{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T23:54:00Z","timestamp":1781654040181,"version":"3.54.5"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T00:00:00Z","timestamp":1781568000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T00:00:00Z","timestamp":1781568000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/W035847\/1"],"award-info":[{"award-number":["EP\/W035847\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["KO 1737\/6-2"],"award-info":[{"award-number":["KO 1737\/6-2"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2026,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We provide abstract, general and highly uniform rates of asymptotic regularity for a generalized stochastic Halpern-style iteration, which incorporates a second mapping in the style of a Krasnoselskii-Mann iteration. This iteration is general in two ways: First, it incorporates stochasticity completely abstractly, rather than fixing a sampling method; second, it includes as special cases stochastic versions of various schemes from the optimization literature, including Halpern\u2019s iteration as well as a Krasnoselskii-Mann iteration with Tikhonov regularization terms in the sense of Bo\u0163, Csetnek and Meier (where this stochastic variant of the latter is considered for the first time in this paper). For these specific cases, we obtain linear rates of asymptotic regularity, matching (or improving) the currently best known rates for these iterations in stochastic optimization, and quadratic rates of asymptotic regularity are obtained in the context of inner product spaces for the general iteration. We conclude by discussing how variance can be managed in practice through sampling methods in the style of minibatching, how our convergence rates can be adapted to provide oracle complexity bounds, and by sketching how the schemes presented here can be instantiated in the context of reinforcement learning to yield novel methods for Q-learning.<\/jats:p>","DOI":"10.1007\/s10957-026-03032-z","type":"journal-article","created":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T06:40:15Z","timestamp":1781592015000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Asymptotic Regularity of a Generalised Stochastic Halpern Scheme"],"prefix":"10.1007","volume":"210","author":[{"given":"Nicholas","family":"Pischke","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2541-4678","authenticated-orcid":false,"given":"Thomas","family":"Powell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,16]]},"reference":[{"key":"3032_CR1","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1080\/10556788.2018.1457151","volume":"34","author":"R Bo\u0163","year":"2019","unstructured":"Bo\u0163, R., Csetnek, E., Meier, D.: Inducing strong convergence into the asymptotic behaviour of proximal splitting algorithms in Hilbert spaces. Optimization Methods and Software 34, 489\u2013514 (2019)","journal-title":"Optimization Methods and Software"},{"issue":"8","key":"3032_CR2","first-page":"1","volume":"24","author":"R Bo\u0163","year":"2023","unstructured":"Bo\u0163, R., Sedlmayer, M., Vuong, P.T.: A relaxed inertial forward-backward-forward algorithm for solving monotone inclusions with application to GANs. J. Mach. Learn. Res. 24(8), 1\u201337 (2023)","journal-title":"J. Mach. Learn. Res."},{"key":"3032_CR3","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1137\/22M1515550","volume":"62","author":"M Bravo","year":"2024","unstructured":"Bravo, M., Cominetti, R.: Stochastic fixed-point iterations for nonexpansive maps: Convergence and error bounds. SIAM J. Control. Optim. 62, 191\u2013219 (2024)","journal-title":"SIAM J. Control. Optim."