Robust learning with anytime-guaranteed feedback
This work addresses the challenge of ensuring performance guarantees in stochastic gradient-based learning for practitioners dealing with heavy-tailed data, though it appears incremental as it builds on existing regret control methods.
The paper tackles the problem of robust learning under heavy-tailed data distributions by introducing a modified anytime online-to-batch mechanism that provides high-probability error bounds with only lower-order moment assumptions on stochastic gradients. The result is an easily implemented stochastic gradient algorithm that achieves sub-Gaussian error bounds for all queried points and shows notable gains on real-world data applications.
Under data distributions which may be heavy-tailed, many stochastic gradient-based learning algorithms are driven by feedback queried at points with almost no performance guarantees on their own. Here we explore a modified "anytime online-to-batch" mechanism which for smooth objectives admits high-probability error bounds while requiring only lower-order moment bounds on the stochastic gradients. Using this conversion, we can derive a wide variety of "anytime robust" procedures, for which the task of performance analysis can be effectively reduced to regret control, meaning that existing regret bounds (for the bounded gradient case) can be robustified and leveraged in a straightforward manner. As a direct takeaway, we obtain an easily implemented stochastic gradient-based algorithm for which all queried points formally enjoy sub-Gaussian error bounds, and in practice show noteworthy gains on real-world data applications.