Efficient Inverse Multiagent Learning
Denizalp Goktas, Amy Greenwald, Sadie Zhao, Alec Koppel, Sumitra, Ganesh
TL;DR
This paper introduces polynomial-time algorithms for inverse multiagent learning and inverse game theory, enabling efficient estimation of game parameters and equilibria from observed behaviors, with applications in market prediction.
Contribution
The paper develops novel polynomial-time algorithms for inverse multiagent learning and inverse game theory, extending to simulacral learning, with theoretical guarantees and practical market prediction applications.
Findings
Outperforms ARIMA in predicting Spanish electricity prices
Provides polynomial-time solutions for inverse game-theoretic problems
Extends methods to simulacral learning with sample efficiency
Abstract
In this paper, we study inverse game theory (resp. inverse multiagent learning) in which the goal is to find parameters of a game's payoff functions for which the expected (resp. sampled) behavior is an equilibrium. We formulate these problems as generative-adversarial (i.e., min-max) optimization problems, for which we develop polynomial-time algorithms to solve, the former of which relies on an exact first-order oracle, and the latter, a stochastic one. We extend our approach to solve inverse multiagent simulacral learning in polynomial time and number of samples. In these problems, we seek a simulacrum, meaning parameters and an associated equilibrium that replicate the given observations in expectation. We find that our approach outperforms the widely-used ARIMA method in predicting prices in Spanish electricity markets based on time-series data.
Peer Reviews
Decision·ICLR 2024 spotlight
* An inverse game theoretic perspective to multi-agent inverse reinforcement learning is certainly a novel direction to approach the problem with. Backed by results in inverse game theory, this approach leads to algorithms with desirable convergence guarantees that prior work in multi-agent imitation learning does not provide. * The low restrictiveness of the assumptions made allow for the framework to be effective on a vast majority of markov games, leading to useful and efficient solutions on
* It would be helpful to expand on the proofs of theorems 6.1, 6.2, and 6.3 in the supplementary material. I know that a reference has been provided, but a slight explanation of the cited result and how it relates to the theorem in question would be nice. * Although a comparison of the method has been shown with the ARIMA model on the spanish electricity market data, it would be beneficial to have a comparison with prior methods in inverse multi-agent reinforcement learning. Especially in terms
1. This paper formulate the inverse game as an generative-adversarial optimization problem and provide polynomial time algorithms.
1. The proofs are not completed, e.g., I cannot find the proofs for Theorem 4.1 and Theorem 5.2. 2. The presentation can be further improved, e.g., more intuitions about the assumptions and theorems.
The simple formulation of the set of inverse Nash equilibria (NE) as a min-max game is elegant and appears to be original. If it is indeed original, for this alone, the paper merits publication and should be highlighted. The paper overall is well written and showcases immediate applications of the proposed solution to an important and practical domain as a proof-of-concept. I believe these results are significant and will be impactful.
As an easily rectified issue, Figure 1 could have been better represented by plotting residuals over time or, by subsampling the data, plotting mean residuals with error bars. As a minor complaint, I do not prefer the language of "generative-adversarial" (especially not in terms of a "discriminator"), even if this is the closest analogy familiar to machine learning practitioners: This is a standard min-max optimization problem that need not be wed to the ML setting.
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Taxonomy
TopicsData Stream Mining Techniques · Neural Networks and Applications · Anomaly Detection Techniques and Applications