the task of optimizing certain objective functional by generating and using stochastic random variables. Usually the Stochastic Optimization is an iterative process of generating random variables that progressively finds out the minima or the maxima of the objective functional. Stochastic Optimization is usually applied in the non-convex functional spaces where the usual deterministic optimization such as linear or quadratic programming or their variants cannot be used.
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Distributed training of deep learning models on large-scale training data is typically conducted with asynchronous stochastic optimization to maximize the rate of updates, at the cost of additional noise introduced from asynchrony.
The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms.
Partial warm restarts are also gaining popularity in gradient-based optimization to improve the rate of convergence in accelerated gradient schemes to deal with ill-conditioned functions.
The learning rate warmup heuristic achieves remarkable success in stabilizing training, accelerating convergence and improving generalization for adaptive stochastic optimization algorithms like RMSprop and Adam.
Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving averages of squared past gradients.
In this paper, we introduce Apollo, a quasi-Newton method for nonconvex stochastic optimization, which dynamically incorporates the curvature of the loss function by approximating the Hessian via a diagonal matrix.
We introduce ADAHESSIAN, a second order stochastic optimization algorithm which dynamically incorporates the curvature of the loss function via ADAptive estimates of the HESSIAN.
The dynamic learning rate bounds are based on the exponential moving averages of the adaptive learning rates themselves, which smooth out unexpected large learning rates and stabilize the training of deep neural networks.
We propose NovoGrad, an adaptive stochastic gradient descent method with layer-wise gradient normalization and decoupled weight decay.