{"type":"ScholarlyArticle","title":"On the Power of Optimism in Constrained Online Convex Optimization","authors":[{"name":"Haobo Zhang","slug":"haobo-zhang","given":"Haobo","family":"Zhang","affiliation":""},{"name":"Hengquan Guo","slug":"hengquan-guo","given":"Hengquan","family":"Guo","affiliation":""},{"name":"Xin Liu","slug":"xin-liu","given":"Xin","family":"Liu","affiliation":""}],"abstract":"This paper studies the constrained online convex optimization problem (COCO) where the learner makes sequential decisions within a constrained set. We present Optimistic-COCO, an adaptive gradient-based algorithm that incorporates optimistic design with the Lyapunov optimization technique. The proposed algorithm achieves strong theoretical guarantees: 1) Optimistic-COCO provides a tight gradient-variation regret bound and constant constraint violation; 2) Optimistic-COCO is environment-agnostic, utilizing adaptive learning rates that rely solely on causal information. These results resolve an open question posed in prior work regarding whether an adaptive algorithm can achieve problem-dependent regret and constant constraint violation in COCO. We establish these robust guarantees through carefully designed adaptive parameters and a refined multi-step Lyapunov drift analysis. Experimental results further validate our theoretical findings, demonstrating the practical efficacy of the proposed algorithm.","doi":"10.24963/ijcai.2025/776","url":"https://ijcai.org/proceedings/2025/776","pdf":"https://ijcai.org/proceedings/2025/0776.pdf","markdown":"https://ijcai.org/proceedings/2025/776.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/776","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Machine Learning","track":"Main Track","number":776,"pages":{"first":6976,"last":6983},"keywords":["Machine Learning: ML: Online learning","Constraint Satisfaction and Optimization: CSO: Constraint optimization problems","Machine Learning: ML: Learning theory"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}