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Peer-reviewedCC BY 4.0Fractal and Fractional

Fractional-Memory Distributed Online Optimization with Long-Term Constraints

  • Menghui Xiong1
  • Mingcheng Dai2
  • Qingyi Liu3
  • Yushun Tan3
  1. 1School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China
  2. 2School of Electronic Information Engineering, Chaohu University, Chaohu 238024, China
  3. 3School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China
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Abstract

This paper is concerned with distributed online optimization with long-term inequality constraints over time-varying unbalanced directed networks. A fractional-memory-based distributed online optimization algorithm is developed to exploit both current and historical first-order information. Its search direction is constructed using normalized power-law memory weights, whose distribution is regulated by the fractional order and whose memory horizon is determined by the maximum memory lag. An auxiliary-weight mechanism is incorporated to cope with the imbalance of directed communication, while the long-term constraint formulation allows projection onto a computationally tractable superset of the original feasible region, thereby avoiding costly constrained projections at every round. Under suitable assumptions and parameter choices, sublinear static regret and cumulative absolute constraint violation bounds are established. Simulations for a distributed online ridge regression problem demonstrate the feasibility of the proposed algorithm.

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Cite

BibTeXRIS
BibTeX
@article{xiong2026fractionalmemory,
  title = {{Fractional-Memory Distributed Online Optimization with Long-Term Constraints}},
  author = {Menghui Xiong and Mingcheng Dai and Qingyi Liu and Yushun Tan},
  journal = {Fractal and Fractional},
  year = {2026},
  month = oct,
  doi = {10.3390/fractalfract10110735},
  url = {https://www.mdpi.com/2504-3110/10/11/735},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Fractional-Memory Distributed Online Optimization with Long-Term Constraints
AU  - Menghui Xiong
AU  - Mingcheng Dai
AU  - Qingyi Liu
AU  - Yushun Tan
PY  - 2026
DA  - 2026/10/22
JO  - Fractal and Fractional
DO  - 10.3390/fractalfract10110735
UR  - https://www.mdpi.com/2504-3110/10/11/735
AB  - This paper is concerned with distributed online optimization with long-term inequality constraints over time-varying unbalanced directed networks. A fractional-memory-based distributed online optimization algorithm is developed to exploit both current and historical first-order information. Its search direction is constructed using normalized power-law memory weights, whose distribution is regulated by the fractional order and whose memory horizon is determined by the maximum memory lag. An auxiliary-weight mechanism is incorporated to cope with the imbalance of directed communication, while the long-term constraint formulation allows projection onto a computationally tractable superset of the original feasible region, thereby avoiding costly constrained projections at every round. Under suitable assumptions and parameter choices, sublinear static regret and cumulative absolute constraint violation bounds are established. Simulations for a distributed online ridge regression problem demonstrate the feasibility of the proposed algorithm.
SN  - 2504-3110
ER  -