{"id":"https://openalex.org/W7137973805","doi":"https://doi.org/10.1609/aaai.v40i30.39746","title":"Methods for Optimization Problems with Markovian Stochasticity and Non-Euclidean Geometry","display_name":"Methods for Optimization Problems with Markovian Stochasticity and Non-Euclidean Geometry","publication_year":2026,"publication_date":"2026-03-14","ids":{"openalex":"https://openalex.org/W7137973805","doi":"https://doi.org/10.1609/aaai.v40i30.39746"},"language":null,"primary_location":{"id":"doi:10.1609/aaai.v40i30.39746","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v40i30.39746","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/39746/43707","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ojs.aaai.org/index.php/AAAI/article/download/39746/43707","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5099097234","display_name":"Vladimir Solodkin","orcid":null},"institutions":[{"id":"https://openalex.org/I4392021246","display_name":"AIRI - Artificial Intelligence Research Institute","ror":"https://ror.org/014a87f14","country_code":"RU","type":"nonprofit","lineage":["https://openalex.org/I4392021246"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Vladimir Solodkin","raw_affiliation_strings":["Moscow Independent Research Institute of Artificial Intelligence (MIRAI)\nBasic Research of Artificial Intelligence Laboratory (BRAIn Lab)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow Independent Research Institute of Artificial Intelligence (MIRAI)\nBasic Research of Artificial Intelligence Laboratory (BRAIn Lab)","institution_ids":["https://openalex.org/I4392021246"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129717165","display_name":"Andrey Veprikov","orcid":null},"institutions":[{"id":"https://openalex.org/I4210164862","display_name":"Artificial Intelligence in Medicine (Canada)","ror":"https://ror.org/05p590m36","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210164862"]},{"id":"https://openalex.org/I4392021246","display_name":"AIRI - Artificial Intelligence Research Institute","ror":"https://ror.org/014a87f14","country_code":"RU","type":"nonprofit","lineage":["https://openalex.org/I4392021246"]}],"countries":["CA","RU"],"is_corresponding":false,"raw_author_name":"Andrey Veprikov","raw_affiliation_strings":["Moscow Independent Research Institute of Artificial Intelligence (MIRAI)\nBasic Research of Artificial Intelligence Laboratory (BRAIn Lab)\nSB AI Lab"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow Independent Research Institute of Artificial Intelligence (MIRAI)\nBasic Research of Artificial Intelligence Laboratory (BRAIn Lab)\nSB AI Lab","institution_ids":["https://openalex.org/I4392021246","https://openalex.org/I4210164862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129705321","display_name":"Alexander Chernyavskiy","orcid":null},"institutions":[{"id":"https://openalex.org/I4392021246","display_name":"AIRI - Artificial Intelligence Research Institute","ror":"https://ror.org/014a87f14","country_code":"RU","type":"nonprofit","lineage":["https://openalex.org/I4392021246"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Alexander Chernyavskiy","raw_affiliation_strings":["Moscow Independent Research Institute of Artificial Intelligence (MIRAI)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow Independent Research Institute of Artificial Intelligence (MIRAI)","institution_ids":["https://openalex.org/I4392021246"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5129698935","display_name":"Aleksandr Beznosikov","orcid":null},"institutions":[{"id":"https://openalex.org/I4392021246","display_name":"AIRI - Artificial Intelligence Research Institute","ror":"https://ror.org/014a87f14","country_code":"RU","type":"nonprofit","lineage":["https://openalex.org/I4392021246"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Aleksandr Beznosikov","raw_affiliation_strings":["Moscow Independent Research Institute of Artificial Intelligence (MIRAI)\nBasic Research of Artificial Intelligence Laboratory (BRAIn Lab)\nInnopolis University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow Independent Research Institute of Artificial Intelligence (MIRAI)\nBasic Research of Artificial Intelligence Laboratory (BRAIn Lab)\nInnopolis University","institution_ids":["https://openalex.org/I4392021246"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1699905,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"30","first_page":"25508","last_page":"25517"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8995000123977661,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8995000123977661,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.032499998807907104,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.02810000069439411,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.722599983215332},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6753000020980835},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6164000034332275},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5825999975204468},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5282999873161316},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5141000151634216},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5020999908447266},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.43470001220703125},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.39399999380111694},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.38339999318122864}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.722599983215332},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6753000020980835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6452999711036682},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6164000034332275},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5932999849319458},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5825999975204468},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5282999873161316},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5141000151634216},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5020999908447266},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46950000524520874},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.43470001220703125},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.39399999380111694},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.38339999318122864},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.3804999887943268},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3797000050544739},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.37860000133514404},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.3718999922275543},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.3158999979496002},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.2971000075340271},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.2824999988079071},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.28119999170303345},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.257099986076355}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1609/aaai.v40i30.39746","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v40i30.39746","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/39746/43707","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1609/aaai.v40i30.39746","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v40i30.39746","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/39746/43707","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.48136889934539795,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7137973805.pdf","grobid_xml":"https://content.openalex.org/works/W7137973805.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"examines":[2],"a":[3,20],"variety":[4],"of":[5,23,39,47],"classical":[6],"optimization":[7],"problems,":[8],"including":[9],"well-known":[10],"minimization":[11,75],"tasks":[12],"and":[13,55,73,77,82],"more":[14],"general":[15],"variational":[16,78],"inequalities.":[17],"We":[18,42],"consider":[19,44],"stochastic":[21,93],"formulation":[22],"these":[24],"problems":[25,76],"and,":[26],"unlike":[27],"most":[28],"previous":[29],"work,":[30],"we":[31,113],"take":[32],"into":[33],"account":[34],"the":[35,40,45,48,61,98,110,115],"complex":[36],"Markov":[37],"nature":[38],"noise.":[41],"also":[43],"geometry":[46],"problem":[49],"in":[50,103],"an":[51],"arbitrary":[52],"non-Euclidean":[53],"setting":[54],"propose":[56],"four":[57],"methods":[58],"based":[59],"on":[60,119],"Mirror":[62],"Descent":[63],"iteration":[64],"technique.":[65],"The":[66,85],"theoretical":[67,111],"analysis":[68],"is":[69],"provided":[70,102],"for":[71,91],"smooth":[72],"convex":[74],"inequalities":[79],"with":[80],"Lipschitz":[81],"monotone":[83],"operators.":[84],"convergence":[86],"guarantees":[87],"obtained":[88],"are":[89],"optimal":[90],"first-order":[92],"methods,":[94],"as":[95],"evidenced":[96],"by":[97],"lower":[99],"bound":[100],"estimates":[101],"this":[104],"paper.":[105],"In":[106],"order":[107],"to":[108],"validate":[109],"results,":[112],"present":[114],"relevant":[116],"numerical":[117],"experiments":[118],"various":[120],"reinforcement":[121],"learning":[122],"tasks.":[123]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-18T00:00:00"}
