Distributed Task Management in Fog Computing: A Socially Concave Bandit Game

TL;DR

This paper introduces a novel game-theoretic framework for distributed task allocation in fog computing, employing bandit feedback and no-regret learning strategies to achieve efficient and adaptive resource management.

Contribution

It formulates the task allocation as a social-concave game with bandit feedback and develops two new no-regret online decision-making algorithms with proven regret bounds.

Findings

Proposed strategies outperform existing methods in simulations.

Theoretical analysis confirms convergence to Nash equilibrium.

Strategies adapt effectively to system heterogeneity and uncertainties.

Abstract

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.