Network Optimization in Dynamic Systems: Fast Adaptation via Zero-Shot Lagrangian Update

This paper addresses network optimization in dynamic systems, where factors such as user composition, service requirements, system capacity, and channel conditions can change abruptly and unpredictably. Unlike existing studies that focus primarily on optimizing long-term performance in steady states, we develop online learning algorithms that enable rapid adaptation to sudden changes. Recognizing that many current network optimization algorithms rely on dual methods to iteratively learn optimal Lagrange multipliers, we propose zero-shot updates for these multipliers using only information available at the time of abrupt changes. By combining Taylor series analysis with complementary slackness conditions, we theoretically derive zero-shot updates applicable to various abrupt changes in two distinct network optimization problems. These updates can be integrated with existing algorithms to significantly improve performance during transitory phases in terms of total utility, operational cost, and constraint violations. Simulation results demonstrate that our zero-shot updates substantially improve transitory performance, often achieving near-optimal outcomes without additional learning, even under severe system changes.