Bayesian method speeds up finding game parameters from noisy data
Bayesian Learning of Parametric Mean Field Games with Common Noise
Computer Science and Game Theory
Summary
The authors address the challenge of figuring out hidden settings that govern how many people behave in large groups facing randomness. Their method uses a new mathematical trick to handle the complexity caused by shared uncertain events, allowing quicker and better guesses of these hidden settings from just a few noisy observations. They tested this approach on made-up examples and real electricity market data and showed it works better than earlier methods.
What this means in practice
- •For energy market analysts: Identify underlying parameters in market models from limited noisy observational data to improve market understanding and forecasting.
- •For algorithm developers: Improve algorithms for inverse learning in large multi-agent systems affected by common uncertainty using the Bayesian-Extended mean field game approach.
Authors
Grégoire Lambrecht, Mathieu Laurière
Abstract
We study the inverse problem of recovering unknown parameters governing the dynamics and rewards of Mean Field Games (MFGs) from partial observations of population trajectories, made stochastic by common noise. The observer seeks to recover a consistent parameter $θ$ via Bayesian inference, facing the challenge that evaluating the likelihood requires solving a new Nash equilibrium (NE) for each candidate $θ$. Due to common noise, the mean-field evolution is stochastic and equilibrium policies are population dependent, which makes solving for each parameter computationally expensive. To overcome this, we introduce the Bayesian-Extended Mean Field Game (BE-MFG), whose single NE simultaneously encodes equilibrium policies for all parameters, enabling efficient learning of the conditional density of mean-field trajectories. We formalize parameter consistency and identifiability in MFGs with common noise and investigate conditions under which consistent parameter recovery is guaranteed. On three synthetic environments of various complexity, we recover the ground-truth parameter accurately from a small number of partial, stochastic observations, outperforming an adaptation of inverse reinforcement learning for MFGs. A fourth experiment, on public electricity market data, suggests that the approach can also be applied to real-world data.