Accelerating Optimization via Adaptive Prediction
This work addresses optimization challenges in machine learning, offering incremental improvements through a unified framework.
The authors tackled the problem of designing data-dependent optimization algorithms by introducing a general framework that unifies adaptive regularization, optimistic gradient predictions, and problem-dependent randomization, resulting in algorithms with more favorable guarantees than recent state-of-the-art methods.
We present a powerful general framework for designing data-dependent 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.