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.

翻译：本文研究动态系统中的网络优化问题，其中用户构成、服务需求、系统容量与信道条件等因素可能发生突发且不可预测的变化。与现有研究主要关注稳态下长期性能优化不同，我们开发了能够快速适应突变的在线学习算法。鉴于当前许多网络优化算法依赖对偶方法迭代学习最优拉格朗日乘子，我们提出仅利用突变发生时可用信息对这些乘子进行零样本更新的方法。通过将泰勒级数分析与互补松弛条件相结合，我们从理论上推导出适用于两类不同网络优化问题中多种突变的零样本更新策略。这些更新机制可与现有算法结合，在过渡阶段显著提升总效用、运营成本及约束违反等方面的性能。仿真结果表明，我们的零样本更新策略大幅改善了过渡期性能，即使在剧烈系统变化下，也常能在无需额外学习的情况下实现接近最优的结果。