Beyond Binary: Continuous State Optimization with Graph-Structured Objectives

2026-08-10

AI Summary

This work addresses the challenge of jointly optimizing multiple objectives—such as fairness, accuracy, and latency—in large-scale learning systems with continuous state spaces, where frequent adjustments often lead to system instability. To tackle this issue, the paper introduces dependency graphs into continuous-state multi-objective online optimization for the first time and proposes the Lazy Graph-LinUCB algorithm. This approach integrates three key mechanisms: asynchronous update scheduling, adaptive graph structure learning, and joint parameter estimation. It achieves near-optimal cumulative regret while substantially reducing state-switching overhead. Empirical evaluations in heterogeneous environments demonstrate that, compared to baseline methods, the proposed algorithm reduces movement cost by more than threefold while maintaining comparable cumulative loss.

Abstract

Large-scale learning systems often face the challenge of balancing multiple, potentially competing objectives, such as fairness, accuracy, and latency. While recent work has formalized this as an optimization problem over binary states, many real-world control parameters, such as fairness thresholds, diversity mixing rates, or resource budgets, are continuous. In this work, we extend the framework to \emph{continuous state spaces}. We model the problem as minimizing a sum of linear objectives subject to \emph{movement costs} that penalize system instability. We capture the local structure of the objectives using a \emph{dependency graph} (or factor graph), where each objective is determined by a subset of the state attributes. To address the tension between exploration and stability, we propose \emph{Lazy Graph-LinUCB}, an algorithm that performs lazy updates to minimize switching costs while maintaining near-optimal regret. Beyond stability, we introduce three advanced mechanisms to exploit the underlying graph structure: (1) an \emph{asynchronous} update schedule that eliminates synchronization overhead in sparse graphs; (2) an \emph{adaptive} algorithm that learns the graph structure from data; and (3) a \emph{joint estimator} that leverages data sharing among correlated objectives to significantly tighten regret bounds. Empirically, we demonstrate that these structural exploitations reduce movement costs by more than a factor of three in heterogeneous systems while maintaining similar cumulative losses.

Problem

• continuous state optimization
• multi-objective balancing
• movement costs
• dependency graph
• system stability

Innovation

• continuous state optimization
• dependency graph
• movement cost
• Lazy Graph-LinUCB
• joint estimator