Unsupervised Solution Operator Learning for Mean-Field Games via
  Sampling-Invariant Parametrizations
Han Huang Rongjie Lai
Recent advances in deep learning has witnessed many innovative frameworks
that solve high dimensional mean-field games (MFG) accurately and efficiently.
These methods, however, are restricted to solving single-instance MFG and
demands extensive computational time per instance, limiting practicality. To
overcome this, we develop a novel framework to learn the MFG solution operator.
Our model takes a MFG instances as input and output their solutions with one
forward pass. To ensure the proposed parametrization is well-suited for
operator learning, we introduce and prove the notion of sampling invariance for
our model, establishing its convergence to a continuous operator in the
sampling limit. Our method features two key advantages. First, it is
discretization-free, making it particularly suitable for learning operators of
high-dimensional MFGs. Secondly, it can be trained without the need for access
to supervised labels, significantly reducing the computational overhead
associated with creating training datasets in existing operator learning
methods. We test our framework on synthetic and realistic datasets with varying
complexity and dimensionality to substantiate its robustness.