Langevin Dynamics for Adaptive Inverse Reinforcement Learning of Stochastic Gradient Algorithms
This work addresses the challenge of reward estimation in IRL for stochastic gradient algorithms, with applications in machine learning domains, but it appears incremental as it builds on existing Langevin dynamics and kernel-based methods.
The paper tackles the problem of inverse reinforcement learning (IRL) for estimating reward functions from noisy gradient estimates generated by stochastic gradient agents, proposing a Langevin dynamics algorithm that asymptotically samples from a distribution proportional to the reward function. The result includes weak convergence proofs and performance illustrations in adaptive Bayesian learning, logistic regression, and constrained Markov decision processes.
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 $R(θ)$; specifically, the resulting Langevin algorithm asymptotically generates samples from the distribution proportional to $\exp(R(θ))$. 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 $R(θ)$ jump changes over time as a slow Markov chain.