Deep neural network learning can be formulated as a non-convex optimization problem. Existing optimization algorithms, e.g., Adam, can learn the models fast, but may get stuck in local optima easily. In this paper, we introduce a novel optimization algorithm, namely GADAM (Genetic-Evolutionary Adam). GADAM learns deep neural network models based on a number of unit models generations by generations: it trains the unit models with Adam, and evolves them to the new generations with genetic algorithm. We will show that GADAM can effectively jump out of the local optima in the learning process to obtain better solutions, and prove that GADAM can also achieve a very fast convergence. Extensive experiments have been done on various benchmark datasets, and the learning results will demonstrate the effectiveness and efficiency of the GADAM algorithm.
: In addressing the optimization problems, SGD (Stochastic Gradient Descent) @cite_5 with sound theoretic foundations has been one of the most frequently used algorithms. Given an objective function @math , SGD adopts an iterative updating schema to learn the model variables as follows: Here, the parameter @math is usually a small constant, which is referred to as the learning rate. Meanwhile, to further accelerate the learning process, a variant of SGD, namely SGDM (SGD with Momentum) @cite_28 , has been proposed, which updates the variables according to the following equations In the equation, @math is a momentum parameter and vector @math is initialized with value @math .
@cite_28 @cite_5
1574269637 2963702144 2766164908 2951196414
Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a low-rank least-squares problem, and we prove that, under broad sampling conditions, our method converges globally from a random starting point within @math steps with constant probability for constant-rank problems. Our modification of SGD relates it to stochastic power iteration. We also show experiments to illustrate the runtime and convergence of the algorithm. It is common practice to decay the learning rate. Here we show one can usually obtain the same learning curve on both training and test sets by instead increasing the batch size during training. This procedure is successful for stochastic gradient descent (SGD), SGD with momentum, Nesterov momentum, and Adam. It reaches equivalent test accuracies after the same number of training epochs, but with fewer parameter updates, leading to greater parallelism and shorter training times. We can further reduce the number of parameter updates by increasing the learning rate @math and scaling the batch size @math . Finally, one can increase the momentum coefficient @math and scale @math , although this tends to slightly reduce the test accuracy. Crucially, our techniques allow us to repurpose existing training schedules for large batch training with no hyper-parameter tuning. We train Inception-ResNet-V2 on ImageNet to @math validation accuracy in under 2500 parameter updates, efficiently utilizing training batches of 65536 images. It is common practice to decay the learning rate. Here we show one can usually obtain the same learning curve on both training and test sets by instead increasing the batch size during training. This procedure is successful for stochastic gradient descent (SGD), SGD with momentum, Nesterov momentum, and Adam. It reaches equivalent test accuracies after the same number of training epochs, but with fewer parameter updates, leading to greater parallelism and shorter training times. We can further reduce the number of parameter updates by increasing the learning rate @math and scaling the batch size @math . Finally, one can increase the momentum coefficient @math and scale @math , although this tends to slightly reduce the test accuracy. Crucially, our techniques allow us to repurpose existing training schedules for large batch training with no hyper-parameter tuning. We train ResNet-50 on ImageNet to @math validation accuracy in under 30 minutes. Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O( (T) T), by running SGD for T iterations and returning the average point. However, recent results showed that using a different algorithm, one can get an optimal O(1 T) rate. This might lead one to believe that standard SGD is suboptimal, and maybe should even be replaced as a method of choice. In this paper, we investigate the optimality of SGD in a stochastic setting. We show that for smooth problems, the algorithm attains the optimal O(1 T) rate. However, for non-smooth problems, the convergence rate with averaging might really be ( (T) T), and this is not just an artifact of the analysis. On the flip side, we show that a simple modification of the averaging step suffices to recover the O(1 T) rate, and no other change of the algorithm is necessary. We also present experimental results which support our findings, and point out open problems.