Quantum algorithm for online convex optimization

Adaptive Bound Optimization for Online Convex Optimization

We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function such as L2-squared, and modify it only via a single time-dependent parameter. Our algorithm’s regret bounds are worst-case optimal, and for certain realistic cl...

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, ...