On the Computational Efficiency of Adaptive and Dynamic Regret Minimization

TL;DR

This paper improves the computational efficiency of algorithms for adaptive and dynamic regret minimization in online convex optimization, reducing the computational penalty from logarithmic to doubly logarithmic growth while maintaining near-optimal regret bounds.

Contribution

It introduces a method to significantly lower the computational penalty in adaptive and dynamic regret algorithms without sacrificing performance.

Findings

Computational penalty reduced to doubly logarithmic growth

Near-optimal adaptive and dynamic regret bounds retained

Enhanced efficiency in online convex optimization algorithms

Abstract

In online convex optimization, the player aims to minimize regret, or the difference between her loss and that of the best fixed decision in hindsight over the entire repeated game. Algorithms that minimize (standard) regret may converge to a fixed decision, which is undesirable in changing or dynamic environments. This motivates the stronger metrics of performance, notably adaptive and dynamic regret. Adaptive regret is the maximum regret over any continuous sub-interval in time. Dynamic regret is the difference between the total cost and that of the best sequence of decisions in hindsight. State-of-the-art performance in both adaptive and dynamic regret minimization suffers a computational penalty - typically on the order of a multiplicative factor that grows logarithmically in the number of game iterations. In this paper we show how to reduce this computational penalty to be doubly logarithmic in the number of game iterations, and retain near optimal adaptive and dynamic regret bounds.