{"ID":2873118,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.07901","arxiv_id":"2509.07901","title":"A Modular Algorithm for Non-Stationary Online Convex-Concave Optimization","abstract":"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.","short_abstract":"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 se...","url_abs":"https://arxiv.org/abs/2509.07901","url_pdf":"https://arxiv.org/pdf/2509.07901v1","authors":"[\"Qing-xin Meng\",\"Xia Lei\",\"Jian-wei Liu\"]","published":"2025-09-09T16:33:38Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.OC\"]","methods":"[]","has_code":false}