An Online Algorithm for Smoothed Online Convex Optimization

Smoothed Online Convex Optimization in High Dimensions via Online Balanced Descent

We study smoothed online convex optimization, a version of online convex optimization where the learner incurs a penalty for changing her actions between rounds. Given a known Ω( √ d) lower bound on the competitive ratio of any online algorithm, where d is the dimension of the action space, we ask under what conditions this bound can be beaten. We introduce a novel algorithmic framework for thi...

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

Online Learning and Online Convex Optimization

Online learning is a well established learning paradigm which has both theoretical and practical appeals. The goal of online learning is to make a sequence of accurate predictions given knowledge of the correct answer to previous prediction tasks and possibly additional available information. Online learning has been studied in several research fields including game theory, information theory, ...