Kati8/ICLR_2023_2025 huggingface dataset:
authors: Denizalp Goktas
authors: David C. Parkes
authors: Ian Gemp
authors: Luke Marris
authors: Georgios Piliouras
authors: Romuald Elie
authors: Guy Lever
authors: Andrea Tacchetti
reviews: 
Comments: In this paper, the authors present a novel neural network-based method for approximating the generalized Nash equilibrium (GNE) within pseudo-games derived from a specific distribution. These pseudo-games consist of players operating within compact and convex action spaces, where the choices made by each player can influence the feasible action space of others.

To facilitate the training of the GNE neural network solver, the authors introduce exploitability as the loss function.  Exploitability quantifies the total utility gains that all players would achieve by deviating to their own best responses. However, calculating exploitability poses a challenge due to the potentially infinite action space. To tackle this issue, an adversarial network is employed to approximate each player's best response.

The authors also establish a theoretical framework by providing a generalization bound for this neural solver. Furthermore, in practical experiments, they apply this approach to identify Nash equilibria in normal-form games, compute competitive equilibria in Arrow-Debreu economic models, and determine GNE in an environmental economic model involving the Kyoto mechanism.
Strengths: - The versatility of this method is evident because it can be applied to a wide range of games, thanks to the inherent generality of pseudo-games.
- The methodology looks strong. The use of two neural networks (a generator and a discriminator) and adversarial training is intriguing to me.
- The concept of employing a neural network as a function approximator to compute GNE is innovative. I believe it has the potential to expedite equilibrium computation in practice.
Weaknesses: - The title in the PDF is still the template title.
- The paper concentrates on finding a single equilibrium, yet many games have multiple equilibria. Incorporating a discussion on equilibrium selection would enhance the work.
- The overall presentation of this paper would benefit from further refinement. The figures within the paper are small and appear blurry due to the absence of vector graphics formats such as .pdf or .svg. Upgrading the figures to vector graphics would improve their clarity and overall visual impact.
Recommendation: 6: marginally above the acceptance threshold
Reviewer confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness/correctness: 4 excellent
Clarity: 2 fair
reviews: 
Comments: This paper study the generalized Nash equilibrium of pseudo games where a player’s action not only affects his utility, but also other players’ action sets. The authors use GAN and employ exploitability as the loss function. The solver is applied to compute the GNE of Arrow-Debreu competitive economies and the Kyoto mechanism.
Strengths: 1. Introduce a novel method to compute GNE by GAN.
2. Provide theoretical guarantee on convergence and generalization bounds.
3. The performance is better according to the experiments.
4. The literature review in the appendix summarizes the current methods to solve GNE and the application of pseudo games.
Weaknesses: 1. Assume strong concavity in assumption 1, however, the utility function is not strong convex in Arrow-Debreu competitive economy.
2. Do not provide guarantee for the performance on the training set.
3. Use different network architecture in two experiments which means GAES is not a general solver for GNE.
Recommendation: 5: marginally below the acceptance threshold
Reviewer confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness/correctness: 2 fair
Clarity: 2 fair
reviews: 
Comments: This work proposes a novel algorithm, General Adversarial Equilibrium Solvers, for training general GNE solvers.

The goal of equilibrium solvers is, given a strategic game between multiple players, to find a (generalized) Nash equilibrium of the game. 

While there has been a few previous work that proposes algorithms to train equilibrium solvers, they all suffers from three technical challenges:
- the gradient of the exploitability requires solving a concave maximization problem
- the exploitability of pseudo-games is in general not Lipschitz-continuous
- the gradients cannot be bounded in general

The authors formulates equilibrium solver training as training a generative adversarial networks, where the generator takes a pseudo-game representation, and outputs a tuple of actions (one per player), and the discriminator takes both the pseudo-game, and the output of the generator, and outputs a best-response for each player.

The goal of discriminator is to output a best-response actions that produces the exploitability, and the goal of generator is to output actions that minimizes the exploitability, i.e., GNE.
Strengths: # Presentation
- The paper is well-organized and easy-to-follow: Sec.1 motivates the readers by illustrating the possible applications of GNE solvers, including network communication, cloud computing, and economic models (e.g., Arrow-Debreu exchange economy, Kyoto joint implementation mechanism)

# Novelty, Technical Contribution
- The formulation of GAES establishes a novel, efficient, simple, and scalable algorithm to train generic GNE solvers.
    - To the best of my knowledge, most of the previous work relied on supervised learning, and suffered from a few technical challenges in terms of computational tractability and stability. 
    - GAES beautifully solves these problems, and provides a simple yet powerful framework for training GNE solvers.
- The formulation is strongly backed up by theoretical guarantees; convergence of the networks towards a stationary point of exploitability, and sample complexity. 
- The experiments are conducted on non-trivial games, namely Arrow-Debreu exchange economies and Kyoto joint implementation mechanism — which are non-monotone or non-jointly convex. Strong empirical results on these games verifies the efficiency of GAES.
Weaknesses: # Weaknesses
- I don’t see any special weakness in this paper. The authors establish a simple yet powerful framework for training GNE solvers, and backs up their algorithm both with strong theoretical guarantees and empirical results.
Recommendation: 10: strong accept, should be highlighted at the conference
Reviewer confidence: 5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.
Soundness/correctness: 4 excellent
Clarity: 4 excellent