{"id":"https://openalex.org/W7214614441","doi":"https://doi.org/10.48550/arxiv.2609.31107","title":"Bayesian Optimization with Fisher Information Geometry: Gradient Bounds and Trust-Region Methods","display_name":"Bayesian Optimization with Fisher Information Geometry: Gradient Bounds and Trust-Region Methods","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214614441","doi":"https://doi.org/10.48550/arxiv.2609.31107"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.31107","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31107","pdf_url":"https://arxiv.org/pdf/2609.31107","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.31107","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010938706","display_name":"Saksham Kiroriwal","orcid":"https://orcid.org/0009-0003-7820-3270","observed_orcids":["https://orcid.org/0009-0003-7820-3270"]},"institutions":[{"id":"https://openalex.org/I4210111500","display_name":"Fraunhofer Institute of Optronics, System Technologies and Image Exploitation","ror":"https://ror.org/01zx97922","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210111500","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kiroriwal, Saksham","raw_affiliation_strings":["Cognitive Industrial Systems , Fraunhofer IOSB , Karlsruhe , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cognitive Industrial Systems , Fraunhofer IOSB , Karlsruhe , Germany","institution_ids":["https://openalex.org/I4210111500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079417865","display_name":"Julius Pfrommer","orcid":"https://orcid.org/0000-0002-4204-6758","observed_orcids":["https://orcid.org/0000-0002-4204-6758"]},"institutions":[{"id":"https://openalex.org/I4210111500","display_name":"Fraunhofer Institute of Optronics, System Technologies and Image Exploitation","ror":"https://ror.org/01zx97922","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210111500","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Pfrommer, Julius","raw_affiliation_strings":["Cognitive Industrial Systems , Fraunhofer IOSB , Karlsruhe , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cognitive Industrial Systems , Fraunhofer IOSB , Karlsruhe , Germany","institution_ids":["https://openalex.org/I4210111500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5153366948","display_name":"J\u00fcrgen Beyerer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I4210111500","display_name":"Fraunhofer Institute of Optronics, System Technologies and Image Exploitation","ror":"https://ror.org/01zx97922","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210111500","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Beyerer, J\u00fcrgen","raw_affiliation_strings":["Cognitive Industrial Systems , Fraunhofer IOSB , Karlsruhe , Germany","Karlsruhe Institute of Technology (KIT) , Karlsruhe , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cognitive Industrial Systems , Fraunhofer IOSB , Karlsruhe , Germany","institution_ids":["https://openalex.org/I4210111500"]},{"raw_affiliation_string":"Karlsruhe Institute of Technology (KIT) , Karlsruhe , Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.986299991607666,"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"}},"topics":[{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.986299991607666,"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"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.004699999932199717,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.003700000001117587,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bayesian-optimization","display_name":"Bayesian optimization","score":1.0},{"id":"https://openalex.org/keywords/fisher-information-metric","display_name":"Fisher information metric","score":0.878000020980835},{"id":"https://openalex.org/keywords/information-geometry","display_name":"information geometry","score":0.9200000166893005},{"id":"https://openalex.org/keywords/acquisition-functions","display_name":"acquisition functions","score":0.7760000228881836},{"id":"https://openalex.org/keywords/gradient-bounds","display_name":"gradient bounds","score":0.9190000295639038},{"id":"https://openalex.org/keywords/trust-region-method","display_name":"trust region method","score":0.8980000019073486},{"id":"https://openalex.org/keywords/reparameterization","display_name":"reparameterization","score":0.6809999942779541},{"id":"https://openalex.org/keywords/vanishing-gradient","display_name":"gradient vanishing","score":0.7609999775886536},{"id":"https://openalex.org/keywords/high-dimensional-optimization","display_name":"high-dimensional optimization","score":0.8730000257492065},{"id":"https://openalex.org/keywords/gaussian-process-kernels","display_name":"Gaussian process kernels","score":0.6690000295639038}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6083999872207642},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.5983999967575073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5831000208854675},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5609999895095825},{"id":"https://openalex.org/C2778049539","wikidata":"https://www.wikidata.org/wiki/Q17002908","display_name":"Bayesian