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Saddle-point problems appear in various settings including machine learning, zero-sum stochastic games, and regression problems. We consider decomposable saddle-point problems and study an extension of the alternating direction method of multipliers to such saddle-point problems. Instead of solving the original saddle-point problem directly, this algorithm solves smaller saddle-point problems by exploiting the decomposable structure. We show the convergence of this algorithm for convex-concave saddle-point problems under a mild assumption. We also provide a sufficient condition for which the assumption holds. We demonstrate the convergence properties of the saddle-point alternating direction method of multipliers with numerical examples on a power allocation problem in communication channels and a network routing problem with adversarial costs.
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This content will become publicly available on May 3, 2026
Spectral Representation for Causal Estimation with Hidden Confounders
We study the problem of causal effect estimation in the presence of unobserved confounders, focusing on two settings: instrumental variable (IV) regression with additional observed confounders, and proxy causal learning. Our approach uses a singular value decomposition of a conditional expectation operator combined with a saddle-point optimization method. In the IV regression setting, this can be viewed as a neural network generalization of the seminal approach due to Darolles et al. (2011). Saddle-point formulations have recently gained attention because they mitigate the double-sampling bias and are compatible with modern function approximation methods. We provide experimental validation across various settings and show that our approach outperforms existing methods on common benchmarks.
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- PAR ID:
- 10600596
- Editor(s):
- Li, Yingzhen; Mandt, Stephan; Agrawal, Shipra; Khan, Emtiyaz
- Publisher / Repository:
- PMLR
- Date Published:
- Volume:
- 258
- Page Range / eLocation ID:
- 2719-2727
- Subject(s) / Keyword(s):
- Spectral Representation, Causal Decision Inference Confounder
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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