{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T10:32:51Z","timestamp":1779100371625,"version":"3.51.4"},"reference-count":22,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2022,11,11]],"date-time":"2022-11-11T00:00:00Z","timestamp":1668124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation China","award":["61971257"],"award-info":[{"award-number":["61971257"]}]},{"name":"National Natural Science Foundation China","award":["61673310"],"award-info":[{"award-number":["61673310"]}]},{"name":"National Natural Science Foundation China","award":["2020QNRC001"],"award-info":[{"award-number":["2020QNRC001"]}]},{"name":"Young Elite Scientist Sponsorship Program by CAST","award":["61971257"],"award-info":[{"award-number":["61971257"]}]},{"name":"Young Elite Scientist Sponsorship Program by CAST","award":["61673310"],"award-info":[{"award-number":["61673310"]}]},{"name":"Young Elite Scientist Sponsorship Program by CAST","award":["2020QNRC001"],"award-info":[{"award-number":["2020QNRC001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The development of automatic underwater vehicles (AUVs) has brought about unprecedented profits and opportunities. In order to discover the hidden valuable data detected by an AUV swarm, it is necessary to aggregate the data detected by AUV swarm to generate a powerful machine learning model. Traditional centralized machine learning generates a large number of data exchanges and faces problems of enormous training data, large-scale models, and communication. In underwater environments, radio waves are strongly absorbed, and acoustic communication is the only feasible technology. Unlike electromagnetic wave communication on land, the bandwidth of underwater acoustic communication is extremely limited, with the transmission rate being only 1\/105 of the electromagnetic wave. Therefore, traditional centralized machine learning cannot support underwater AUV swarm training. In recent years, federated learning could only interact with model parameters without interacting with data, which greatly reduced communication costs. Therefore, this paper introduces federated learning into the collaboration of an AUV swarm. In order to further reduce the constraints of underwater scarce communication resources on federated learning and alleviate the straggler effect, in this work, we designed an asynchronous federated learning method. Finally, we constructed the optimization problem of minimizing the weighted sum of delay and energy consumption, relying on jointly optimizing the AUV CPU frequency and signal transmission power. In order to solve this complex optimization problem of high-dimensional non-convex time series accumulation, we transformed the problem into a Markov decision process (MDP) and use the proximal policy optimization 2 (PPO2) algorithm to solve this problem. The simulation results demonstrate the effectiveness and superiority of our method.<\/jats:p>","DOI":"10.3390\/s22228727","type":"journal-article","created":{"date-parts":[[2022,11,14]],"date-time":"2022-11-14T04:30:52Z","timestamp":1668400252000},"page":"8727","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Efficient Asynchronous Federated Learning for AUV Swarm"],"prefix":"10.3390","volume":"22","author":[{"given":"Zezhao","family":"Meng","sequence":"first","affiliation":[{"name":"School of Mechano-Electronic Engineering, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechano-Electronic Engineering, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangwang","family":"Hou","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Du","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3189-4222","authenticated-orcid":false,"given":"Jianrui","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Wei","sequence":"additional","affiliation":[{"name":"Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 514231, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"10132","DOI":"10.1109\/TVT.2022.3176819","article-title":"Average Peak Age of Information in Underwater Information Collection With Sleep-Scheduling","volume":"71","author":"Fang","year":"2022","journal-title":"IEEE Trans. Vehicular Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/MCOM.001.2000831","article-title":"MagicNet: The Maritime Giant Cellular Network","volume":"59","author":"Guan","year":"2021","journal-title":"IEEE Commun. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"14559","DOI":"10.1109\/JIOT.2021.3049239","article-title":"AoI-Inspired Collaborative Information Collection for AUV-Assisted Internet of Underwater Things","volume":"8","author":"Fang","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.1109\/JIOT.2021.3088279","article-title":"Stochastic Optimization-Aided Energy-Efficient Information Collection in Internet of Underwater Things Networks","volume":"9","author":"Fang","year":"2022","journal-title":"IEEE Internet Things J."},{"key":"ref_5","unstructured":"McMahan, H.B., Moore, E., Ramage, D., Hampson, S., and y Arcas, B.A. (2017, January 20\u201322). Communication-Efficient Learning of Deep Networks from Decentralized Data. