Accelerating Online Convex Optimization via Adaptive Prediction
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:848-856, 2016.
We present a powerful general framework for designing data-dependent online convex optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We first present a series of new regret guarantees that hold at any time and under very minimal assumptions, and then show how different relaxations recover existing algorithms, both basic as well as more recent sophisticated ones. Finally, we show how combining adaptivity, optimism, and problem-dependent randomization can guide the design of algorithms that benefit from more favorable guarantees than recent state-of-the-art methods.