Competing in the Dark: An Efficient Algorithm for Bandit Linear Optimization

We introduce an efficient algorithm for the problem of online linear optimization in the bandit setting which achieves the optimal O ( T) regret. The setting is a natural generalization of the nonstochastic multi-armed bandit problem, and the existence of an efficient optimal algorithm has been posed as an open problem in a number of recent papers. We show how the difficulties encountered by previous approaches are overcome by the use of a self-concordant potential function. Our approach presents a novel connection between online learning and interior point methods.

• Type: Conference
• Year: 2008
• Where: COLT
• Authors: Jacob Abernethy, Elad Hazan, Alexander Rakhlin
• Keywords: COLT 2008, Efficient Optimal Algorithm, Machine Learning, Multi-armed Bandit Problem, Online Linear Optimization