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

Ali Zeynali, Mahsa Sahebdel, Qingsong Liu, Ramesh K. Sitaraman, Mohammad Hajiesmaili

Keywords: Online Convex Optimization, Learning-Augmented Algorithms, Target Tracking

TL;DR: We propose robust algorithms for smoothed target tracking, where an agent aims to follow time-varying target trajectories that may be perturbed by an adversary.

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 for elastic workloads, like LLM training, against sudden demand spikes for inelastic workloads, like 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.

Submission Number: 121