This paper discusses model estimation in offline model-based reinforcement learning (MBRL), which is important for subsequent policy improvement using an estimated model. From the viewpoint of covariate shift, a natural idea is model estimation weighted by the ratio of the state-action distributions of offline data and real future data. However, estimating such a natural weight is one of the main challenges for off-policy evaluation, which is not easy to use. As an artificial alternative, this paper considers weighting with the state-action distribution ratio of offline data and simulated future data, which can be estimated relatively easily by standard density ratio estimation techniques for supervised learning. Based on the artificial weight, this paper defines a loss function for offline MBRL and presents an algorithm to optimize it. Weighting with the artificial weight is justified as evaluating an upper bound of the policy evaluation error. Numerical experiments demonstrate the effectiveness of weighting with the artificial weight.

Typical methods for solving reinforcement learning problems iterate two steps, policy evaluation and policy improvement. This paper proposes algorithms for the policy evaluation to improve learning efficiency. The proposed algorithms are based on the Krylov Subspace Method (KSM), which is a nonstationary iterative method. The algorithms based on KSM are tens to hundreds times more efficient than existing algorithms based on the stationary iterative methods. Algorithms based on KSM are far more efficient than they have been generally expected. This paper clarifies what makes algorithms based on KSM makes more efficient with numerical examples and theoretical discussions.