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arXiv · 2207.11161

Lagrangian Method for Q-Function Learning (with Applications to Machine Translation)

Huang Bojun
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Abstract

This paper discusses a new approach to the fundamental problem of learning optimal Q-functions. In this approach, optimal Q-functions are formulated as saddle points of a nonlinear Lagrangian function derived from the classic Bellman optimality equation. The paper shows that the Lagrangian enjoys strong duality, in spite of its nonlinearity, which paves the way to a general Lagrangian method to Q-function learning. As a demonstration, the paper develops an imitation learning algorithm based on the duality theory, and applies the algorithm to a state-of-the-art machine translation benchmark. The paper then turns to demonstrate a symmetry breaking phenomenon regarding the optimality of the Lagrangian saddle points, which justifies a largely overlooked direction in developing the Lagrangian method.

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Huang Bojun. 2022-07-22. Lagrangian Method for Q-Function Learning (with Applications to Machine Translation). https://arxiv.org/abs/2207.11161

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