Distributed risk-averse optimization via CVaR
Abstract
Distributed systems often operate under uncertainty, where minimizing expected loss may overlook rare but severe events. This paper studies a distributed risk-averse convex optimization problem in which agents cooperatively minimize the average of local conditional value-at-risk (CVaR) objectives over a time-varying network. Each agent has access only to noisy evaluations of its local loss function, rather than to its CVaR objective or gradient. We therefore develop a zeroth-order algorithm that uses sampled losses to construct empirical CVaR estimates and their gradient estimates. At each iteration, agents combine neighboring decisions and perform a local update. Under convexity and Lipschitz continuity assumptions, we prove that the agents reach exact asymptotic consensus. We also establish a finite-time expected suboptimality bound for the weighted ergodic iterate. With diminishing step sizes and fixed sample sizes, the local last iterates converge almost surely to a common optimum, and their limiting expected CVaR gap is bounded in terms of the smoothing and finite-sample errors. This distributed bound matches the parameter dependence of the centralized benchmark provided in this paper. Finally, simulations on a distributed sensor network estimation problem illustrate the efficacy of the method.
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BibTeX
@misc{wang2026distributed,
title = {{Distributed risk-averse optimization via CVaR}},
author = {Siyi Wang and Kun Huang and Lei Xu and Karl H. Johansson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04460},
eprint = {2609.04460},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04460},
note = {CC0},
}
RIS
TY - UNPB
TI - Distributed risk-averse optimization via CVaR
AU - Siyi Wang
AU - Kun Huang
AU - Lei Xu
AU - Karl H. Johansson
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04460
UR - https://arxiv.org/abs/2609.04460
AB - Distributed systems often operate under uncertainty, where minimizing expected loss may overlook rare but severe events. This paper studies a distributed risk-averse convex optimization problem in which agents cooperatively minimize the average of local conditional value-at-risk (CVaR) objectives over a time-varying network. Each agent has access only to noisy evaluations of its local loss function, rather than to its CVaR objective or gradient. We therefore develop a zeroth-order algorithm that uses sampled losses to construct empirical CVaR estimates and their gradient estimates. At each iteration, agents combine neighboring decisions and perform a local update. Under convexity and Lipschitz continuity assumptions, we prove that the agents reach exact asymptotic consensus. We also establish a finite-time expected suboptimality bound for the weighted ergodic iterate. With diminishing step sizes and fixed sample sizes, the local last iterates converge almost surely to a common optimum, and their limiting expected CVaR gap is bounded in terms of the smoothing and finite-sample errors. This distributed bound matches the parameter dependence of the centralized benchmark provided in this paper. Finally, simulations on a distributed sensor network estimation problem illustrate the efficacy of the method.
ER -