A Game Theoretic Approach to Meta-Learning: Nash Model-Agnostic Meta-Learning

Jihwan Yu, Jaeyeon Jo, Taeyoung Yun, Jinkyoo Park

Keywords: Meta learning, Game Theory, Generalized Stackelberg Equilibrium

TL;DR: This paper proposes a new modeling framework for model-agnostic meta-learning and an algorithm that the convergence to the generalized Stackelberg equilibrium is proved.

Abstract: Meta-learning, or learning to learn, aims to develop algorithms that can quickly adapt to new tasks and environments. Model-agnostic meta-learning (MAML), proposed as a bi-level optimization problem, is widely used as a baseline for gradient-based meta-learning algorithms that learn meta-parameters. In MAML, task-specific parameters are adapted independently in the inner-loop. After learning the task-specific parameters, the meta-parameters are learned in the outer-loop by minimizing the average task loss. After MAML, some gradient-based meta-learning research has explored objectives beyond average task losses, such as minimizing worst-case task losses for risk management and improving zero-shot performance in unadaptable environments. However, if the purpose of learning meta-parameters changes, the inner-loop formulation must change accordingly. Therefore, we propose a novel gradient-based meta-learning framework that imposes joint strategy sets and utility functions among tasks, making each task affected by other tasks. To solve this complex problem, we first show the proposed framework can be formulated as a generalized Stackelberg game. After that, we propose the NashMAML algorithm to compute the generalized Stackelberg equilibrium of this model and theoretically prove its convergence. We validate our approach on sinusoidal regression and few-shot image classification tasks. The results demonstrate that our approach outperforms previous methods in handling few-shot learning problems.

Primary Area: transfer learning, meta learning, and lifelong learning

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Submission Number: 5455