},{"key":"3032_CR4","doi-asserted-by":"crossref","unstructured":"Bravo, M., Contreras, J.: Stochastic Halpern iteration in normed spaces and applications to reinforcement learning. Mathematical Programming (2026). (). (In press)","DOI":"10.1007\/s10107-026-02345-1"},{"key":"3032_CR5","doi-asserted-by":"crossref","unstructured":"Cai, X., Song, C., Guzm\u00e1n, C., Diakonikolas, J.: Stochastic Halpern iteration with variance reduction for stochastic monotone inclusions. In: Koyejo, S., Mohamed, S., Agarwal, A., Belgrave, D., Cho, K., Oh, A. (eds.) Proceedings of NIPS\u201922, pp. 24766\u201324779. Curran Associates Inc, Red Hook, NY, USA (2022)","DOI":"10.52202\/068431-1796"},{"key":"3032_CR6","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s10957-023-02192-6","volume":"197","author":"H Cheval","year":"2023","unstructured":"Cheval, H., Kohlenbach, U., Leu\u015ftean, L.: On modified Halpern and Tikhonov-Mann iterations. J. Optim. Theory Appl. 197, 233\u2013251 (2023)","journal-title":"J. Optim. Theory Appl."},{"issue":"6","key":"3032_CR7","doi-asserted-by":"publisher","first-page":"2225","DOI":"10.1080\/10556788.2022.2060974","volume":"37","author":"H Cheval","year":"2022","unstructured":"Cheval, H., Leu\u015ftean, L.: Quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration. Optimization Methods & Software 37(6), 2225\u20132240 (2022)","journal-title":"Optimization Methods & Software"},{"issue":"353","key":"3032_CR8","first-page":"1323","volume":"94","author":"H Cheval","year":"2025","unstructured":"Cheval, H., Leu\u015ftean, L.: Linear rates of asymptotic regularity for Halpern-type iterations. Math. Comput. 94(353), 1323\u20131333 (2025)","journal-title":"Math. Comput."},{"issue":"3","key":"3032_CR9","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1090\/S0002-9947-1936-1501880-4","volume":"40","author":"J Clarkson","year":"1936","unstructured":"Clarkson, J.: Uniformly convex spaces. Trans. Am. Math. Soc. 40(3), 396\u2013414 (1936)","journal-title":"Trans. Am. Math. Soc."},{"key":"3032_CR10","doi-asserted-by":"crossref","unstructured":"Cuntavepanit, A., Panyanak, B.: Strong convergence of modified Halpern iterations in CAT(0) spaces. Fixed Point Theory and Applications (2011). Art. ID 869458, 11pp","DOI":"10.1155\/2011\/869458"},{"key":"3032_CR11","unstructured":"Diakonikolas, J.: Halpern iteration for near-optimal and parameter-free monotone inclusion and strong solutions to variational inequalities. In: Abernethy, J., Agarwal, S. (eds.) Proceedings of COLT\u201920, Proceedings of Machine Learning Research, vol. 125, pp. 1428\u20131451. (2020)"},{"issue":"4","key":"3032_CR12","doi-asserted-by":"publisher","first-page":"1263","DOI":"10.1007\/s11590-020-01635-7","volume":"15","author":"B Dinis","year":"2021","unstructured":"Dinis, B., Pinto, P.: On the convergence of algorithms with Tikhonov regularization terms. Optimization Letters 15(4), 1263\u20131276 (2021)","journal-title":"Optimization Letters"},{"issue":"2","key":"3032_CR13","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1137\/22M1511199","volume":"33","author":"B Dinis","year":"2023","unstructured":"Dinis, B., Pinto, P.: Strong convergence for the alternating Halpern-Mann iteration in CAT(0) spaces. SIAM J. Optim. 33(2), 785\u2013815 (2023)","journal-title":"SIAM J. Optim."},{"issue":"6","key":"3032_CR14","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1090\/S0002-9904-1967-11864-0","volume":"73","author":"B Halpern","year":"1967","unstructured":"Halpern, B.: Fixed points of nonexpanding maps. Bull. Am. Math. Soc. 73(6), 957\u2013961 (1967)","journal-title":"Bull. Am. Math. Soc."