{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T10:26:34Z","timestamp":1774434394796,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T00:00:00Z","timestamp":1768867200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T00:00:00Z","timestamp":1769558400000},"content-version":"vor","delay-in-days":8,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"name":"JST SPRING","award":["JPMJSP2135"],"award-info":[{"award-number":["JPMJSP2135"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1007\/s40747-026-02228-0","type":"journal-article","created":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T07:33:07Z","timestamp":1768894387000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Attention-enhanced safe reinforcement learning for metaverse user perception utility optimization in edge metaverse services"],"prefix":"10.1007","volume":"12","author":[{"given":"Ziyue","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9905-8952","authenticated-orcid":false,"given":"Ruidong","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dusit","family":"Niyato","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,20]]},"reference":[{"issue":"4","key":"2228_CR1","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1109\/MWC.018.2100716","volume":"30","author":"WYB Lim","year":"2022","unstructured":"Lim WYB, Xiong Z, Niyato D, Cao X, Miao C, Sun S, Yang Q (2022) Realizing the metaverse with edge intelligence: a match made in heaven. IEEE Wirel Commun 30(4):64\u201371","journal-title":"IEEE Wirel Commun"},{"key":"2228_CR2","unstructured":"Lee L-H, Braud T, Zhou P, Wang L, Xu D, Lin Z, Kumar A, Bermejo C, Hui P (2021) All one needs to know about metaverse: a complete survey on technological singularity, virtual ecosystem, and research agenda. arXiv:2110.05352"},{"issue":"1","key":"2228_CR3","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1109\/COMST.2022.3202047","volume":"25","author":"Y Wang","year":"2022","unstructured":"Wang Y, Su Z, Zhang N, Xing R, Liu D, Luan TH, Shen X (2022) A survey on metaverse: fundamentals, security, and privacy. IEEE Commun Surv Tutor 25(1):319\u2013352","journal-title":"IEEE Commun Surv Tutor"},{"issue":"1","key":"2228_CR4","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1109\/JIOT.2021.3103320","volume":"9","author":"DC Nguyen","year":"2021","unstructured":"Nguyen DC, Ding M, Pathirana PN, Seneviratne A, Li J, Niyato D, Dobre O, Poor HV (2021) 6g internet of things: a comprehensive survey. IEEE Internet Things J 9(1):359\u2013383","journal-title":"IEEE Internet Things J"},{"issue":"2","key":"2228_CR5","doi-asserted-by":"publisher","first-page":"905","DOI":"10.1109\/COMST.2023.3249835","volume":"25","author":"C-X Wang","year":"2023","unstructured":"Wang C-X, You X, Gao X, Zhu X, Li Z, Zhang C, Wang H, Huang Y, Chen Y, Haas H et al (2023) On the road to 6g: visions, requirements, key technologies, and testbeds. IEEE Commun Surv Tutor 25(2):905\u2013974","journal-title":"IEEE Commun Surv Tutor"},{"key":"2228_CR6","doi-asserted-by":"crossref","unstructured":"Tan YW, Tan A, Nge N, Bhojan A (2022) Dhr: distributed hybrid rendering for metaverse experiences. In: Proceedings of the 1st workshop on interactive extended reality, pp 51\u201359","DOI":"10.1145\/3552483.3556455"},{"key":"2228_CR7","doi-asserted-by":"crossref","unstructured":"Hsu C-F, Chen A, Hsu C-H, Huang C-Y, Lei C-L, Chen K-T (2017) Is foveated rendering perceivable in virtual reality? exploring the efficiency and consistency of quality assessment methods. In: Proceedings of the 25th ACM international conference on multimedia, pp 55\u201363","DOI":"10.1145\/3123266.3123434"},{"issue":"4","key":"2228_CR8","doi-asserted-by":"publisher","first-page":"2255","DOI":"10.1109\/COMST.2022.3208773","volume":"24","author":"S Mihai","year":"2022","unstructured":"Mihai S, Yaqoob M, Hung DV, Davis W, Towakel P, Raza M, Karamanoglu M, Barn B, Shetve D, Prasad RV et al (2022) Digital twins: a survey on enabling technologies, challenges, trends and future prospects. IEEE Commun Surv Tutor 24(4):2255\u20132291","journal-title":"IEEE Commun Surv Tutor"},{"key":"2228_CR9","doi-asserted-by":"crossref","unstructured":"Li J, Wang J, Chen Q, Li Y, Zomaya AY (2023) Digital twin-enabled service satisfaction enhancement in edge computing. In: IEEE INFOCOM 2023-IEEE conference on computer communications. IEEE, pp 1\u201310","DOI":"10.1109\/INFOCOM53939.2023.10228893"},{"issue":"7","key":"2228_CR10","doi-asserted-by":"publisher","first-page":"2158","DOI":"10.1109\/JSAC.2023.3280978","volume":"41","author":"H Du","year":"2023","unstructured":"Du H, Liu J, Niyato D, Kang J, Xiong Z, Zhang J, Kim DI (2023) Attention-aware resource allocation and qoe analysis for metaverse xurllc services. IEEE J Sel Areas Commun 41(7):2158\u20132175","journal-title":"IEEE J Sel Areas Commun"},{"key":"2228_CR11","doi-asserted-by":"crossref","unstructured":"LaValle SM, Yershova A, Katsev M, Antonov M (2014) Head tracking for the oculus rift. In: 2014 IEEE international conference on robotics and automation (ICRA). IEEE, pp 187\u2013194","DOI":"10.1109\/ICRA.2014.6906608"},{"key":"2228_CR12","doi-asserted-by":"crossref","unstructured":"Chen J, Yi C, Du H, Niyato D, Kang J, Cai J, Shen X (2024) A revolution of personalized healthcare: enabling human digital twin with mobile aigc. IEEE Netw","DOI":"10.1109\/MNET.2024.3366560"},{"key":"2228_CR13","doi-asserted-by":"crossref","unstructured":"Yu J, Alhilal A, Zhou T, Hui P, Tsang DH (2024) Attention-based qoe-aware digital twin empowered edge computing for immersive virtual reality. IEEE Trans Wirel Commun","DOI":"10.1109\/TWC.2024.3380820"},{"key":"2228_CR14","doi-asserted-by":"crossref","unstructured":"Li J, Guo S, Liang W, Wang J, Chen Q, Xu Z, Xu W (2023) Aoi-aware user service satisfaction enhancement in digital twin-empowered edge computing. IEEE\/ACM Trans Netw","DOI":"10.1109\/TNET.2023.3324704"},{"issue":"6","key":"2228_CR15","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1109\/MNET.131.2200503","volume":"37","author":"H Du","year":"2023","unstructured":"Du H, Ma B, Niyato D, Kang J, Xiong Z, Yang Z (2023) Rethinking quality of experience for metaverse services: a consumer-based economics perspective. IEEE Netw 37(6):255\u2013263","journal-title":"IEEE Netw"},{"key":"2228_CR16","doi-asserted-by":"crossref","unstructured":"Shen XS, Huang X, Xue J, Zhou C, Shi X, Zhuang W (2025) Revolutionizing qoe-driven network management with digital agents in 6g. IEEE Commun Mag","DOI":"10.36227\/techrxiv.173386055.59491439\/v1"},{"issue":"10","key":"2228_CR17","doi-asserted-by":"publisher","first-page":"2200","DOI":"10.1109\/JSAC.2019.2933762","volume":"37","author":"C He","year":"2019","unstructured":"He C, Hu Y, Chen Y, Zeng B (2019) Joint power allocation and channel assignment for noma with deep reinforcement learning. IEEE J Sel Areas Commun 37(10):2200\u20132210. https:\/\/doi.org\/10.1109\/JSAC.2019.2933762","journal-title":"IEEE J Sel Areas Commun"},{"issue":"10","key":"2228_CR18","doi-asserted-by":"publisher","first-page":"9517","DOI":"10.1109\/JIOT.2020.3003449","volume":"7","author":"J Du","year":"2020","unstructured":"Du J, Yu FR, Lu G, Wang J, Jiang J, Chu X (2020) Mec-assisted immersive vr video streaming over terahertz wireless networks: a deep reinforcement learning approach. IEEE Internet Things J 7(10):9517\u20139529","journal-title":"IEEE Internet Things J"},{"key":"2228_CR19","doi-asserted-by":"crossref","unstructured":"Truong TP, Tran A-T, Dao N-N, Cho S, et al (2024) Noma-enhanced quantized uplink multi-user mimo communications. In: IEEE INFOCOM 2024-IEEE conference on computer communications. IEEE, pp 281\u2013290","DOI":"10.1109\/INFOCOM52122.2024.10621204"},{"key":"2228_CR20","doi-asserted-by":"crossref","unstructured":"Zhou X, Li Y, Zhao J (2025) Resource allocation of federated learning-assisted mobile augmented reality systems in the metaverse via uplink and downlink noma. IEEE Trans Wirel Commun","DOI":"10.1109\/TWC.2025.3554361"},{"issue":"11","key":"2228_CR21","doi-asserted-by":"publisher","first-page":"2581","DOI":"10.1109\/TMC.2019.2928811","volume":"19","author":"L Huang","year":"2019","unstructured":"Huang L, Bi S, Zhang Y-JA (2019) Deep reinforcement learning for online computation offloading in wireless powered mobile-edge computing networks. IEEE Trans Mob Comput 19(11):2581\u20132593","journal-title":"IEEE Trans Mob Comput"},{"issue":"9","key":"2228_CR22","doi-asserted-by":"publisher","first-page":"5800","DOI":"10.1109\/TWC.2023.3237202","volume":"22","author":"S Wang","year":"2023","unstructured":"Wang S, Bi S, Zhang Y-JA (2023) Edge video analytics with adaptive information gathering: a deep reinforcement learning approach. IEEE Trans Wirel Commun 22(9):5800\u20135813","journal-title":"IEEE Trans Wirel Commun"},{"issue":"11","key":"2228_CR23","doi-asserted-by":"publisher","first-page":"7519","DOI":"10.1109\/TWC.2021.3085319","volume":"20","author":"S Bi","year":"2021","unstructured":"Bi S, Huang L, Wang H, Zhang Y-JA (2021) Lyapunov-guided deep reinforcement learning for stable online computation offloading in mobile-edge computing networks. IEEE Trans Wirel Commun 20(11):7519\u20137537","journal-title":"IEEE Trans Wirel Commun"},{"key":"2228_CR24","doi-asserted-by":"crossref","unstructured":"Dai P, Hu K, Wu X, Xing H, Yu Z (2021) Asynchronous deep reinforcement learning for data-driven task offloading in mec-empowered vehicular networks. In: IEEE INFOCOM 2021-IEEE conference on computer communications. IEEE, pp 1\u201310","DOI":"10.1109\/INFOCOM42981.2021.9488886"},{"issue":"9","key":"2228_CR25","doi-asserted-by":"publisher","first-page":"6949","DOI":"10.1109\/TWC.2022.3153316","volume":"21","author":"N Zhao","year":"2022","unstructured":"Zhao N, Ye Z, Pei Y, Liang Y-C, Niyato D (2022) Multi-agent deep reinforcement learning for task offloading in uav-assisted mobile edge computing. IEEE Trans Wirel Commun 21(9):6949\u20136960","journal-title":"IEEE Trans Wirel Commun"},{"key":"2228_CR26","unstructured":"Ray A, Achiam J, Amodei D (2019) Benchmarking safe exploration in deep reinforcement learning. 7(1):2. arXiv:1910.01708"},{"key":"2228_CR27","first-page":"15084","volume":"34","author":"L Chen","year":"2021","unstructured":"Chen L, Lu K, Rajeswaran A, Lee K, Grover A, Laskin M, Abbeel P, Srinivas A, Mordatch I (2021) Decision transformer: reinforcement learning via sequence modeling. Adv Neural Inf Process Syst 34:15084\u201315097","journal-title":"Adv Neural Inf Process Syst"},{"key":"2228_CR28","first-page":"9111","volume":"35","author":"L Yang","year":"2022","unstructured":"Yang L, Ji J, Dai J, Zhang L, Zhou B, Li P, Yang Y, Pan G (2022) Constrained update projection approach to safe policy optimization. Adv Neural Inf Process Syst 35:9111\u20139124","journal-title":"Adv Neural Inf Process Syst"},{"key":"2228_CR29","unstructured":"Achiam J, Held D, Tamar A, Abbeel P (2017) Constrained policy optimization. In: International conference on machine learning. PMLR, pp 22\u201331"},{"key":"2228_CR30","doi-asserted-by":"crossref","unstructured":"Alshiekh M, Bloem R, Ehlers R, K\u00f6nighofer B, Niekum S, Topcu U (2018) Safe reinforcement learning via shielding. In: Proceedings of the AAAI conference on artificial intelligence, vol 32, pp 2669\u20132678","DOI":"10.1609\/aaai.v32i1.11797"},{"key":"2228_CR31","unstructured":"Chow Y, Nachum O, Duenez-Guzman E, Ghavamzadeh M (2018) A lyapunov-based approach to safe reinforcement learning. Adv Neural Inf Process Syst 31"},{"key":"2228_CR32","doi-asserted-by":"crossref","unstructured":"Huang W, Li T, Cao Y, Lyu Z, Liang Y, Yu L, Jin D, Zhang J, Li Y (2023) Safe-NORA: safe reinforcement learning-based mobile network resource allocation for diverse user demands. In: Proceedings of the 32nd ACM international conference on information and knowledge management (CIKM), pp 885\u2013894","DOI":"10.1145\/3583780.3615043"},{"key":"2228_CR33","doi-asserted-by":"crossref","unstructured":"Alhilal A, Shatilov K, Tyson G, Braud T, Hui P (2023) Network traffic in the metaverse: the case of social vr. In: 2023 IEEE 43rd international conference on distributed computing systems workshops (ICDCSW). IEEE, pp 109\u2013114","DOI":"10.1109\/ICDCSW60045.2023.00025"},{"key":"2228_CR34","doi-asserted-by":"publisher","unstructured":"Liu C, Chua TJ, Zhao J (2024) Optimization for the metaverse over mobile edge computing with play to earn. In: IEEE INFOCOM 2024\u2014IEEE conference on computer communications, pp 2269\u20132278. https:\/\/doi.org\/10.1109\/INFOCOM52122.2024.10621355","DOI":"10.1109\/INFOCOM52122.2024.10621355"},{"key":"2228_CR35","doi-asserted-by":"crossref","unstructured":"Lin Y, Gao Z, Du H, Niyato D, Kang J, Jamalipour A, Shen XS (2023) A unified framework for integrating semantic communication and ai-generated content in metaverse. IEEE Netw","DOI":"10.1109\/MNET.2023.3321539"},{"key":"2228_CR36","doi-asserted-by":"crossref","unstructured":"Xu C, Chen Z, Tao M, Zhang W (2023) Edge-device collaborative rendering for wireless multi-user interactive virtual reality in metaverse. In: GLOBECOM 2023-2023 IEEE global communications conference. IEEE, pp 3542\u20133547","DOI":"10.1109\/GLOBECOM54140.2023.10437783"},{"key":"2228_CR37","doi-asserted-by":"crossref","unstructured":"Xu C, Chen Z, Tao M, Zhang W (2025) Wireless multi-user interactive virtual reality in metaverse with edge-device collaborative computing. IEEE Trans Wirel Commun","DOI":"10.1109\/TWC.2025.3551938"},{"issue":"8","key":"2228_CR38","doi-asserted-by":"publisher","first-page":"1794","DOI":"10.1109\/JSAC.2017.2710918","volume":"35","author":"Z Zhang","year":"2017","unstructured":"Zhang Z, Ma Z, Xiao Y, Xiao M, Karagiannidis GK, Fan P (2017) Non-orthogonal multiple access for cooperative multicast millimeter wave wireless networks. IEEE J Sel Areas Commun 35(8):1794\u20131808","journal-title":"IEEE J Sel Areas Commun"},{"issue":"7","key":"2228_CR39","doi-asserted-by":"publisher","first-page":"2138","DOI":"10.1109\/JSAC.2023.3280988","volume":"41","author":"W Yu","year":"2023","unstructured":"Yu W, Chua TJ, Zhao J (2023) Asynchronous hybrid reinforcement learning for latency and reliability optimization in the metaverse over wireless communications. IEEE J Sel Areas Commun 41(7):2138\u20132157","journal-title":"IEEE J Sel Areas Commun"},{"key":"2228_CR40","unstructured":"Wimmer M, Wonka P (2003) Rendering time estimation for real-time rendering. In: Rendering techniques, pp 118\u2013129"},{"key":"2228_CR41","unstructured":"Huawei iLab (2017) Cloud VR bearer networks: VR technology white paper. Technical report, Huawei Technologies Co., Ltd. https:\/\/www-file.huawei.com\/-\/media\/corporate\/pdf\/ilab\/cloud_vr_oriented_bearer_network_white_paper_en_v2.pdf"},{"issue":"4","key":"2228_CR42","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/S1364-6613(03)00055-X","volume":"7","author":"S Dehaene","year":"2003","unstructured":"Dehaene S (2003) The neural basis of the Weber-Fechner law: a logarithmic mental number line. Trends Cogn Sci 7(4):145\u2013147","journal-title":"Trends Cogn Sci"},{"issue":"4","key":"2228_CR43","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1037\/rev0000278","volume":"128","author":"D Algom","year":"2021","unstructured":"Algom D (2021) The Weber-Fechner law: a misnomer that persists but that should go away. Psychol Rev 128(4):757","journal-title":"Psychol Rev"},{"issue":"3","key":"2228_CR44","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/s001860050035","volume":"48","author":"E Altman","year":"1998","unstructured":"Altman E (1998) Constrained Markov decision processes with total cost criteria: Lagrangian approach and dual linear program. Math Methods Oper Res 48(3):387\u2013417","journal-title":"Math Methods Oper Res"},{"issue":"1","key":"2228_CR45","first-page":"1437","volume":"16","author":"J Garc\u0131a","year":"2015","unstructured":"Garc\u0131a J, Fern\u00e1ndez F (2015) A comprehensive survey on safe reinforcement learning. J Mach Learn Res 16(1):1437\u20131480","journal-title":"J Mach Learn Res"},{"key":"2228_CR46","unstructured":"Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser \u0141, Polosukhin I (2017) Attention is all you need. Adv Neural Inf Process Syst 30"},{"key":"2228_CR47","unstructured":"Schulman J, Wolski F, Dhariwal P, Radford A, Klimov O (2017) Proximal policy optimization algorithms. arXiv:1707.06347"},{"issue":"11","key":"2228_CR48","doi-asserted-by":"publisher","first-page":"8799","DOI":"10.1109\/JIOT.2020.3048992","volume":"8","author":"T Jiang","year":"2021","unstructured":"Jiang T, Zhang J, Tang P, Tian L, Zheng Y, Dou J, Asplund H, Raschkowski L, D\u2019Errico R, J\u00e4ms\u00e4 T (2021) 3g pp standardized 5g channel model for iiot scenarios: a survey. IEEE Internet Things J 8(11):8799\u20138815","journal-title":"IEEE Internet Things J"}],"container-title":["Complex & Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-026-02228-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-026-02228-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-026-02228-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T07:55:01Z","timestamp":1774425301000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-026-02228-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,20]]},"references-count":48,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["2228"],"URL":"https:\/\/doi.org\/10.1007\/s40747-026-02228-0","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,20]]},"assertion":[{"value":"2 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 January 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest with Kanazawa University, National Institute of Information and Communications Technology, Guang Cheng, Wei He, Xiaoyan Hu, Jian Li, Jie Li, Haihan Nan, Zhou Su, Kaiping Xue, Qichao Xu, Huaming Wu.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"101"}}