Lazifying Conditional Gradient Algorithms
This work addresses efficiency issues for practitioners using conditional gradient algorithms in online learning and optimization, representing an incremental improvement.
The paper tackles the high computational cost of implementing linear optimization oracles in conditional gradient algorithms by introducing a lazification method that uses a faster separation oracle, resulting in several orders of magnitude speedup in wall-clock time.
Conditional gradient algorithms (also often called Frank-Wolfe algorithms) are popular due to their simplicity of only requiring a linear optimization oracle and more recently they also gained significant traction for online learning. While simple in principle, in many cases the actual implementation of the linear optimization oracle is costly. We show a general method to lazify various conditional gradient algorithms, which in actual computations leads to several orders of magnitude of speedup in wall-clock time. This is achieved by using a faster separation oracle instead of a linear optimization oracle, relying only on few linear optimization oracle calls.