Structured Prediction in Online Learning
Pierre Boudart, Alessandro Rudi, Pierre Gaillard
TL;DR
This work addresses online structured prediction where outputs lack a vector structure by introducing OSKAAR, an online algorithm built on Implicit Loss Embedding (ILE) and KAAR that achieves regret bounds tied to the RKHS effective dimension and interpolation error. It also develops SALAMI, a non-stationary extension that uses expert aggregation and restart mechanisms to handle changing environments, with regret rates depending on measures of distributional variation and under capacity conditions. The paper provides both worst-case and high-probability guarantees, along with online-to-batch conversions yielding competitive excess-risk bounds in the IID setting. Together, these results enable principled, scalable online guarantees for complex structured prediction tasks in non-i.i.d. and adversarial contexts, with practical strategies for tuning and computation.</p>
Abstract
We study a theoretical and algorithmic framework for structured prediction in the online learning setting. The problem of structured prediction, i.e. estimating function where the output space lacks a vectorial structure, is well studied in the literature of supervised statistical learning. We show that our algorithm is a generalisation of optimal algorithms from the supervised learning setting, and achieves the same excess risk upper bound also when data are not i.i.d. Moreover, we consider a second algorithm designed especially for non-stationary data distributions, including adversarial data. We bound its stochastic regret in function of the variation of the data distributions.