# Coordinated Online Learning for Multi-Agent Systems with Coupled Constraints and Perturbed Utility Observations

arXiv: https://arxiv.org/abs/2010.10878 · HTML: https://mlsanity.com/paper/2010.10878/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2020.

## Built on by (most cited first, 1 of 1)

- [Personalized incentives as feedback design in generalized Nash equilibrium problems](https://mlsanity.com/paper/2203.12948/) (2022)

## Abstract (arXiv)

Competitive non-cooperative online decision-making agents whose actions increase congestion of scarce resources constitute a model for widespread modern large-scale applications. To ensure sustainable resource behavior, we introduce a novel method to steer the agents toward a stable population state, fulfilling the given coupled resource constraints. The proposed method is a decentralized resource pricing method based on the resource loads resulting from the augmentation of the game's Lagrangian. Assuming that the online learning agents have only noisy first-order utility feedback, we show that for a polynomially decaying agents' step size/learning rate, the population's dynamic will almost surely converge to generalized Nash equilibrium. A particular consequence of the latter is the fulfillment of resource constraints in the asymptotic limit. Moreover, we investigate the finite-time quality of the proposed algorithm by giving a nonasymptotic time decaying bound for the expected amount of resource constraint violation.