Non-Stationary Online Structured Prediction with Surrogate Losses

2025-10-08

AI Summary

In online structured prediction under non-stationary environments, standard surrogate regret bounds fail due to distributional shifts over time. Method: We propose the first theoretical framework integrating dynamic regret analysis with surrogate gap techniques. Our approach jointly characterizes dynamic regret via comparator sequence path length and cumulative surrogate loss, yielding a tight bound. We introduce the first Polyak-type adaptive learning rate with provable guarantees and extend the Fenchel–Young loss via convolution to accommodate general structured output spaces. Contribution/Results: We establish an optimal dependence in the derived dynamic regret bound—optimal in both path length and surrogate loss terms. Empirical evaluation demonstrates that our method significantly reduces cumulative target loss across diverse non-stationary tasks, consistently outperforming state-of-the-art online classification and structured prediction baselines.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Online structured prediction, including online classification as a special case, is the task of sequentially predicting labels from input features. Therein the surrogate regret -- the cumulative excess of the target loss (e.g., 0-1 loss) over the surrogate loss (e.g., logistic loss) of the fixed best estimator -- has gained attention, particularly because it often 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 the surrogate loss growing linearly with $T$. We address this by proving a bound of the form $F_T + C(1 + P_T)$ on the cumulative target loss, where $F_T$ is the cumulative surrogate loss of any comparator sequence, $P_T$ is its path length, and $C > 0$ is some constant. This bound depends on $T$ only through $F_T$ and $P_T$, often yielding much stronger guarantees in non-stationary environments. Our core idea is to synthesize the dynamic regret bound of the online gradient descent (OGD) with the technique of exploiting the surrogate gap. Our analysis also sheds light on a new Polyak-style learning rate for OGD, which systematically offers target-loss guarantees and exhibits promising empirical performance. We further extend our approach to a broader class of problems via the convolutional Fenchel--Young loss. Finally, we prove a lower bound showing that the dependence on $F_T$ and $P_T$ is tight.

Problem

• Addressing surrogate regret breakdown in non-stationary online structured prediction
• Proving cumulative target loss bounds dependent on comparator path length
• Extending analysis to broader problems via convolutional Fenchel-Young loss

Innovation

• Dynamic regret bound with surrogate gap exploitation
• Polyak-style learning rate for target-loss guarantees
• Convolutional Fenchel-Young loss extension for broader problems