Mind the Duality Gap: Logarithmic regret algorithms for online optimization

We describe a primal-dual framework for the design and analysis of online strongly convex optimization algorithms. Our framework yields the tightest known logarithmic regret bounds for Follow-The-Leader and for the gradient descent algorithm proposed in Hazan et al. [2006]. We then show that one can interpolate between these two extreme cases. In particular, we derive a new algorithm that shares the computational simplicity of gradient descent but achieves lower regret in many practical situations. Finally, we further extend our framework for generalized strongly convex functions.

• Type: Conference
• Year: 2008
• Where: NIPS
• Authors: Shai Shalev-Shwartz, Sham M. Kakade
• Keywords: Gradient Descent, Gradient Descent Algorithm, Information Technology, Logarithmic Regret Bounds, NIPS 2008