| Abstract: |
| This work studies the Inverse Reinforcement Learning (IRL) problem for infinite-horizon stationary Mean Field Games (MFGs) under the maximum causal entropy principle. The unknown reward function is embedded in a Reproducing Kernel Hilbert Space (RKHS), enabling the inference of rich and nonlinear reward structures directly from expert demonstrations. This approach addresses fundamental limitations of existing IRL methods that rely on linear reward models and finite-horizon settings. A Lagrangian relaxation is introduced to reformulate the IRL objective as an unconstrained log-likelihood maximization, solved via gradient ascent. Theoretical consistency is established by proving the smoothness of the log-likelihood objective through Frechet differentiability of the associated soft Bellman operators. Numerical experiments on a mean-field traffic routing game validate the effectiveness of the method, demonstrating that the learned policies successfully replicate expert behavior. |
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