{"title":"自适应量化的分布式受限在线凸优化","authors":"","doi":"10.1016/j.automatica.2024.111828","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study distributed constrained online convex optimization (OCO) problem in a system consisting of a parameter server and <span><math><mi>n</mi></math></span> clients. Each client is associated with a local constraint function and time-varying local loss functions, which are disclosed sequentially. The clients seek to minimize the accumulated total loss subject to the total constraint by choosing sequential decisions based on causal information of the loss functions. Existing distributed constrained OCO algorithms require clients to send their raw decisions to the server, leading to large communication overhead unaffordable in many applications. To reduce the communication cost, we devise an adaptive quantization method, where the center and the radius of the quantizer are adjusted in an adaptive manner as the OCO algorithm progresses. We first examine the scenario of full information feedback, where the complete information of the loss functions is revealed at each time. We propose a distributed online saddle point algorithm with adaptive quantization, which can reduce the communication overhead considerably. The performance of this algorithm is analyzed, and an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msqrt><mrow><mi>T</mi></mrow></msqrt><mo>)</mo></mrow></mrow></math></span> regret bound and an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow></mrow></math></span> constraint violation bound are established, which are the same as (in order sense) those for existing algorithm transmitting raw decisions without quantization. We further extend the adaptive quantization method to the scenario of bandit feedback, where only the values of the local loss functions at two points are revealed at each time. A bandit OCO algorithm with adaptive quantization is developed and is shown to possess the same (in order sense) regret and constraint violation bounds as in the full information feedback case. Finally, numerical results on distributed online rate control problem are presented to corroborate the efficacy of the proposed algorithms.</p></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":null,"pages":null},"PeriodicalIF":4.8000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Distributed constrained online convex optimization with adaptive quantization\",\"authors\":\"\",\"doi\":\"10.1016/j.automatica.2024.111828\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we study distributed constrained online convex optimization (OCO) problem in a system consisting of a parameter server and <span><math><mi>n</mi></math></span> clients. Each client is associated with a local constraint function and time-varying local loss functions, which are disclosed sequentially. The clients seek to minimize the accumulated total loss subject to the total constraint by choosing sequential decisions based on causal information of the loss functions. Existing distributed constrained OCO algorithms require clients to send their raw decisions to the server, leading to large communication overhead unaffordable in many applications. To reduce the communication cost, we devise an adaptive quantization method, where the center and the radius of the quantizer are adjusted in an adaptive manner as the OCO algorithm progresses. We first examine the scenario of full information feedback, where the complete information of the loss functions is revealed at each time. We propose a distributed online saddle point algorithm with adaptive quantization, which can reduce the communication overhead considerably. The performance of this algorithm is analyzed, and an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msqrt><mrow><mi>T</mi></mrow></msqrt><mo>)</mo></mrow></mrow></math></span> regret bound and an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow></mrow></math></span> constraint violation bound are established, which are the same as (in order sense) those for existing algorithm transmitting raw decisions without quantization. We further extend the adaptive quantization method to the scenario of bandit feedback, where only the values of the local loss functions at two points are revealed at each time. A bandit OCO algorithm with adaptive quantization is developed and is shown to possess the same (in order sense) regret and constraint violation bounds as in the full information feedback case. Finally, numerical results on distributed online rate control problem are presented to corroborate the efficacy of the proposed algorithms.</p></div>\",\"PeriodicalId\":55413,\"journal\":{\"name\":\"Automatica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.8000,\"publicationDate\":\"2024-08-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Automatica\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0005109824003224\",\"RegionNum\":2,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109824003224","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Distributed constrained online convex optimization with adaptive quantization
In this paper, we study distributed constrained online convex optimization (OCO) problem in a system consisting of a parameter server and clients. Each client is associated with a local constraint function and time-varying local loss functions, which are disclosed sequentially. The clients seek to minimize the accumulated total loss subject to the total constraint by choosing sequential decisions based on causal information of the loss functions. Existing distributed constrained OCO algorithms require clients to send their raw decisions to the server, leading to large communication overhead unaffordable in many applications. To reduce the communication cost, we devise an adaptive quantization method, where the center and the radius of the quantizer are adjusted in an adaptive manner as the OCO algorithm progresses. We first examine the scenario of full information feedback, where the complete information of the loss functions is revealed at each time. We propose a distributed online saddle point algorithm with adaptive quantization, which can reduce the communication overhead considerably. The performance of this algorithm is analyzed, and an regret bound and an constraint violation bound are established, which are the same as (in order sense) those for existing algorithm transmitting raw decisions without quantization. We further extend the adaptive quantization method to the scenario of bandit feedback, where only the values of the local loss functions at two points are revealed at each time. A bandit OCO algorithm with adaptive quantization is developed and is shown to possess the same (in order sense) regret and constraint violation bounds as in the full information feedback case. Finally, numerical results on distributed online rate control problem are presented to corroborate the efficacy of the proposed algorithms.
期刊介绍:
Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field.
After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience.
Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.