{"id":"https://openalex.org/W4382056236","doi":"https://doi.org/10.1137/22m1508613","title":"Data-Driven Mirror Descent with Input-Convex Neural Networks","display_name":"Data-Driven Mirror Descent with Input-Convex Neural Networks","publication_year":2023,"publication_date":"2023-06-26","ids":{"openalex":"https://openalex.org/W4382056236","doi":"https://doi.org/10.1137/22m1508613"},"language":"en","primary_location":{"id":"doi:10.1137/22m1508613","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1508613","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/22m1508613","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090328438","display_name":"Hong Ye Tan","orcid":"https://orcid.org/0000-0001-5057-7535"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Hong Ye Tan","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102928532","display_name":"Subhadip Mukherjee","orcid":"https://orcid.org/0000-0002-7957-8758"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]},{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB","IN"],"is_corresponding":false,"raw_author_name":"Subhadip Mukherjee","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK","Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur, India","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054394663","display_name":"Junqi Tang","orcid":"https://orcid.org/0000-0003-4996-6079"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Junqi Tang","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK","School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033880300","display_name":"Carola\u2010Bibiane Sch\u00f6nlieb","orcid":"https://orcid.org/0000-0003-0099-6306"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Carola-Bibiane Sch\u00f6nlieb","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1825,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.73751666,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"5","issue":"2","first_page":"558","last_page":"587"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998000264167786,"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/T10057","display_name":"Face and Expression Recognition","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6000233292579651},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5705444812774658},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5609884262084961},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5550647974014282},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4987173080444336},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48670294880867004},{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.45583322644233704},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.44329845905303955},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4160490036010742},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39271408319473267},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.38362395763397217},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3406914472579956},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3392876088619232},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.1461193561553955}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6000233292579651},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5705444812774658},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5609884262084961},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5550647974014282},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4987173080444336},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48670294880867004},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.45583322644233704},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44329845905303955},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4160490036010742},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39271408319473267},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.38362395763397217},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3406914472579956},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3392876088619232},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.1461193561553955},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m1508613","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1508613","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/c0516413-7872-4789-9397-ed7fc9631d56","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/c0516413-7872-4789-9397-ed7fc9631d56","pdf_url":"https://pure-oai.bham.ac.uk/ws/files/205887569/ICNN_Mirror_Descent_pure.pdf","source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Tan, H Y, Mukherjee, S, Tang, J & Scho\u0308nlieb, C-B 2023, 'Data-Driven Mirror Descent with Input-Convex Neural Networks', SIAM Journal on Mathematics of Data Science, vol. 5, no. 2, pp. 558-587. https://doi.org/10.1137/22M1508613","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1137/22m1508613","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1508613","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1424764954","display_name":null,"funder_award_id":"EP/T017961/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1755984640","display_name":null,"funder_award_id":"EP/N014588/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2861870519","display_name":"Robust and Efficient Analysis Approaches of Remote Imagery for Assessing Population and Forest Health in India","funder_award_id":"EP/T003553/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2978676218","display_name":null,"funder_award_id":"EP/S026045/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6096796963","display_name":"Cambridge Mathematics of Information in Healthcare (CMIH)","funder_award_id":"EP/T017961/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6579398875","display_name":"EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging","funder_award_id":"EP/N014588/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7243674615","display_name":null,"funder_award_id":"EP/V029428/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7534764778","display_name":"Combining Knowledge And Data Driven Approaches to Inverse Imaging Problems","funder_award_id":"EP/V029428/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G763414266","display_name":"PET++: Improving Localisation, Diagnosis and Quantification in Clinical and Medical PET Imaging with Randomised Optimisation","funder_award_id":"EP/S026045/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320307773","display_name":"GlaxoSmithKline","ror":"https://ror.org/01xsqw823"},{"id":"https://openalex.org/F4320313467","display_name":"Alan Turing Institute","ror":"https://ror.org/035dkdb55"},{"id":"https://openalex.org/F4320317743","display_name":"Masason Foundation","ror":null},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1506806321","https://openalex.org/W2016384870","https://openalex.org/W2018493294","https://openalex.org/W2024484010","https://openalex.org/W2030161963","https://openalex.org/W2087416986","https://openalex.org/W2092663520","https://openalex.org/W2129427957","https://openalex.org/W2535496140","https://openalex.org/W2541711215","https://openalex.org/W2964037929","https://openalex.org/W2999156669","https://openalex.org/W3140735157","https://openalex.org/W4206742934","https://openalex.org/W4212774754","https://openalex.org/W4249513058","https://openalex.org/W4287691839"],"related_works":["https://openalex.org/W2774022454","https://openalex.org/W1971945429","https://openalex.org/W4309208344","https://openalex.org/W4293271904","https://openalex.org/W4313177131","https://openalex.org/W3163340401","https://openalex.org/W3020853991","https://openalex.org/W2400034325","https://openalex.org/W4292651679","https://openalex.org/W2499557797"],"abstract_inverted_index":{"Learning-to-optimize":[0],"is":[1,135,146],"an":[2,100,163],"emerging":[3],"framework":[4],"that":[5],"seeks":[6],"to":[7,26,86,148],"speed":[8],"up":[9],"the":[10,49,54,60,77,88,95,108,114,120,132,143,156],"solution":[11],"of":[12,33,107,127,131],"certain":[13],"optimization":[14,21,29,43,73],"problems":[15,176],"by":[16,93,112],"leveraging":[17],"training":[18],"data.":[19,62],"Learned":[20],"solvers":[22,74],"have":[23],"been":[24],"shown":[25],"outperform":[27],"classical":[28,78],"algorithms":[30],"in":[31],"terms":[32],"convergence":[34,152],"speed,":[35],"especially":[36],"for":[37,70,155],"convex":[38,72,97,175],"problems.":[39],"Many":[40],"existing":[41],"data-driven":[42],"methods":[44],"are":[45,110],"based":[46,75],"on":[47,76,173,194],"parameterizing":[48],"update":[50],"step":[51],"and":[52,168,182],"learning":[53,183],"optimal":[55,89],"parameters":[56,106],"(typically":[57],"scalars)":[58],"from":[59],"available":[61],"We":[63,150],"propose":[64],"a":[65,124,184],"novel":[66],"functional":[67],"parameterization":[68],"approach":[69,161],"learned":[71,111,158],"mirror":[79,133,159,166],"descent":[80,160],"(MD)":[81],"algorithm.":[82],"Specifically,":[83],"we":[84],"seek":[85],"learn":[87],"Bregman":[90],"distance<br/>in":[91],"MD":[92,121],"modeling":[94],"underlying":[96],"function":[98,117],"using":[99,138],"input-convex":[101],"neural":[102,140],"network":[103],"(ICNN).":[104],"The":[105,129],"ICNN":[109],"minimizing":[113],"target":[115],"objective":[116],"evaluated":[118],"at":[119],"iterate":[122],"after":[123],"predetermined":[125],"number":[126],"iterations.":[128],"inverse":[130,145,165],"map":[134,167],"modeled":[136],"approximately":[137],"another":[139],"network,":[141],"as":[142,178],"exact":[144],"intractable":[147],"compute.":[149],"derive":[151],"rate":[153],"bounds":[154],"proposed":[157],"with":[162],"approximate":[164],"perform":[169],"extensive":[170],"numerical":[171],"evaluation":[172],"various":[174],"such":[177],"image":[179],"inpainting,":[180],"denoising,":[181],"two-class":[185],"support":[186],"vector":[187],"machine":[188],"classifier":[189,193],"and<br/>a":[190],"multiclass":[191],"linear":[192],"fixed":[195],"features.":[196]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}