{"type":"ScholarlyArticle","title":"A First Runtime Analysis of Parallel Tempering in Quadratic Optimization","authors":[{"name":"Tiago Paixão","slug":"tiago-paixao","given":"Tiago","family":"Paixão","affiliation":""},{"name":"Jorge Pérez Heredia","slug":"jorge-perez-heredia","given":"Jorge","family":"Pérez Heredia","affiliation":""},{"name":"Dirk Sudholt","slug":"dirk-sudholt","given":"Dirk","family":"Sudholt","affiliation":""},{"name":"Andrew M. Sutton","slug":"andrew-m-sutton","given":"Andrew M.","family":"Sutton","affiliation":""}],"abstract":"Parallel tempering, or the replica exchange method, is a Markov Chain Monte Carlo (MCMC) sampling technique for finding low-energy states in complex landscapes by executing multiple processes at different temperatures and allowing for states to migrate between parallel processes based on the Metropolis criterion. Despite a growing interest in the technique as a randomized search heuristic, it is not clear when and why parallel tempering is effective. We conduct a first runtime analysis of the parallel tempering algorithm on a simple quadratic unconstrained binary optimization problem that induces a rugged energy landscape with tunable parameters. We prove that a single-temperature Metropolis process fails to efficiently optimize the problem at any temperature. In sharp contrast, a two-state parallel tempering approach using a low and a high temperature typically solves the problem in O(n^2 log n) iterations. The low-temperature process ensures stability, as it is unlikely to accept worsenings, whereas the high-temperature process facilitates exploration by traversing energy barriers. Improvements are discovered through exploration in the high-temperature process and transferred to the low-temperature process, where they are permanently retained. This effective interplay between processes demonstrates the power of parallel tempering and lends credence to its design.","doi":"10.24963/ijcai.2026/706","url":"https://ijcai.org/proceedings/2026/706","pdf":"https://ijcai.org/proceedings/2026/0706.pdf","markdown":"https://ijcai.org/proceedings/2026/706.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/706","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Search","track":"Main Track","number":706,"pages":{"first":6343,"last":6351},"keywords":["Search: Evolutionary computation","Search: Combinatorial search and optimisation","Search: Local search"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}