Stochastic Extragradient with Flip-Flop Shuffling & Anchoring: Provable Improvements
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| Format: | Preprint |
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2024
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| _version_ | 1866915087323758592 |
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| author | Chae, Jiseok Yun, Chulhee Kim, Donghwan |
| author_facet | Chae, Jiseok Yun, Chulhee Kim, Donghwan |
| contents | In minimax optimization, the extragradient (EG) method has been extensively studied because it outperforms the gradient descent-ascent method in convex-concave (C-C) problems. Yet, stochastic EG (SEG) has seen limited success in C-C problems, especially for unconstrained cases. Motivated by the recent progress of shuffling-based stochastic methods, we investigate the convergence of shuffling-based SEG in unconstrained finite-sum minimax problems, in search of convergent shuffling-based SEG. Our analysis reveals that both random reshuffling and the recently proposed flip-flop shuffling alone can suffer divergence in C-C problems. However, with an additional simple trick called anchoring, we develop the SEG with flip-flop anchoring (SEG-FFA) method which successfully converges in C-C problems. We also show upper and lower bounds in the strongly-convex-strongly-concave setting, demonstrating that SEG-FFA has a provably faster convergence rate compared to other shuffling-based methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_00511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Extragradient with Flip-Flop Shuffling & Anchoring: Provable Improvements Chae, Jiseok Yun, Chulhee Kim, Donghwan Machine Learning Optimization and Control In minimax optimization, the extragradient (EG) method has been extensively studied because it outperforms the gradient descent-ascent method in convex-concave (C-C) problems. Yet, stochastic EG (SEG) has seen limited success in C-C problems, especially for unconstrained cases. Motivated by the recent progress of shuffling-based stochastic methods, we investigate the convergence of shuffling-based SEG in unconstrained finite-sum minimax problems, in search of convergent shuffling-based SEG. Our analysis reveals that both random reshuffling and the recently proposed flip-flop shuffling alone can suffer divergence in C-C problems. However, with an additional simple trick called anchoring, we develop the SEG with flip-flop anchoring (SEG-FFA) method which successfully converges in C-C problems. We also show upper and lower bounds in the strongly-convex-strongly-concave setting, demonstrating that SEG-FFA has a provably faster convergence rate compared to other shuffling-based methods. |
| title | Stochastic Extragradient with Flip-Flop Shuffling & Anchoring: Provable Improvements |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2501.00511 |