Distributed Convex Optimization with State-Dependent (Social) Interactions over Random Networks
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917881125535744 |
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| author | Alaviani, Seyyed Shaho Kelkar, Atul |
| author_facet | Alaviani, Seyyed Shaho Kelkar, Atul |
| contents | This paper aims at distributed multi-agent convex optimization where the
communications network among the agents are presented by a random
sequence of possibly state-dependent weighted graphs. This is the first work to consider both random arbitrary communication networks and state-dependent interactions among agents. The state-dependent weighted random operator of the graph is shown to be quasi-nonexpansive;
this property neglects a priori distribution assumption
of random communication topologies to be imposed on the operator. Therefore, it contains more general class of
random networks with or without asynchronous protocols. A more general mathematical optimization
problem than that addressed in the literature is presented, namely minimization of a convex function over the fixed-value point set of a quasi-nonexpansive random operator.
A discrete-time algorithm is provided that is able to converge both almost surely and in mean square to the global solution of the optimization problem. Hence, as a special case,
it reduces to a totally asynchronous algorithm for the
distributed optimization problem. The algorithm is able to converge even if the weighted matrix of the graph is periodic and irreducible under synchronous protocol. Finally, a case study on a network of robots in an automated warehouse is
given where there is distribution dependency among random communication graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributed Convex Optimization with State-Dependent (Social) Interactions over Random Networks Alaviani, Seyyed Shaho Kelkar, Atul Systems and Control This paper aims at distributed multi-agent convex optimization where the communications network among the agents are presented by a random sequence of possibly state-dependent weighted graphs. This is the first work to consider both random arbitrary communication networks and state-dependent interactions among agents. The state-dependent weighted random operator of the graph is shown to be quasi-nonexpansive; this property neglects a priori distribution assumption of random communication topologies to be imposed on the operator. Therefore, it contains more general class of random networks with or without asynchronous protocols. A more general mathematical optimization problem than that addressed in the literature is presented, namely minimization of a convex function over the fixed-value point set of a quasi-nonexpansive random operator. A discrete-time algorithm is provided that is able to converge both almost surely and in mean square to the global solution of the optimization problem. Hence, as a special case, it reduces to a totally asynchronous algorithm for the distributed optimization problem. The algorithm is able to converge even if the weighted matrix of the graph is periodic and irreducible under synchronous protocol. Finally, a case study on a network of robots in an automated warehouse is given where there is distribution dependency among random communication graphs. |
| title | Distributed Convex Optimization with State-Dependent (Social) Interactions over Random Networks |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2412.20354 |