Bayesian learning of noisy Markov decision processes

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the structure of a Markov decision process. Adopting a Bayesian approach to inference, we show how latent variables of the model can be estimated, and how predictions about actions can be made, in a unified framework. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from the posterior distribution. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller

Trace-class Gaussian priors for Bayesian learning of neural networks with MCMC

This paper introduces a new neural network based prior for real valued functions on $\mathbb R^d$ which, by construction, is more easily and cheaply scaled up in the domain dimension $d$ compared to the usual Karhunen-Lo\`eve function space prior. The new prior is a Gaussian neural network prior, where each weight and bias has an independent Gaussian prior, but with the key difference that the variances decrease in the width of the network in such a way that the resulting function is almost surely well defined in the limit of an infinite width network. We show that in a Bayesian treatment of inferring unknown functions, the induced posterior over functions is amenable to Monte Carlo sampling using Hilbert space Markov chain Monte Carlo (MCMC) methods. This type of MCMC is popular, e.g. in the Bayesian Inverse Problems literature, because it is stable under mesh refinement, i.e. the acceptance probability does not shrink to $0$ as more parameters of the function's prior are introduced, even ad infinitum. In numerical examples we demonstrate these stated competitive advantages over other function space priors. We also implement examples in Bayesian Reinforcement Learning to automate tasks from data and demonstrate, for the first time, stability of MCMC to mesh refinement for these type of problems.Comment: 24 pages, 21 figure

Bayesian learning of noisy Markov decision processes

This work addresses the problem of estimating the optimal value function in a Markov Decision Process from observed state-action pairs. We adopt a Bayesian approach to inference, which allows both the model to be estimated and predictions about actions to be made in a unified framework, providing a principled approach to mimicry of a controller on the basis of observed data. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from theposterior distribution over the optimal value function. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller

Bayesian Learning of Noisy Markov Decision Processes

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the structure of a Markov decision process. Adopting a Bayesian approach to inference, we show how latent variables of the model can be estimated, and how predictions about actions can be made, in a unified framework. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from the posterior distribution. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller

Bayesian Learning of Noisy Markov Decision Processes

This work addresses the problem of estimating the optimal value function in a MarkovDecision Process from observed state-action pairs. We adopt a Bayesian approach toinference, which allows both the model to be estimated and predictions about actions tobe made in a unified framework, providing a principled approach to mimicry of a controlleron the basis of observed data. A new Markov chain Monte Carlo (MCMC) sampler isdevised for simulation from the posterior distribution over the optimal value function.This step includes a parameter expansion step, which is shown to be essential for goodconvergence properties of the MCMC sampler. As an illustration, the method is appliedto learning a human controller.