Distributed Online Convex Optimization With an Aggregative Variable

Distributed Convex Optimization with Many Convex Constraints

We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago, ADMM so far can be applied only to unconstrained problems and problems with...

Online Convex Optimization

A convex repeated game is a two players game that is performed in a sequence of consecutive rounds. On round t of the repeated game, the first player chooses a vector wt from a convex set A. Next, the second player responds with a convex function gt : A → R. Finally, the first player suffers an instantaneous loss gt(wt). We study the game from the viewpoint of the first player. In offline conve...

Online convex optimization

1.1 Definitions We say a set S ⊆ Rd is convex if for any two points x,x′ ∈ S, the line segment conv{x,x′} := {(1−α)x+αx′ : α ∈ [0, 1]} between x and x′ (also called the convex hull of {x,x′}) is contained in S. Overloading terms, we say a function f : S → R is convex if its epigraph epi(f) := {(x, t) ∈ S × R : f(x) ≤ t} is a convex set (in Rd × R). Proposition 1. A function f : S → R is convex ...

Online Convex Optimization

Deep Online Convex Optimization with Gated Games

Methods from convex optimization are widely used as building blocks for deep learning algorithms. However, the reasons for their empirical success are unclear, since modern convolutional networks (convnets), incorporating rectifier units and max-pooling, are neither smooth nor convex. Standard guarantees therefore do not apply. This paper provides the first convergence rates for gradient descen...