Adaptive Algorithm for Non-Stationary Online Convex-Concave Optimization

Xia Lei, Qing-xin Meng

Keywords: Non-Stationary Online Learning, Online Convex-Concave Optimization, Dynamic Duality Gap, Adaptive Algorithm

TL;DR: This paper presents a novel algorithm for Online Convex-Concave Optimization, achieving near-optimal performance in minimizing the dynamic duality gap through adaptive, multi-predictor, and integration modules.

Abstract:

This paper addresses the problem of Online Convex-Concave Optimization, an extension of Online Convex Optimization to two-player time-varying convex-concave games.
Our objective is to minimize the dynamic duality gap (D-DGap), a key performance metric that evaluates the players' strategies against arbitrary comparator sequences.
Existing algorithms struggle to achieve optimal performance, particularly in stationary or predictable environments.
We propose a novel, modular algorithm comprising three key components: an Adaptive Module that adjusts to varying levels of non-stationarity, a Multi-Predictor Aggregator that selects the optimal predictor from multiple candidates, and an Integration Module that seamlessly combines the strengths of both.
Our algorithm guarantees a minimax optimal D-DGap upper bound, up to a logarithmic factor, while also achieving a prediction error-based D-DGap bound.
Empirical results further demonstrate the effectiveness and adaptability of the proposed method.

Primary Area: optimization

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Submission Number: 3073