# An active learning method for solving competitive multi-agent decision-making and control problems

arXiv: https://arxiv.org/abs/2212.12561 · HTML: https://mlsanity.com/paper/2212.12561/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 69 references that are in the map.
- First posted on arXiv 23 Dec 2022.

## Builds on (most cited first, 18 of 18)

- [Global optimization via inverse distance weighting and radial basis functions](https://mlsanity.com/paper/1906.06498/) (2019)
- [Reliably-stabilizing piecewise-affine neural network controllers](https://mlsanity.com/paper/2111.07183/) (2021)
- [A Bayesian optimization approach to find Nash equilibria](https://mlsanity.com/paper/1611.02440/) (2016)
- [Active Learning for Regression by Inverse Distance Weighting](https://mlsanity.com/paper/2204.07177/) (2022)
- [Learning Equilibria of Games via Payoff Queries](https://mlsanity.com/paper/1302.3116/) (2013)
- [Learning Probably Approximately Correct Maximin Strategies in Simulation-Based Games with Infinite Strategy Spaces](https://mlsanity.com/paper/1911.07755/) (2019)
- [Recurrent Neural Network Training with Convex Loss and Regularization Functions by Extended Kalman Filtering](https://mlsanity.com/paper/2111.02673/) (2021)
- [Query Complexity of Approximate Nash Equilibria](https://mlsanity.com/paper/1306.6686/) (2013)
- [On the Communication Complexity of Approximate Nash Equilibria](https://mlsanity.com/paper/1302.3793/) (2013)
- [The Query Complexity of Correlated Equilibria](https://mlsanity.com/paper/1305.4874/) (2013)
- [Charging plug-in electric vehicles as a mixed-integer aggregative game](https://mlsanity.com/paper/1910.10272/) (2019)
- [Dynamic control of agents playing aggregative games with coupling constraints](https://mlsanity.com/paper/1609.08962/) (2016)
- [Approximating Nash Equilibria for Black-Box Games: A Bayesian Optimization Approach](https://mlsanity.com/paper/1804.10586/) (2018)
- [Efficient Learning of a Linear Dynamical System with Stability Guarantees](https://mlsanity.com/paper/2102.03664/) (2021)
- [Learning Convex Partitions and Computing Game-theoretic Equilibria from Best Response Queries](https://mlsanity.com/paper/1807.06170/) (2018)
- [Learning equilibria with personalized incentives in a class of nonmonotone games](https://mlsanity.com/paper/2111.03854/) (2021)
- [Distributed Stochastic Nash Equilibrium Learning in Locally Coupled Network Games with Unknown Parameters](https://mlsanity.com/paper/2204.00100/) (2022)
- [Personalized incentives as feedback design in generalized Nash equilibrium problems](https://mlsanity.com/paper/2203.12948/) (2022)

## Abstract (arXiv)

To identify a stationary action profile for a population of competitive agents, each executing private strategies, we introduce a novel active-learning scheme where a centralized external observer (or entity) can probe the agents' reactions and recursively update simple local parametric estimates of the action-reaction mappings. Under very general working assumptions (not even assuming that a stationary profile exists), sufficient conditions are established to assess the asymptotic properties of the proposed active learning methodology so that, if the parameters characterizing the action-reaction mappings converge, a stationary action profile is achieved. Such conditions hence act also as certificates for the existence of such a profile. Extensive numerical simulations involving typical competitive multi-agent control and decision-making problems illustrate the practical effectiveness of the proposed learning-based approach.