{"id":{"repo_id":"byu","oai_identifier":"oai:scholarsarchive.byu.edu:etd-2221"},"canonical_url":"https://search.dev.ndltd.org/etd/byu/oai:scholarsarchive.byu.edu:etd-2221","repository":{"repo_id":"byu","name":"Brigham Young University","base_url":"https://scholarsarchive.byu.edu/do/oai/"},"display":{"title":"Limitations and Extensions of the WoLF-PHC Algorithm","abstract":"Policy Hill Climbing (PHC) is a reinforcement learning algorithm that extends Q-learning to learn probabilistic policies for multi-agent games. WoLF-PHC extends PHC with the \"win or learn fast\" principle. A proof that PHC will diverge in self-play when playing Shapley's game is given, and WoLF-PHC is shown empirically to diverge as well. Various WoLF-PHC based modifications were created, evaluated, and compared in an attempt to obtain convergence to the single shot Nash equilibrium when playing Shapley's game in self-play without using more information than WoLF-PHC uses. Partial Commitment WoLF-PHC (PCWoLF-PHC), which performs best on Shapley's game, is tested on other matrix games and shown to produce satisfactory results.","abstract_html":"Policy Hill Climbing (PHC) is a reinforcement learning algorithm that extends Q-learning to learn probabilistic policies for multi-agent games. WoLF-PHC extends PHC with the "win or learn fast" principle. A proof that PHC will diverge in self-play when playing Shapley's game is given, and WoLF-PHC is shown empirically to diverge as well. Various WoLF-PHC based modifications were created, evaluated, and compared in an attempt to obtain convergence to the single shot Nash equilibrium when playing Shapley's game in self-play without using more information than WoLF-PHC uses. Partial Commitment WoLF-PHC (PCWoLF-PHC), which performs best on Shapley's game, is tested on other matrix games and shown to produce satisfactory results.","abstract_has_math":false,"creators":["Cook, Philip R."],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:28:54Z","subjects":["Matrix Games","Multi-agent Systems","Nash equilibrium","convergence","reinforcement learning","machine learning","algorithm","Computer Sciences"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/1222","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Cook, Philip R."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2007-09-27T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Matrix Games","Multi-agent Systems","Nash equilibrium","convergence","reinforcement learning","machine learning","algorithm","Computer Sciences"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsarchive.byu.edu/etd/1222","https://scholarsarchive.byu.edu/context/etd/article/2221/viewcontent/ETD_CISOPTR_1226.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Physical and Mathematical Sciences; Computer Science"]},{"key":"dc:description.abstract","label":"Abstract","values":["Policy Hill Climbing (PHC) is a reinforcement learning algorithm that extends Q-learning to learn probabilistic policies for multi-agent games. WoLF-PHC extends PHC with the \"win or learn fast\" principle. A proof that PHC will diverge in self-play when playing Shapley's game is given, and WoLF-PHC is shown empirically to diverge as well. Various WoLF-PHC based modifications were created, evaluated, and compared in an attempt to obtain convergence to the single shot Nash equilibrium when playing Shapley's game in self-play without using more information than WoLF-PHC uses. Partial Commitment WoLF-PHC (PCWoLF-PHC), which performs best on Shapley's game, is tested on other matrix games and shown to produce satisfactory results."]},{"key":"dc:format","label":"Dc Format","values":["application:pdf"]},{"key":"dc:source","label":"Dc Source","values":["Brigham Young University - Provo"]},{"key":"dc:title","label":"Title","values":["Limitations and Extensions of the WoLF-PHC Algorithm"]}]}],"canonical_facts":{"dc:creator":["Cook, Philip R."],"dc:date":["2007-09-27T07:00:00Z"],"dc:description":["Physical and Mathematical Sciences; Computer Science"],"dc:description.abstract":["Policy Hill Climbing (PHC) is a reinforcement learning algorithm that extends Q-learning to learn probabilistic policies for multi-agent games. WoLF-PHC extends PHC with the \"win or learn fast\" principle. A proof that PHC will diverge in self-play when playing Shapley's game is given, and WoLF-PHC is shown empirically to diverge as well. Various WoLF-PHC based modifications were created, evaluated, and compared in an attempt to obtain convergence to the single shot Nash equilibrium when playing Shapley's game in self-play without using more information than WoLF-PHC uses. Partial Commitment WoLF-PHC (PCWoLF-PHC), which performs best on Shapley's game, is tested on other matrix games and shown to produce satisfactory results."],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/1222","https://scholarsarchive.byu.edu/context/etd/article/2221/viewcontent/ETD_CISOPTR_1226.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["Matrix Games","Multi-agent Systems","Nash equilibrium","convergence","reinforcement learning","machine learning","algorithm","Computer Sciences"],"dc:title":["Limitations and Extensions of the WoLF-PHC Algorithm"],"dc:type":["Thesis"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:28:54Z"}