In this paper, we study distributed constrained online convex optimization for a wireless system consisting of a parameter server and multiple agents. Each agent has a local constraint function and a time-varying local loss function, and needs to choose sequential actions based on causal information. The goal of the overall system is to minimize the accumulated total loss of all agents over a time horizon subject to total constraints of the agents. To this end, the agents communicate with the server over multiple access noisy fading channels, where the information is exchanged imperfectly. We first consider the full information scenario, where the local loss function of each agent is fully revealed to the corresponding agent in each time slot. We propose a modified saddle-point algorithm, where each agent sends an analog signal pertaining to the current value of the local constraint function and the server receives a superposition of these signals distorted by the noisy fading channels. We analyze the performance of the proposed algorithm, and establish $\mathcal {O}(\sqrt{T})$ regret bound and $\mathcal {O}(T^\frac{3}{4})$ constraint violation bound for the algorithm, where $T$ is the time horizon. Further, we extend the algorithm and performance analyses to the scenario of bandit feedback, where only the values of the local loss functions at two random points are disclosed to the agents in every time slot. In such a case, performance bounds similar to the full information scenario are established. Finally, numerical examples are presented to corroborate the efficacy of the proposed algorithms.

中文翻译：

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多接入衰落信道上的分布式约束在线凸优化

在本文中，我们研究了由参数服务器和多个代理组成的无线系统的分布式约束在线凸优化。每个智能体都有一个局部约束函数和一个时变局部损失函数，需要根据因果信息选择顺序动作。整个系统的目标是在一个时间范围内最小化所有代理的累积总损失，该时间范围受代理的总约束。为此，代理通过多个访问噪声衰落信道与服务器通信，其中信息交换不完美。我们首先考虑全信息场景，其中每个代理的局部损失函数在每个时隙中完全显示给相应的代理。我们提出了一种改进的鞍点算法，其中每个代理发送一个与本地约束函数的当前值有关的模拟信号，服务器接收这些信号的叠加，这些信号被噪声衰落通道扭曲。我们分析了所提出算法的性能，并建立$\mathcal {O}(\sqrt{T})$后悔束缚和$\mathcal {O}(T^\frac{3}{4})$算法的约束违反界限，其中$T$是时间范围。此外，我们将算法和性能分析扩展到老虎机反馈的场景，其中只有两个随机点的局部损失函数的值在每个时隙中向代理披露。在这种情况下，将建立类似于完整信息场景的性能界限。最后，给出了数值例子来证实所提出算法的有效性。