  Inverse reinforcement learning (IRL) aims to estimate the reward function of
optimizing agents by observing their response (estimates or actions). This
paper considers IRL when noisy estimates of the gradient of a reward function
generated by multiple stochastic gradient agents are observed. We present a
generalized Langevin dynamics algorithm to estimate the reward function
$R(\theta)$; specifically, the resulting Langevin algorithm asymptotically
generates samples from the distribution proportional to $\exp(R(\theta))$. The
proposed IRL algorithms use kernel-based passive learning schemes. We also
construct multi-kernel passive Langevin algorithms for IRL which are suitable
for high dimensional data. The performance of the proposed IRL algorithms are
illustrated on examples in adaptive Bayesian learning, logistic regression
(high dimensional problem) and constrained Markov decision processes. We prove
weak convergence of the proposed IRL algorithms using martingale averaging
methods. We also analyze the tracking performance of the IRL algorithms in
non-stationary environments where the utility function $R(\theta)$ jump changes
over time as a slow Markov chain.
