In many dynamic systems, decisions on system operation are updated over time, and the decision maker requires an online learning approach to optimize its strategy in response to the changing environment. When the loss and constraint functions are convex, this belongs to the general family of online convex optimization (OCO). In existing OCO works, the environment is assumed to vary in a time-slotted fashion, while the decisions are updated at each time slot. However, many wireless communication systems permit only periodic decision updates, i.e., each decision is fixed over multiple time slots, while the environment changes between the decision epochs. The standard OCO model is inadequate for these systems. Therefore, in this work, we consider periodic decision updates for OCO. We aim to minimize the accumulation of time-varying convex loss functions, subject to both short-term and long-term constraints. Information about the loss functions within the current update period may be incomplete and is revealed to the decision maker only after the decision is made. We propose an efficient algorithm, termed Periodic Queueing and Gradient Aggregation (PQGA), which employs novel periodic queues together with possibly multi-step aggregated gradient descent to update the decisions over time. We derive upper bounds on the dynamic regret, static regret, and constraint violation of PQGA. As an example application, we study the performance of PQGA in a large-scale multi-antenna system shared by multiple wireless service providers. Simulation results show that PQGA converges fast and substantially outperforms the known best alternative.
翻译:在许多动态系统中,关于系统运行的决定会随着时间的变化而更新,而决策者则要求采用在线学习方法,以优化其战略,以应对不断变化的环境。当损失和制约功能是连接时,这属于在线 convex优化(OCO)的一般家庭。在现有的 OCO 工作中,环境假定会因时间变化而变化,而每个时间档都会更新决定。然而,许多无线通信系统只允许定期更新决定,即每个决定都是在多个时间档中固定的,而决定区之间的环境变化。标准 OCO 模型对这些系统来说是不够的。因此,我们考虑定期更新OCO的决定。我们的目标是尽可能减少时间变化变异的 convex损失功能的累积,但受短期和长期限制。关于当前更新期损失功能的信息可能不完整,只有在作出决定后才会向决策者披露。我们提议一种高效的算法,称为定期降级和累进 Agrient Agregation 模型(PQGA QGA 模型),我们考虑定期递增递增的多级PGA,我们可能同时更新了多级PGA 。