Online strongly convex optimization with unknown delays

Adversarial Delays in Online Strongly-Convex Optimization

We consider the problem of strongly-convex online optimization in presence of adversarial delays [1]; in a T -iteration online game, the feedback of the player’s query at time t is arbitrarily delayed by an adversary for dt rounds and delivered before the game ends, at iteration t+ dt − 1. Specifically for online-gradient-descent algorithm we show it has a simple regret bound of O (∑T t=1 log(1...

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...