ترغب بنشر مسار تعليمي؟ اضغط هنا

Accelerated Stochastic Gradient Descent for Minimizing Finite Sums

206   0   0.0 ( 0 )
 نشر من قبل Atsushi Nitanda
 تاريخ النشر 2015
والبحث باللغة English
 تأليف Atsushi Nitanda




اسأل ChatGPT حول البحث

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike SVRG, our method can be directly applied to non-strongly and strongly convex problems. We show that our method achieves a lower overall complexity than the recently proposed methods that supports non-strongly convex problems. Moreover, this method has a fast rate of convergence for strongly convex problems. Our experiments show the effectiveness of our method.

قيم البحث

اقرأ أيضاً

The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex neural netwo rks use $L^1$-regularization with the non-negative constraint. However, due to the difficulty of handling $L^1$-regularization, these problems require early stopping or a rough approximation to solve it inexactly. In this paper, we propose a new ensemble learning method that performs in a space of probability measures, that is, our method can handle the $L^1$-constraint and the non-negative constraint in a rigorous way. Such an optimization is realized by proposing a general purpose stochastic optimization method for learning probability measures via parameterization using transport maps on base models. As a result of running the method, a transport map to output an infinite ensemble is obtained, which forms a residual-type network. From the perspective of functional gradient methods, we give a convergence rate as fast as that of a stochastic optimization method for finite dimensional nonconvex problems. Moreover, we show an interior optimality property of a local optimality condition used in our analysis.
Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value functions , i.e., problems of the form $min_x mathbf{E}_v [f_vbig(mathbf{E}_w [g_w(x)]big)]$. In order to solve this stochastic composition problem, we propose a class of stochastic compositional gradient descent (SCGD) algorithms that can be viewed as stochast
We present a unifying framework for adapting the update direction in gradient-based iterative optimization methods. As natural special cases we re-derive classical momentum and Nesterovs accelerated gradient method, lending a new intuitive interpreta tion to the latter algorithm. We show that a new algorithm, which we term Regularised Gradient Descent, can converge more quickly than either Nesterovs algorithm or the classical momentum algorithm.
We analyze the convergence of the averaged stochastic gradient descent for overparameterized two-layer neural networks for regression problems. It was recently found that a neural tangent kernel (NTK) plays an important role in showing the global con vergence of gradient-based methods under the NTK regime, where the learning dynamics for overparameterized neural networks can be almost characterized by that for the associated reproducing kernel Hilbert space (RKHS). However, there is still room for a convergence rate analysis in the NTK regime. In this study, we show that the averaged stochastic gradient descent can achieve the minimax optimal convergence rate, with the global convergence guarantee, by exploiting the complexities of the target function and the RKHS associated with the NTK. Moreover, we show that the target function specified by the NTK of a ReLU network can be learned at the optimal convergence rate through a smooth approximation of a ReLU network under certain conditions.
We learn recurrent neural network optimizers trained on simple synthetic functions by gradient descent. We show that these learned optimizers exhibit a remarkable degree of transfer in that they can be used to efficiently optimize a broad range of de rivative-free black-box functions, including Gaussian process bandits, simple control objectives, global optimization benchmarks and hyper-parameter tuning tasks. Up to the training horizon, the learned optimizers learn to trade-off exploration and exploitation, and compare favourably with heavily engineered Bayesian optimization packages for hyper-parameter tuning.

الأسئلة المقترحة

التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا