Abstract:Online structured prediction, including online classification as a special case, is the task of sequentially predicting labels from input features. In this setting, the surrogate regret -- the cumulative excess of the actual target loss (e.g., the 0-1 loss) over the surrogate loss (e.g., the logistic loss) incurred by the best fixed estimator -- has gained attention because it admits a finite bound independent of the time horizon $T$. However, such guarantees break down in non-stationary environments, where every fixed estimator may incur surrogate loss that grows linearly with $T$. To address this limitation, we obtain an upper bound of $F_T + O(1 + P_T)$ on the cumulative target loss, where $F_T$ is the cumulative surrogate loss of any comparator sequence and $P_T$ is its path length. This bound depends on $T$ only through $F_T$ and $P_T$, thus offering stronger guarantees under non-stationarity. Our core idea is to combine the dynamic regret analysis of online gradient descent (OGD) with the exploit-the-surrogate-gap technique. This viewpoint sheds light on the usefulness of a Polyak-style learning rate for OGD, which systematically yields target-loss bounds and performs well empirically. We then extend our approach to broader settings beyond prior work via the convolutional Fenchel--Young loss. Finally, a lower bound shows that the dependence on $F_T$ and $P_T$ is tight.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2510.07086 [cs.LG] |
| (or arXiv:2510.07086v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2510.07086 arXiv-issued DOI via DataCite |
Submission history
From: Shinsaku Sakaue [view email]
[v1]
Wed, 8 Oct 2025 14:43:44 UTC (1,511 KB)
[v2]
Thu, 14 May 2026 03:35:06 UTC (3,242 KB)