# Using Inverse Optimization to Learn Cost Functions in Generalized Nash Games

arXiv: https://arxiv.org/abs/2102.12415 · HTML: https://mlsanity.com/paper/2102.12415/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 87 references that are in the map.
- First posted on arXiv 24 Feb 2021.

## Builds on (most cited first, 17 of 17)

- [Inverse Optimization with Noisy Data](https://mlsanity.com/paper/1507.03266/) (2015)
- [Data-driven Inverse Optimization with Imperfect Information](https://mlsanity.com/paper/1512.05489/) (2015)
- [Data-Driven Estimation in Equilibrium Using Inverse Optimization](https://mlsanity.com/paper/1308.3397/) (2013)
- [Computational Rationalization: The Inverse Equilibrium Problem](https://mlsanity.com/paper/1308.3506/) (2013)
- [Econometrics for Learning Agents](https://mlsanity.com/paper/1505.00720/) (2015)
- [An Online-Learning Approach to Inverse Optimization](https://mlsanity.com/paper/1810.12997/) (2018)
- [Learning Linear Programs from Optimal Decisions](https://mlsanity.com/paper/2006.08923/) (2020)
- [Inverse Optimization: Closed-form Solutions, Geometry and Goodness of fit](https://mlsanity.com/paper/1511.04650/) (2015)
- [Generalized Inverse Optimization through Online Learning](https://mlsanity.com/paper/1810.01920/) (2018)
- [Inverse optimization for the recovery of constraint parameters](https://mlsanity.com/paper/1811.00726/) (2018)
- [Robust Multi-agent Counterfactual Prediction](https://mlsanity.com/paper/1904.02235/) (2019)
- [Short-term Forecasting of Price-responsive Loads Using Inverse Optimization](https://mlsanity.com/paper/1607.07209/) (2016)
- [Forecasting the Price-Response of a Pool of Buildings via Homothetic Inverse Optimization](https://mlsanity.com/paper/2004.09819/) (2020)
- [Data-Driven Estimation of Travel Latency Cost Functions via Inverse Optimization in Multi-Class Transportation Networks](https://mlsanity.com/paper/1703.04010/) (2017)
- [A Robust Utility Learning Framework via Inverse Optimization](https://mlsanity.com/paper/1704.07933/) (2017)
- [Achieving Target Equilibria in Network Routing Games without Knowing the Latency Functions](https://mlsanity.com/paper/1408.1429/) (2014)
- [Network learning via multi-agent inverse transportation problems](https://mlsanity.com/paper/1609.04117/) (2016)

## Built on by (most cited first, 3 of 3)

- [Is Nash Equilibrium Approximator Learnable?](https://mlsanity.com/paper/2108.07472/) (2021)
- [Operator Splitting for Learning to Predict Equilibria in Convex Games](https://mlsanity.com/paper/2106.00906/) (2021)
- [Online Parameter Identification of Generalized Non-cooperative Game](https://mlsanity.com/paper/2310.09511/) (2023)

## Abstract (arXiv)

As demonstrated by Ratliff et al. (2014), inverse optimization can be used to recover the objective function parameters of players in multi-player Nash games. These games involve the optimization problems of multiple players in which the players can affect each other in their objective functions. In generalized Nash equilibrium problems (GNEPs), a player's set of feasible actions is also impacted by the actions taken by other players in the game; see Facchinei and Kanzow (2010) for more background on this problem. One example of such impact comes in the form of joint/"coupled" constraints as referenced by Rosen (1965), Harker (1991), and Facchinei et al. (2007) which involve other players' variables in the constraints of the feasible region. We extend the framework of Ratliff et al. (2014) to find inverse optimization solutions for the class of GNEPs with joint constraints. The resulting formulation is then applied to a simulated multi-player transportation problem on a road network. Also, we provide some theoretical results related to this transportation problem regarding runtime of the extended framework as well as uniqueness and non-uniqueness of solutions to our simulation experiments. We see that our model recovers parameterizations that produce the same flow patterns as the original parameterizations and that this holds true across multiple networks, different assumptions regarding players' perceived costs, and the majority of restrictive capacity settings and the associated numbers of players. Code for the project can be found at: https://github.com/sallen7/IO_GNEP.