相关论文: Revisiting Stochastic Extragradient

This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…

The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…

Generative adversarial networks (GANs) are a class of generative models, known for producing accurate samples. The key feature of GANs is that there are two antagonistic neural networks: the generator and the discriminator. The main…

We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…

Recently, several methods based on generative adversarial network (GAN) have been proposed for the task of aligning cross-domain images or learning a joint distribution of cross-domain images. One of the methods is to use conditional GAN…

Most modern learning problems are highly overparameterized, meaning that there are many more parameters than the number of training data points, and as a result, the training loss may have infinitely many global minima (parameter vectors…

One of the training strategies of generative models is to minimize the Jensen--Shannon divergence between the model distribution and the data distribution. Since data distribution is unknown, generative adversarial networks (GANs) formulate…

We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…

We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…

Despite the successes in capturing continuous distributions, the application of generative adversarial networks (GANs) to discrete settings, like natural language tasks, is rather restricted. The fundamental reason is the difficulty of…

We study the unconstrained and the minimax saddle point variants of the convex multi-stage stochastic programming problem, where consecutive decisions are coupled through the objective functions, rather than through the constraints. We…

While deep learning in the form of recurrent neural networks (RNNs) has caused a significant improvement in neural language modeling, the fact that they are extremely prone to overfitting is still a mainly unresolved issue. In this paper we…

We present a novel method and analysis to train generative adversarial networks (GAN) in a stable manner. As shown in recent analysis, training is often undermined by the probability distribution of the data being zero on neighborhoods of…

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…

We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…

The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…

A major obstacle to achieving global convergence in distributed and federated learning is the misalignment of gradients across clients, or mini-batches due to heterogeneity and stochasticity of the distributed data. In this work, we show…

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…

Generative Adversarial Networks have become one of the most studied frameworks for unsupervised learning due to their intuitive formulation. They have also been shown to be capable of generating convincing examples in limited domains, such…

Generative adversarial networks (GAN) have been effective for learning generative models for real-world data. However, existing GANs (GAN and its variants) tend to suffer from training problems such as instability and mode collapse. In this…