Multi-Task Deep Learning Games: Investigating Nash Equilibria and Convergence Properties

Abstract

This paper conducts a rigorous game-theoretic analysis on multi-task deep learning, providing mathematical insights into the dynamics and interactions of tasks within these models. Multi-task deep learning has attracted significant attention in recent years due to its ability to leverage shared representations across multiple correlated tasks, leading to improved generalization and reduced training time. However, understanding and examining the interactions between tasks within a multi-task deep learning system poses a considerable challenge. In this paper, we present a game-theoretic investigation of multi-task deep learning, focusing on the existence and convergence of Nash equilibria. Game theory provides a suitable framework for modeling the interactions among various tasks in a multi-task deep learning system, as it captures the strategic behavior of learning agents sharing a common set of parameters. Our primary contributions include: casting the multi-task deep learning problem as a game where each task acts as a player aiming to minimize its task-specific loss function; introducing the notion of a Nash equilibrium for the multi-task deep learning game; demonstrating the existence of at least one Nash equilibrium under specific convexity and Lipschitz continuity assumptions for the loss functions; examining the convergence characteristics of the Nash equilibrium; and providing a comprehensive analysis of the implications and limitations of our theoretical findings. We also discuss potential extensions and directions for future research in the multi-task deep learning landscape.