2021/12/24 by Jonathan Lorraine, Lorraine, Jonathan, Paul Vicol +9 · 1 citation
Computer Science · Decision Sciences · Mathematics · Social Sciences · #Computer Science and Game Theory (cs.GT) #Evolutionary Game Theory and Cooperation #FOS: Computer and information sciences #Game Theory and Applications #Machine Learning (cs.LG) #Mathematical Biology Tumor Growth #Multiagent Systems (cs.MA) #cs.GT #cs.LG #cs.MA
paper · pdf · doi:10.48550/arxiv.2112.14570
AAMAS2022, 24 pages
arxiv created 2021/12/24 · openalex publication_date 2021/12/24 · arxiv updated 2021/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Ridge Rider (RR) is an algorithm for finding diverse solutions to optimization problems by following eigenvectors of the Hessian ("ridges"). RR is designed for conservative gradient systems (i.e., settings involving a single loss function), where it branches at saddles - easy-to-find bifurcation points. We generalize this idea to non-conservative, multi-agent gradient systems by proposing a method - denoted Generalized Ridge Rider (GRR) - for finding arbitrary bifurcation points. We give theoretical motivation for our method by leveraging machinery from the field of dynamical systems. We construct novel toy problems where we can visualize new phenomena while giving insight into high-dimensional problems of interest. Finally, we empirically evaluate our method by finding diverse solutions in the iterated prisoners' dilemma and relevant machine learning problems including generative adversarial networks.