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.