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics\u2014AISTATS, Ft. Lauderdale, FL, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"65728","DOI":"10.1109\/ACCESS.2019.2917948","article-title":"Medium Access Control Protocols for Unmanned Aerial Vehicle-Aided Wireless Sensor Networks: A Survey","volume":"7","author":"Poudel","year":"2019","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1109\/TMECH.2016.2612689","article-title":"Integrated Path Planning and Tracking Control of an AUV: A Unified Receding Horizon Optimization Approach","volume":"22","author":"Shen","year":"2017","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3519","DOI":"10.1109\/JSYST.2017.2789283","article-title":"Energy-Efficient Data Collection Over AUV-Assisted Underwater Acoustic Sensor Network","volume":"12","author":"Yan","year":"2018","journal-title":"IEEE Syst. J."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Cai, L., Zhou, G., and Zhang, S. (2018, January 18\u201320). Multi-AUV Collaborative Hunting Method for the Non-cooperative Target in Underwater Environment. Proceedings of the 2018 3rd International Conference on Advanced Robotics and Mechatronics (ICARM), Singapore.","DOI":"10.1109\/ICARM.2018.8610805"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1109\/TSMC.2015.2500027","article-title":"Mutual Information-Based Multi-AUV Path Planning for Scalar Field Sampling Using Multidimensional RRT*","volume":"46","author":"Cui","year":"2016","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Noguchi, Y., and Maki, T. (2019, January 16\u201319). Path Planning Method Based on Artificial Potential Field and Reinforcement Learning for Intervention the AUVs. Proceedings of the 2019 IEEE Underwater Technology (UT), Kaohsiung, Taiwan.","DOI":"10.1109\/UT.2019.8734314"},{"key":"ref_12","unstructured":"Huang, H., Zhu, D., and Yuan, F. (2012, January 23\u201325). Dynamic task assignment and path planning for multi-AUV system in 2D variable ocean current environment. Proceedings of the 24th Chinese Control and Decision Conference (CCDC), Taiyuan, China."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Cao, X., and Sun, C. (2018, January 18\u201320). Multi-AUV cooperative target hunting based on improved potential field in underwater environment. Proceedings of the 33rd Youth Academic Annual Conference of Chinese Association of Automation (YAC), Nanjing, China.","DOI":"10.1109\/YAC.2018.8406357"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"13447","DOI":"10.1109\/TVT.2021.3121004","article-title":"Latency Minimization in Covert Communication-Enabled Federated Learning Network","volume":"70","author":"Van","year":"2021","journal-title":"IEEE Trans. Vehicular Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2276","DOI":"10.1109\/JIOT.2020.3015772","article-title":"Communication-Efficient Federated Learning and Permissioned Blockchain for Digital Twin Edge Networks","volume":"8","author":"Lu","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2457","DOI":"10.1109\/TWC.2020.3042530","article-title":"Convergence Time Optimization for Federated Learning Over Wireless Networks","volume":"20","author":"Chen","year":"2021","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1109\/JSAC.2020.3036971","article-title":"Accelerating DNN Training in Wireless Federated Edge Learning Systems","volume":"39","author":"Ren","year":"2021","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1109\/TNNLS.2020.2979762","article-title":"LAGC: Lazily Aggregated Gradient Coding for Straggler-Tolerant and Communication-Efficient Distributed Learning","volume":"32","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4637","DOI":"10.1109\/TSP.2021.3099977","article-title":"Communication-Adaptive Stochastic Gradient Methods for Distributed Learning","volume":"69","author":"Chen","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2031","DOI":"10.1109\/TPAMI.2020.3033286","article-title":"Lazily Aggregated Quantized Gradient Innovation for Communication-Efficient Federated Learning","volume":"44","author":"Sun","year":"2022","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Jensen, F.B., Kuperman, W.A., Porter, M.B., Schmidt, H., and Tolstoy, A. (2011). Computational Ocean Acoustics, Springer.","DOI":"10.1007\/978-1-4419-8678-8"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1145\/1347364.1347373","article-title":"On the relationship between capacity and distance in an underwater acoustic communication channel","volume":"11","author":"Stojanovic","year":"2007","journal-title":"ACM SIGMOBILE Mob. Comput. Commun. Rev."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/8727\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:14:41Z","timestamp":1760145281000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/8727"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,11]]},"references-count":22,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["s22228727"],"URL":"https:\/\/doi.org\/10.3390\/s22228727","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,11]]}}}