{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/value-approximation-for-two-player-general","title":"Value Approximation for Two-Player General-Sum Differential Games with State Constraints","arxiv_id":"2311.16520","date":"2023-11-28","proceeding":null,"authors":["Lei Zhang","Mukesh Ghimire","Wenlong Zhang","Zhe Xu","Yi Ren"],"abstract":"Solving Hamilton-Jacobi-Isaacs (HJI) PDEs numerically enables equilibrial feedback control in two-player differential games, yet faces the curse of dimensionality (CoD). While physics-informed neural networks (PINNs) have shown promise in alleviating CoD in solving PDEs, vanilla PINNs fall short in learning discontinuous solutions due to their sampling nature, leading to poor safety performance of the resulting policies when values are discontinuous due to state or temporal logic constraints. In this study, we explore three potential solutions to this challenge: (1) a hybrid learning method that is guided by both supervisory equilibria and the HJI PDE, (2) a value-hardening method where a sequence of HJIs are solved with increasing Lipschitz constant on the constraint violation penalty, and (3) the epigraphical technique that lifts the value to a higher dimensional state space where it becomes continuous. Evaluations through 5D and 9D vehicle and 13D drone simulations reveal that the hybrid method outperforms others in terms of generalization and safety performance by taking advantage of both the supervisory equilibrium values and costates, and the low cost of PINN loss gradients.","url_abs":"https://arxiv.org/abs/2311.16520v3","url_pdf":"https://arxiv.org/pdf/2311.16520v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"value-approximation-for-two-player-general","repo_url":"https://github.com/dayanbatuofu/value_appro_game","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"physics-informed-machine-learning","task_name":"Physics-informed machine learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2311.16520","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2311.16520"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/dayanbatuofu/value_appro_game","reach":{"status":"ok"}}],"summary":{"ran":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"84e7cd62fc8379e1","entry":"pointInRect","repo":"dayanbatuofu/value_appro_game","repo_kind":"official","path":"Uncontrolled_intersection_complete_information_game/validation_scripts/trajectory_with_value_gelu.py","file_url":"https://github.com/dayanbatuofu/value_appro_game/blob/HEAD/Uncontrolled_intersection_complete_information_game/validation_scripts/trajectory_with_value_gelu.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"84e7cd62fc8379e1"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}