Fog computing leverages the task offloading capabilities at the network's edge to improve efficiency and enable swift responses to application demands. However, the design of task allocation strategies in a fog computing network is still challenging because of the heterogeneity of fog nodes and uncertainties in system dynamics. We formulate the distributed task allocation problem as a social-concave game with bandit feedback and show that the game has a unique Nash equilibrium, which is implementable using no-regret learning strategies (regret with sublinear growth). We then develop two no-regret online decision-making strategies. One strategy, namely bandit gradient ascent with momentum, is an online convex optimization algorithm with bandit feedback. The other strategy, Lipschitz bandit with initialization, is an EXP3 multi-armed bandit algorithm. We establish regret bounds for both strategies and analyze their convergence characteristics. Moreover, we compare the proposed strategies with an allocation strategy named learning with linear rewards. Theoretical- and numerical analysis shows the superior performance of the proposed strategies for efficient task allocation compared to the state-of-the-art methods.

翻译：雾计算利用网络边缘的任务卸载能力提升效率并快速响应应用需求。然而，由于雾节点的异构性及系统动态不确定性，雾计算网络中的任务分配策略设计仍面临挑战。本文将分布式任务分配问题建模为具有老虎机反馈的社交凹博弈，并证明该博弈存在唯一的纳什均衡，该均衡可通过无遗憾学习策略（具有次线性增长遗憾）实现。我们随后提出两种无遗憾在线决策策略：动量梯度上升老虎机算法（一种基于老虎机反馈的在线凸优化算法），以及初始化Lipschitz老虎机算法（一种EXP3多臂老虎机算法）。我们建立了两种策略的遗憾界并分析了其收敛特性。此外，我们将所提策略与线性奖励学习分配策略进行对比。理论与数值分析表明，与现有最优方法相比，所提策略在高效任务分配方面具有优越性能。