optimization","level":2,"score":0.5501000285148621},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.5351999998092651},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5091999769210815},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.48249998688697815},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4708000123500824},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4162999987602234},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41589999198913574},{"id":"https://openalex.org/C3020402766","wikidata":"https://www.wikidata.org/wiki/Q104376712","display_name":"Prior information","level":2,"score":0.41359999775886536},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.41269999742507935},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4106999933719635},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4097999930381775},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.35420000553131104},{"id":"https://openalex.org/C83282275","wikidata":"https://www.wikidata.org/wiki/Q7435350","display_name":"Scoring algorithm","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3310999870300293},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.30559998750686646},{"id":"https://openalex.org/C113336015","wikidata":"https://www.wikidata.org/wiki/Q574010","display_name":"Complete information","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2605000138282776},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.257099986076355},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.2558000087738037}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.31107","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31107","pdf_url":"https://arxiv.org/pdf/2609.31107","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.31107","doi":"https://doi.org/10.48550/arxiv.2609.31107","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.31107","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.31107","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31107","pdf_url":"https://arxiv.org/pdf/2609.31107","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214614441.pdf","grobid_xml":"https://content.openalex.org/works/W7214614441.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1699163263","https://openalex.org/W2247585390","https://openalex.org/W2765934517","https://openalex.org/W2775304796","https://openalex.org/W2873705236","https://openalex.org/W3170604603","https://openalex.org/W3172979332","https://openalex.org/W4379089641","https://openalex.org/W4391591380","https://openalex.org/W4391631267","https://openalex.org/W4407571899","https://openalex.org/W4415036091","https://openalex.org/W4416932885","https://openalex.org/W6969750329","https://openalex.org/W7014847825"],"related_works":["https://openalex.org/W7077870131","https://openalex.org/W4415036091","https://openalex.org/W3158958981","https://openalex.org/W2964066221","https://openalex.org/W2963792467","https://openalex.org/W4416932885","https://openalex.org/W4295690859","https://openalex.org/W7128742833","https://openalex.org/W4415795393","https://openalex.org/W4412828489"],"abstract_inverted_index":{"We":[0],"study":[1],"Bayesian":[2],"optimization":[3],"(BO)":[4],"through":[5,17],"the":[6,13,18,28,38,78,93,109],"lens":[7],"of":[8,40,58,80,108],"information":[9,15],"geometry.":[10],"Pulling":[11],"back":[12],"Fisher":[14],"metric":[16],"surrogate":[19],"posterior":[20],"map":[21],"yields":[22],"a":[23,55,73,112,124],"local":[24,133],"sensitivity":[25],"tensor":[26],"on":[27,37,118,156],"input":[29,88,102],"space,":[30],"which":[31],"leads":[32],"to":[33,76,104,140,149],"an":[34,101,106],"upper":[35,67],"bound":[36,68],"gradient":[39],"reparameterizable":[41],"acquisition":[42,82],"functions":[43,83],"(AFs).":[44],"This":[45],"view":[46],"explains":[47],"vanishing-gradient":[48],"behavior":[49,79],"in":[50,86],"high-dimensional":[51],"BO":[52,126],"and":[53,63,146],"provides":[54],"common":[56],"interpretation":[57],"heuristics":[59],"such":[60],"as":[61,72,90],"RAASP":[62],"dimension-scaled":[64],"lengthscales.":[65],"The":[66],"can":[69],"also":[70,96],"serve":[71],"generic":[74],"recipe":[75],"understand":[77],"new":[81],"or":[84],"surrogates":[85],"high":[87],"dimensions":[89],"well.":[91],"Using":[92],"bounds,":[94],"we":[95,121],"identify":[97],"necessary":[98],"conditions":[99],"for":[100,111],"location":[103],"be":[105],"optimizer":[107],"AF":[110],"univariate":[113],"Gaussian":[114],"predictive":[115],"posterior.":[116],"Building":[117],"this":[119],"analysis,":[120],"propose":[122],"FITR,":[123],"trust-region-based":[125],"method":[127],"that":[128],"replaces":[129],"lengthscale-based":[130],"scaling":[131],"with":[132,143],"pullback-Fisher":[134],"weights.":[135],"FITR":[136,152],"is":[137],"not":[138],"restricted":[139],"GP":[141],"kernels":[142],"explicit":[144],"lengthscales":[145],"easily":[147],"generalizes":[148],"non-isotropic":[150],"surrogates.":[151],"shows":[153],"competitive":[154],"performance":[155],"several":[157],"benchmarks.":[158]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-29T00:00:00"}