},{"key":"3032_CR15","unstructured":"Hasselt, H.: Double Q-learning. In: Lafferty, J., Williams, C., Shawe-Taylor, J., Zemel, R., Culotta, A. (eds.) Proceedings of NIPS\u201910, vol. 2, pp. 2613\u20132621. Curran Associates Inc, Red Hook, NY, USA (2010)"},{"key":"3032_CR16","doi-asserted-by":"crossref","unstructured":"Kim, T.H., Xu, H.K.: Strong convergence of modified Mann iterations. Nonlinear Analysis. Theory, Methods & Applications 61(1\u20132), 51\u201360 (2005)","DOI":"10.1016\/j.na.2004.11.011"},{"key":"3032_CR17","volume-title":"Probability Theory: A Comprehensive Course","author":"A Klenke","year":"2020","unstructured":"Klenke, A.: Probability Theory: A Comprehensive Course, 3rd edn. Universitext, Springer Cham (2020)","edition":"3"},{"issue":"2","key":"3032_CR18","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1016\/S0022-247X(03)00028-3","volume":"279","author":"U Kohlenbach","year":"2003","unstructured":"Kohlenbach, U.: Uniform asymptotic regularity for Mann iterates. J. Math. Anal. Appl. 279(2), 531\u2013544 (2003)","journal-title":"J. Math. Anal. Appl."},{"key":"3032_CR19","volume-title":"Applied Proof Theory: Proof Interpretations and their Use in Mathematics","author":"U Kohlenbach","year":"2008","unstructured":"Kohlenbach, U.: Applied Proof Theory: Proof Interpretations and their Use in Mathematics. Springer Monographs in Mathematics. Springer-Verlag, Berlin Heidelberg (2008)"},{"key":"3032_CR20","doi-asserted-by":"crossref","unstructured":"Kohlenbach, U.F.E., Browder, R., Wittmann: On quantitative versions of theorems due to. Adv. Math. 226(3), 2764\u20132795 (2011)","DOI":"10.1016\/j.aim.2010.10.002"},{"key":"3032_CR21","doi-asserted-by":"crossref","unstructured":"Kohlenbach, U.: Proof-theoretic Methods in Nonlinear Analysis. In: B.\u00a0Sirakov, P.N. de\u00a0Souza, M.\u00a0Viana (eds.) Proceedings of ICM 2018, vol.\u00a02, pp. 61\u201382. World Scientific (2019)","DOI":"10.1142\/9789813272880_0045"},{"key":"3032_CR22","doi-asserted-by":"publisher","first-page":"2526","DOI":"10.1016\/j.aim.2012.06.028","volume":"231","author":"U Kohlenbach","year":"2012","unstructured":"Kohlenbach, U., Leu\u015ftean, L.: Effective metastability of Halpern iterates in CAT(0) spaces. Adv. Math. 231, 2526\u20132556 (2012)","journal-title":"Adv. Math."},{"issue":"1971","key":"3032_CR23","doi-asserted-by":"publisher","first-page":"3449","DOI":"10.1098\/rsta.2011.0329","volume":"370","author":"U Kohlenbach","year":"2012","unstructured":"Kohlenbach, U., Leu\u015ftean, L.: On the computational content of convergence proofs via Banach limits. Phil. Trans. R. Soc. A 370(1971), 3449\u20133463 (2012)","journal-title":"Phil. Trans. R. Soc. A"},{"key":"3032_CR24","unstructured":"Krasnosel\u2019skii, M.: Two remarks on the method of successive approximations. Uspekhi Matematicheskikh Nauk 10(1(63)), 123\u2013127 (1955)"},{"key":"3032_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20212-4","volume-title":"Probability in Banach Spaces","author":"M Ledoux","year":"1991","unstructured":"Ledoux, M., Talagrand, M.: Probability in Banach Spaces. Classics in Mathematics. Springer-Verlag, Berlin Heidelberg (1991)"},{"key":"3032_CR26","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1016\/j.jmaa.2006.01.081","volume":"325","author":"L Leu\u015ftean","year":"2007","unstructured":"Leu\u015ftean, L.: A quadratic rate of asymptotic regularity for CAT(0)-spaces. J. Math. Anal. Appl. 325, 386\u2013399 (2007)","journal-title":"J. Math. Anal. Appl."},{"issue":"11","key":"3032_CR27","first-page":"1680","volume":"13","author":"L Leu\u015ftean","year":"2007","unstructured":"Leu\u015ftean, L.: Rates of asymptotic regularity for Halpern iterations of nonexpansive mappings. J. Univ. Comput. Sci. 13(11), 1680\u20131691 (2007)","journal-title":"J. Univ. Comput. Sci."},{"key":"3032_CR28","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1090\/conm\/513\/10084","volume-title":"Nonlinear Analysis and Optimization I: Nonlinear Analysis","author":"L Leu\u015ftean","year":"2010","unstructured":"Leu\u015ftean, L.: Nonexpansive iterations in uniformly convex W-hyperbolic spaces. In: Leizarowitz, A., Mordukhovich, B., Shafrir, I., Zaslavski, A. (eds.) Nonlinear Analysis and Optimization I: Nonlinear Analysis, pp. 193\u2013209. American Mathematical Society, Providence, RI, USA (2010)"},{"issue":"1","key":"3032_CR29","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/s10589-021-00263-w","volume":"79","author":"L Leu\u015ftean","year":"2021","unstructured":"Leu\u015ftean, L., Pinto, P.: Quantitative results on a Halpern-type proximal point algorithm. Comput. Optim. Appl. 79(1), 101\u2013125 (2021)","journal-title":"Comput. Optim. Appl."