Smoothed Online Optimization for Target Tracking: Robust and Learning-Augmented Algorithms

2025-09-07

AI Summary

This paper introduces the Smooth Online Object Tracking (SOOTT) problem, which unifies three objectives: dynamic target tracking, adversarial perturbation suppression, and switching cost minimization—motivated by real-world AI cluster scheduling scenarios involving co-scheduling of elastic (e.g., LLM training) and rigid (e.g., real-time inference) workloads. Methodologically, we design BEST, a robust online algorithm with provable competitive ratio guarantees, and propose CoRT—a novel prediction-augmented algorithm that achieves near-optimal performance under accurate predictions while maintaining strong robustness against prediction errors. Our approach integrates online optimization theory, competitive analysis, and learning-enhanced mechanisms to support black-box predictor-driven dynamic decision-making. Experiments demonstrate that both algorithms effectively balance tracking accuracy, decision smoothness, and adversarial robustness, with theoretical guarantees corroborated by empirical results.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We introduce the Smoothed Online Optimization for Target Tracking (SOOTT) problem, a new framework that integrates three key objectives in online decision-making under uncertainty: (1) tracking cost for following a dynamically moving target, (2) adversarial perturbation cost for withstanding unpredictable disturbances, and (3) switching cost for penalizing abrupt changes in decisions. This formulation captures real-world scenarios such as elastic and inelastic workload scheduling in AI clusters, where operators must balance long-term service-level agreements (e.g., LLM training) against sudden demand spikes (e.g., real-time inference). We first present BEST, a robust algorithm with provable competitive guarantees for SOOTT. To enhance practical performance, we introduce CoRT, a learning-augmented variant that incorporates untrusted black-box predictions (e.g., from ML models) into its decision process. Our theoretical analysis shows that CoRT strictly improves over BEST when predictions are accurate, while maintaining robustness under arbitrary prediction errors. We validate our approach through a case study on workload scheduling, demonstrating that both algorithms effectively balance trajectory tracking, decision smoothness, and resilience to external disturbances.

Problem

• Tracking dynamically moving targets under uncertainty
• Withstanding adversarial perturbations and unpredictable disturbances
• Balancing trajectory tracking, decision smoothness, and resilience

Innovation

• Smoothed online optimization for target tracking
• Robust algorithm with competitive guarantees
• Learning-augmented variant using black-box predictions