{"publication":"arXiv:2105.04230","date_updated":"2022-04-06T08:04:37Z","type":"preprint","_id":"30792","title":"Practical sufficient conditions for convergence of distributed\n  optimisation algorithms over communication networks with interference","date_created":"2022-04-06T06:54:02Z","citation":{"apa":"Redder, A., Ramaswamy, A., &#38; Karl, H. (2021). Practical sufficient conditions for convergence of distributed   optimisation algorithms over communication networks with interference. In <i>arXiv:2105.04230</i>.","ieee":"A. Redder, A. Ramaswamy, and H. Karl, “Practical sufficient conditions for convergence of distributed   optimisation algorithms over communication networks with interference,” <i>arXiv:2105.04230</i>. 2021.","ama":"Redder A, Ramaswamy A, Karl H. Practical sufficient conditions for convergence of distributed   optimisation algorithms over communication networks with interference. <i>arXiv:210504230</i>. Published online 2021.","mla":"Redder, Adrian, et al. “Practical Sufficient Conditions for Convergence of Distributed  Optimisation Algorithms over Communication Networks with Interference.” <i>ArXiv:2105.04230</i>, 2021.","short":"A. Redder, A. Ramaswamy, H. Karl, ArXiv:2105.04230 (2021).","chicago":"Redder, Adrian, Arunselvan Ramaswamy, and Holger Karl. “Practical Sufficient Conditions for Convergence of Distributed  Optimisation Algorithms over Communication Networks with Interference.” <i>ArXiv:2105.04230</i>, 2021.","bibtex":"@article{Redder_Ramaswamy_Karl_2021, title={Practical sufficient conditions for convergence of distributed   optimisation algorithms over communication networks with interference}, journal={arXiv:2105.04230}, author={Redder, Adrian and Ramaswamy, Arunselvan and Karl, Holger}, year={2021} }"},"external_id":{"arxiv":["2105.04230"]},"user_id":"52265","year":"2021","status":"public","abstract":[{"text":"Information exchange over networks can be affected by various forms of delay.\nThis causes challenges for using the network by a multi-agent system to solve a\ndistributed optimisation problem. Distributed optimisation schemes, however,\ntypically do not assume network models that are representative for real-world\ncommunication networks, since communication links are most of the time\nabstracted as lossless. Our objective is therefore to formulate a\nrepresentative network model and provide practically verifiable network\nconditions that ensure convergence of distributed algorithms in the presence of\ninterference and possibly unbounded delay. Our network is modelled by a\nsequence of directed-graphs, where to each network link we associate a process\nfor the instantaneous signal-to-interference-plus-noise ratio. We then\nformulate practical conditions that can be verified locally and show that the\nage of information (AoI) associated with data communicated over the network is\nin $\\mathcal{O}(\\sqrt{n})$. Under these conditions we show that a penalty-based\ngradient descent algorithm can be used to solve a rich class of stochastic,\nconstrained, distributed optimisation problems. The strength of our result lies\nin the bridge between practical verifiable network conditions and an abstract\noptimisation theory. We illustrate numerically that our algorithm converges in\nan extreme scenario where the average AoI diverges.","lang":"eng"}],"author":[{"first_name":"Adrian","last_name":"Redder","full_name":"Redder, Adrian"},{"full_name":"Ramaswamy, Arunselvan","last_name":"Ramaswamy","first_name":"Arunselvan"},{"first_name":"Holger","full_name":"Karl, Holger","last_name":"Karl"}]}