We describe a primal-dual framework for the design and analysis of online strongly convex optimization algorithms. Our framework yields the tightest known logarithmic regret bounds for Follow-The-Leader and for the gradient descent algorithm proposed in Hazan et al. [2006]. We then show that one can interpolate between these two extreme cases. In particular, we derive a new algorithm that share...

We present here a new model and algorithm which performs an efficient Natural gradient descent for Multilayer Perceptrons. Natural gradient descent was originally proposed from a point of view of information geometry, and it performs the steepest descent updates on manifolds in a Riemannian space. In particular, we extend an approach taken by the “Whitened neural networks” model. We make the wh...

Nowadays, asynchronous parallel algorithms have received much attention in the optimization field due to the crucial demands for modern large-scale optimization problems. However, most asynchronous algorithms focus on convex problems. Analysis on nonconvex problems is lacking. For the Asynchronous Stochastic Descent (ASGD) algorithm, the best result from (Lian et al., 2015) can only achieve an ...

We present and study a distributed optimization algorithm by employing a stochastic dual coordinate ascent method. Stochastic dual coordinate ascent methods enjoy strong theoretical guarantees and often have better performances than stochastic gradient descent methods in optimizing regularized loss minimization problems. It still lacks of efforts in studying them in a distributed framework. We ...

We present tools for the analysis of Follow-The-Regularized-Leader (FTRL), Dual Averaging, and Mirror Descent algorithms when the regularizer (equivalently, proxfunction or learning rate schedule) is chosen adaptively based on the data. Adaptivity can be used to prove regret bounds that hold on every round, and also allows for data-dependent regret bounds as in AdaGrad-style algorithms (e.g., O...

Margin-based strategies and model change based strategies represent two important types of strategies for active learning. While margin-based strategies have been dominant for Support Vector Machines (SVMs), most methods are based on heuristics and lack a solid theoretical support. In this paper, we propose an active learning strategy for SVMs based on Maximum Model Change (MMC). The model chan...

This paper proposes an alternating back-propagation algorithm for learning the generator network model. The model is a nonlinear generalization of factor analysis. In this model, the mapping from the continuous latent factors to the observed signal is parametrized by a convolutional neural network. The alternating back-propagation algorithm iterates the following two steps: (1) Inferential back...

We propose a family of nonconvex optimization algorithms that are able to save gradient and negative curvature computations to a large extent, and are guaranteed to find an approximate local minimum with improved runtime complexity. At the core of our algorithms is the division of the entire domain of the objective function into small and large gradient regions: our algorithms only perform grad...

Momentum based stochastic gradient methods such as heavy ball (HB) and Nesterov’s accelerated gradient descent (NAG) method are widely used in practice for training deep networks and other supervised learning models, as they often provide significant improvements over stochastic gradient descent (SGD). Theoretically, these “fast gradient” methods have provable improvements over gradient descent...

The move from hand-designed features to learned features in machine learning has been wildly successful. In spite of this, optimization algorithms are still designed by hand. In this paper we show how the design of an optimization algorithm can be cast as a learning problem, allowing the algorithm to learn to exploit structure in the problems of interest in an automatic way. Our learned algorit...