A Modular Algorithm for Non-Stationary Online Convex-Concave Optimization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916943106146304 |
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| author | Meng, Qing-xin Lei, Xia Liu, Jian-wei |
| author_facet | Meng, Qing-xin Lei, Xia Liu, Jian-wei |
| contents | This paper investigates the problem of Online Convex-Concave Optimization, which extends Online Convex Optimization to two-player time-varying convex-concave games. The goal is to minimize the dynamic duality gap (D-DGap), a critical performance measure that evaluates players' strategies against arbitrary comparator sequences. Existing algorithms fail to deliver optimal performance, particularly in stationary or predictable environments. To address this, we propose a novel modular algorithm with three core components: an Adaptive Module that dynamically adjusts to varying levels of non-stationarity, a Multi-Predictor Aggregator that identifies the best predictor among multiple candidates, and an Integration Module that effectively combines their strengths. Our algorithm achieves a minimax optimal D-DGap upper bound, up to a logarithmic factor, while also ensuring prediction error-driven D-DGap bounds. The modular design allows for the seamless replacement of components that regulate adaptability to dynamic environments, as well as the incorporation of components that integrate ``side knowledge'' from multiple predictors. Empirical results further demonstrate the effectiveness and adaptability of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Modular Algorithm for Non-Stationary Online Convex-Concave Optimization Meng, Qing-xin Lei, Xia Liu, Jian-wei Machine Learning Optimization and Control This paper investigates the problem of Online Convex-Concave Optimization, which extends Online Convex Optimization to two-player time-varying convex-concave games. The goal is to minimize the dynamic duality gap (D-DGap), a critical performance measure that evaluates players' strategies against arbitrary comparator sequences. Existing algorithms fail to deliver optimal performance, particularly in stationary or predictable environments. To address this, we propose a novel modular algorithm with three core components: an Adaptive Module that dynamically adjusts to varying levels of non-stationarity, a Multi-Predictor Aggregator that identifies the best predictor among multiple candidates, and an Integration Module that effectively combines their strengths. Our algorithm achieves a minimax optimal D-DGap upper bound, up to a logarithmic factor, while also ensuring prediction error-driven D-DGap bounds. The modular design allows for the seamless replacement of components that regulate adaptability to dynamic environments, as well as the incorporation of components that integrate ``side knowledge'' from multiple predictors. Empirical results further demonstrate the effectiveness and adaptability of the proposed method. |
| title | A Modular Algorithm for Non-Stationary Online Convex-Concave Optimization |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2509.07901 |