延迟容忍约束OCO及其在网络资源分配中的应用
Delay-Tolerant Constrained OCO with Application to Network Resource Allocation
摘要：
我们考虑在线凸优化（OCO）与多时隙反馈延迟，其中一个代理作出一系列的在线决策，以尽量减少积累的时变凸损失函数，受到短期和长期的约束，可能是时变的。当前凸损失函数和长期约束函数只有在决策完成后才能向智能体揭示，并且它们可能会延迟多个时隙。现有的工作OCO在这个一般的设置集中在静态后悔，它衡量的差距之间的损失在线决策序列和离线基准，是固定的。在这项工作中，我们认为静态遗憾和更实际的有意义的动态遗憾，其中的基准是一个随时间变化的序列的每槽优化。我们提出了一种高效的算法，称为延迟容忍约束OCO（DTC-OCO），它使用了一种新的约束惩罚与双重正则化，以解决信息反馈和决策更新之间的矛盾。我们推导出上界的动态遗憾，静态遗憾，约束违反，证明他们是次线性温和的条件下。我们进一步应用DTC-OCO一般的网络资源分配问题，这出现在许多系统，如数据网和云计算。仿真结果表明，DTC-OCO在已知的最佳替代品的显着的性能增益。
英文摘要：
We consider online convex optimization (OCO) with multi-slot feedback delay, where an agent makes a sequence of online decisions to minimize the accumulation of time-varying convex loss functions, subject to short-term and long-term constraints that are possibly time-varying. The current convex loss function and the long-term constraint function are revealed to the agent only after the decision is made, and they may be delayed for multiple time slots. Existing work on OCO under this general setting has focused on the static regret, which measures the gap of losses between the online decision sequence and an offline benchmark that is fixed over time. In this work, we consider both the static regret and the more practically meaningful dynamic regret, where the benchmark is a time-varying sequence of per-slot optimizers. We propose an efficient algorithm, termed Delay-Tolerant Constrained-OCO (DTC-OCO), which uses a novel constraint penalty with double regularization to tackle the asynchrony between information feedback and decision updates. We derive upper bounds on its dynamic regret, static regret, and constraint violation, proving them to be sublinear under mild conditions. We further apply DTC-OCO to a general network resource allocation problem, which arises in many systems such as data networks and cloud computing. Simulation results demonstrate substantial performance gain of DTC-OCO over the known best alternative.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
