Solving Hidden Monotone Variational Inequalities with Surrogate Losses

• URL: http://arxiv.org/abs/2411.05228v2
• Date: Mon, 11 Nov 2024 15:20:03 GMT
• Title: Solving Hidden Monotone Variational Inequalities with Surrogate Losses
• Authors: Ryan D'Orazio, Danilo Vucetic, Zichu Liu, Junhyung Lyle Kim, Ioannis Mitliagkas, Gauthier Gidel,
• Abstract summary: We propose a principled surrogate-based approach compatible with deep learning to solve variational inequality (VI) problems. We demonstrate our surrogate-based approach is effective in min-max optimization and minimizing projected Bellman error. In the deep reinforcement learning case, we propose a novel variant of TD(0) which is more compute and sample efficient.
• Score: 23.565183680315073
• License:
• Abstract: Deep learning has proven to be effective in a wide variety of loss minimization problems. However, many applications of interest, like minimizing projected Bellman error and min-max optimization, cannot be modelled as minimizing a scalar loss function but instead correspond to solving a variational inequality (VI) problem. This difference in setting has caused many practical challenges as naive gradient-based approaches from supervised learning tend to diverge and cycle in the VI case. In this work, we propose a principled surrogate-based approach compatible with deep learning to solve VIs. We show that our surrogate-based approach has three main benefits: (1) under assumptions that are realistic in practice (when hidden monotone structure is present, interpolation, and sufficient optimization of the surrogates), it guarantees convergence, (2) it provides a unifying perspective of existing methods, and (3) is amenable to existing deep learning optimizers like ADAM. Experimentally, we demonstrate our surrogate-based approach is effective in min-max optimization and minimizing projected Bellman error. Furthermore, in the deep reinforcement learning case, we propose a novel variant of TD(0) which is more compute and sample efficient.

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