Dual Averaging Method for Online Graph-structured Sparsity

Online learning algorithms update models via one sample per iteration, thus efficient to process large-scale datasets and useful to detect malicious events for social benefits, such as disease outbreak and traffic congestion on the fly. However, existing algorithms for graph-structured models focused on the offline setting and the least square loss, incapable for online setting, while methods designed for online setting cannot be directly applied to the problem of complex (usually non-convex) graph-structured sparsity model. To address these limitations, in this paper we propose a new algorithm for graph-structured sparsity constraint problems under online setting, which we call \textsc{GraphDA}. The key part in \textsc{GraphDA} is to project both averaging gradient (in dual space) and primal variables (in primal space) onto lower dimensional subspaces, thus capturing the graph-structured sparsity effectively. Furthermore, the objective functions assumed here are generally convex so as to handle different losses for online learning settings. To the best of our knowledge, \textsc{GraphDA} is the first online learning algorithm for graph-structure constrained optimization problems. To validate our method, we conduct extensive experiments on both benchmark graph and real-world graph datasets. Our experiment results show that, compared to other baseline methods, \textsc{GraphDA} not only improves classification performance, but also successfully captures graph-structured features more effectively, hence stronger interpretability.Comment: 11 pages, 14 figure

A Unified View of Large-scale Zero-sum Equilibrium Computation

The task of computing approximate Nash equilibria in large zero-sum extensive-form games has received a tremendous amount of attention due mainly to the Annual Computer Poker Competition. Immediately after its inception, two competing and seemingly different approaches emerged---one an application of no-regret online learning, the other a sophisticated gradient method applied to a convex-concave saddle-point formulation. Since then, both approaches have grown in relative isolation with advancements on one side not effecting the other. In this paper, we rectify this by dissecting and, in a sense, unify the two views.Comment: AAAI Workshop on Computer Poker and Imperfect Informatio

A Stochastic Majorize-Minimize Subspace Algorithm for Online Penalized Least Squares Estimation

Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct computation is too intensive, and they have thus to be estimated online from the observed signals. For batch optimization of an objective function being the sum of a data fidelity term and a penalization (e.g. a sparsity promoting function), Majorize-Minimize (MM) methods have recently attracted much interest since they are fast, highly flexible, and effective in ensuring convergence. The goal of this paper is to show how these methods can be successfully extended to the case when the data fidelity term corresponds to a least squares criterion and the cost function is replaced by a sequence of stochastic approximations of it. In this context, we propose an online version of an MM subspace algorithm and we study its convergence by using suitable probabilistic tools. Simulation results illustrate the good practical performance of the proposed algorithm associated with a memory gradient subspace, when applied to both non-adaptive and adaptive filter identification problems