In this paper we present the greedy step averaging(GSA) method, a parameter-free stochastic optimization algorithm for a variety of machine learning problems. As a gradient-based optimization method, GSA makes use of the information from the minimizer of a single sample's loss function, and takes average strategy to calculate reasonable learning rate sequence. While most existing gradient-based algorithms introduce an increasing number of hyper parameters or try to make a trade-off between computational cost and convergence rate, GSA avoids the manual tuning of learning rate and brings in no more hyper parameters or extra cost. We perform exhaustive numerical experiments for logistic and softmax regression to compare our method with the other state of the art ones on 16 datasets. Results show that GSA is robust on various scenarios.
Stochastic variance reduced gradient(SVRG) introduces an explicit variance reduction method for SGD @cite_17 . SVRG method separates the training process into several epochs, in the beginning of each epoch, it requires the computation of full gradient. And during each epoch, one randomly chooses a sample's gradient to refresh the full gradient. The update scheme reads @math where @math is the full gradient, @math is updated at the beginning of each epoch.
@cite_17
2962798535 2574426558 2107438106 1501362825
We study optimization algorithms based on variance reduction for stochastic gradient descent (SGD). Remarkable recent progress has been made in this direction through development of algorithms like SAG, SVRG, SAGA. These algorithms have been shown to outperform SGD, both theoretically and empirically. However, asynchronous versions of these algorithms—a crucial requirement for modern large-scale applications—have not been studied. We bridge this gap by presenting a unifying framework for many variance reduction techniques. Subsequently, we propose an asynchronous algorithm grounded in our framework, and prove its fast convergence. An important consequence of our general approach is that it yields asynchronous versions of variance reduction algorithms such as SVRG and SAGA as a byproduct. Our method achieves near linear speedup in sparse settings common to machine learning. We demonstrate the empirical performance of our method through a concrete realization of asynchronous SVRG. Variance Reducing (VR) stochastic methods are fast-converging alternatives to the classical Stochastic Gradient Descent (SGD) for solving large-scale regularized finite sum problems, especially when a highly accurate solution is required. One critical step in VR is the function sampling. State-of-the-art VR algorithms such as SVRG and SAGA, employ either Uniform Probability (UP) or Importance Probability (IP), which is deficient in reducing the variance and hence leads to suboptimal convergence rate. In this paper, we propose a novel sampling scheme that explicitly computes some Adaptive Probability (AP) at each iteration. Analysis shows that, equipped with AP, both SVRG and SAGA yield provably better convergence rate than the ones with UP or IP, which is confirmed in experiments. Additionally, to cut down the per iteration computation load, an efficient variant is proposed by utilizing AP periodically, whose performance is empirically validated. Stochastic gradient descent is popular for large scale optimization but has slow convergence asymptotically due to the inherent variance. To remedy this problem, we introduce an explicit variance reduction method for stochastic gradient descent which we call stochastic variance reduced gradient (SVRG). For smooth and strongly convex functions, we prove that this method enjoys the same fast convergence rate as those of stochastic dual coordinate ascent (SDCA) and Stochastic Average Gradient (SAG). However, our analysis is significantly simpler and more intuitive. Moreover, unlike SDCA or SAG, our method does not require the storage of gradients, and thus is more easily applicable to complex problems such as some structured prediction problems and neural network learning. We study optimization algorithms based on variance reduction for stochastic gradient descent (SGD). Remarkable recent progress has been made in this direction through development of algorithms like SAG, SVRG, SAGA. These algorithms have been shown to outperform SGD, both theoretically and empirically. However, asynchronous versions of these algorithms---a crucial requirement for modern large-scale applications---have not been studied. We bridge this gap by presenting a unifying framework for many variance reduction techniques. Subsequently, we propose an asynchronous algorithm grounded in our framework, and prove its fast convergence. An important consequence of our general approach is that it yields asynchronous versions of variance reduction algorithms such as SVRG and SAGA as a byproduct. Our method achieves near linear speedup in sparse settings common to machine learning. We demonstrate the empirical performance of our method through a concrete realization of asynchronous SVRG.