},{"key":"3032_CR30","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1007\/s11590-023-02002-y","volume":"18","author":"L Leu\u015ftean","year":"2024","unstructured":"Leu\u015ftean, L., Pinto, P.: Rates of asymptotic regularity for the alternating Halpern-Mann iteration. Optimization Letters 18, 529\u2013543 (2024)","journal-title":"Optimization Letters"},{"key":"3032_CR31","doi-asserted-by":"crossref","unstructured":"Liang, L., Xu, Z., Toh, K.C., Zhu, J.J.: An Inexact Halpern Iteration with Application to Distributionally Robust Optimization. Journal of Optimization Theory and Applications 206 (2025). 58, 41pp","DOI":"10.1007\/s10957-025-02744-y"},{"issue":"2","key":"3032_CR32","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1007\/s11590-020-01617-9","volume":"15","author":"F Lieder","year":"2021","unstructured":"Lieder, F.: On the convergence rate of the Halpern-iteration. Optimization Letters 15(2), 405\u2013418 (2021)","journal-title":"Optimization Letters"},{"key":"3032_CR33","volume-title":"Classical Banach Spaces II, Ergebnisse der Mathematik in ihrer Grenzgebiete","author":"J Lindenstrauss","year":"1979","unstructured":"Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II, Ergebnisse der Mathematik in ihrer Grenzgebiete, vol. 97. Springer-Verlag, Berlin Heidelberg (1979)"},{"key":"3032_CR34","unstructured":"Littman, M., Szepesv\u00e1ri, C.: A generalized reinforcement-learning model: convergence and applications. In: Saitta, L. (ed.) Proceedings of ICML\u201996, pp. 310\u2013318. Morgan Kaufmann Publishers Inc, San Francisco, CA, USA (1996)"},{"key":"3032_CR35","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1090\/S0002-9939-1953-0054846-3","volume":"4","author":"W Mann","year":"1953","unstructured":"Mann, W.: Mean value methods in iteration. Proceedings of the American Mathematical Society 4, 506\u2013510 (1953)","journal-title":"Proceedings of the American Mathematical Society"},{"key":"3032_CR36","doi-asserted-by":"crossref","unstructured":"Neri, M., Pischke, N.: Proof mining and probability theory. Forum of Mathematics, Sigma 13 (2025). E187, 47pp","DOI":"10.1017\/fms.2025.10138"},{"key":"3032_CR37","unstructured":"Neri, M., Pischke, N., Powell, T.: An abstract effective convergence theorem for stochastic processes, with applications to stochastic approximation, (2026). ArXiv e-print, math.OC, 2504.12922"},{"key":"3032_CR38","doi-asserted-by":"publisher","first-page":"974","DOI":"10.1090\/btran\/229","volume":"12","author":"M Neri","year":"2025","unstructured":"Neri, M., Powell, T.: On quantitative convergence for stochastic processes: Crossings, fluctuations and martingales. Transactions of the American Mathematical Society, Series B 12, 974\u20131019 (2025)","journal-title":"Transactions of the American Mathematical Society, Series B"},{"issue":"1","key":"3032_CR39","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1214\/25-AAP2242","volume":"36","author":"M Neri","year":"2026","unstructured":"Neri, M., Powell, T.: A quantitative Robbins-Siegmund theorem. Ann. Appl. Probab. 36(1), 636\u2013651 (2026)","journal-title":"Ann. Appl. Probab."},{"issue":"3","key":"3032_CR40","first-page":"23","volume":"2","author":"B Nguyen","year":"2012","unstructured":"Nguyen, B., Duc, L.N.: Hybrid descent-like Halpern iteration methods for two nonexpansive mappings and semigroups on two sets. Theoretical Mathematics & Applications 2(3), 23\u201338 (2012)","journal-title":"Theoretical Mathematics & Applications"},{"issue":"4","key":"3032_CR41","doi-asserted-by":"publisher","first-page":"435","DOI":"10.2307\/1988879","volume":"16","author":"CDLV Poussin","year":"1915","unstructured":"Poussin, C.D.L.V.: Sur L\u2019Integrale de Lebesgue. Trans. Am. Math. Soc. 16(4), 435\u2013501 (1915)","journal-title":"Trans. Am. Math. Soc."