Adversarial Regularization as Stackelberg Game: An Unrolled Optimization Approach

TL;DR

This paper introduces SALT, a novel Stackelberg game formulation for adversarial regularization in deep learning, using unrolled optimization to improve model generalization in NLP tasks.

Contribution

It proposes a leader-follower Stackelberg game approach for adversarial regularization, capturing strategic interactions with unrolled optimization, outperforming existing methods.

Findings

SALT outperforms existing adversarial regularization methods on NLP tasks.

The Stackelberg formulation improves model fitting to unperturbed data.

Unrolled optimization effectively captures the leader's strategic advantage.

Abstract

Adversarial regularization has been shown to improve the generalization performance of deep learning models in various natural language processing tasks. Existing works usually formulate the method as a zero-sum game, which is solved by alternating gradient descent/ascent algorithms. Such a formulation treats the adversarial and the defending players equally, which is undesirable because only the defending player contributes to the generalization performance. To address this issue, we propose Stackelberg Adversarial Regularization (SALT), which formulates adversarial regularization as a Stackelberg game. This formulation induces a competition between a leader and a follower, where the follower generates perturbations, and the leader trains the model subject to the perturbations. Different from conventional approaches, in SALT, the leader is in an advantageous position. When the leader moves, it recognizes the strategy of the follower and takes the anticipated follower's outcomes into consideration. Such a leader's advantage enables us to improve the model fitting to the unperturbed data. The leader's strategic information is captured by the Stackelberg gradient, which is obtained using an unrolling algorithm. Our experimental results on a set of machine translation and natural language understanding tasks show that SALT outperforms existing adversarial regularization baselines across all tasks. Our code is available at https://github.com/SimiaoZuo/Stackelberg-Adv.