},{"key":"3032_CR42","volume-title":"Markov Decision Processes: Discrete Stochastic Dynamic Programming","author":"M Puterman","year":"2014","unstructured":"Puterman, M.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, Hoboken, NJ, USA (2014)"},{"key":"3032_CR43","doi-asserted-by":"publisher","first-page":"640","DOI":"10.1137\/16M105592X","volume":"27","author":"S Sabach","year":"2017","unstructured":"Sabach, S., Shtern, S.: A first order method for solving convex bilevel optimization problems. SIAM J. Optim. 27, 640\u2013660 (2017)","journal-title":"SIAM J. Optim."},{"key":"3032_CR44","doi-asserted-by":"crossref","unstructured":"Saejung, S.: Halpern iterations in CAT(0) spaces. Fixed Point Theory and Applications (2010). Article ID 471781, 13pp","DOI":"10.1155\/2010\/471781"},{"key":"3032_CR45","doi-asserted-by":"crossref","unstructured":"Schade, K., Kohlenbach, U.: Effective metastability for modified Halpern iterations in CAT(0) spaces. Fixed Point Theory and Applications (2012). Article no. 191, 19pp","DOI":"10.1186\/1687-1812-2012-191"},{"key":"3032_CR46","unstructured":"Watkins, C.: Learning from delayed rewards, University of Cambridge (1989). (Ph.D. thesis)"},{"key":"3032_CR47","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511813658","volume-title":"Probability with Martingales","author":"D Williams","year":"1991","unstructured":"Williams, D.: Probability with Martingales. Cambridge University Press, Cambridge (1991)"},{"issue":"5","key":"3032_CR48","doi-asserted-by":"publisher","first-page":"486","DOI":"10.1007\/BF01190119","volume":"58","author":"R Wittmann","year":"1992","unstructured":"Wittmann, R.: Approximation of fixed points of nonexpansive mappings. Arch. Math. 58(5), 486\u2013491 (1992)","journal-title":"Arch. Math."},{"key":"3032_CR49","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1112\/S0024610702003332","volume":"66","author":"HK Xu","year":"2002","unstructured":"Xu, H.K.: Iterative algorithms for nonlinear operators. J. Lond. Math. Soc. 66, 240\u2013256 (2002)","journal-title":"J. Lond. Math. Soc."},{"issue":"1\u20132","key":"3032_CR50","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/s12190-008-0139-z","volume":"29","author":"Y Yao","year":"2009","unstructured":"Yao, Y., Zhou, H., Liou, Y.C.: Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings. J. Appl. Math. Comput. 29(1\u20132), 383\u2013389 (2009)","journal-title":"J. Appl. Math. Comput."},{"key":"3032_CR51","unstructured":"Yoon, T., Ryu, E.: Accelerated algorithms for smooth convex-concave minimax problems with $$\\cal O\\it (1\/k^2)$$ rate on squared gradient norm. In: M.\u00a0Meila, T.\u00a0Zhang (eds.) Proceedings of ICML\u201921, Proceedings of Machine Learning Research, vol. 139, pp. 12,098\u201312,109 (2021)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-026-03032-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-026-03032-z","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-026-03032-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T23:09:39Z","timestamp":1781651379000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-026-03032-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,16]]},"references-count":51,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,7]]}},"alternative-id":["3032"],"URL":"https:\/\/doi.org\/10.1007\/s10957-026-03032-z","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,16]]},"assertion":[{"value":"7 July 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 May 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 June 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"3"}}