An Incremental Off-policy Search in a Model-free Markov Decision Process Using a Single Sample Path

TL;DR

This paper introduces a data-efficient, stable, and robust stochastic approximation algorithm based on the cross entropy method for solving a modified control problem in model-free MDPs using a single sample trajectory, without a generative model.

Contribution

It presents a novel off-policy search algorithm that converges globally to the optimal policy in a restricted setting with limited data and no generative model.

Findings

Algorithm is proven to converge to a globally optimal policy.

Experimental results show superior performance over state-of-the-art methods.

Method is computationally and storage efficient.

Abstract

In this paper, we consider a modified version of the control problem in a model free Markov decision process (MDP) setting with large state and action spaces. The control problem most commonly addressed in the contemporary literature is to find an optimal policy which maximizes the value function, i.e., the long run discounted reward of the MDP. The current settings also assume access to a generative model of the MDP with the hidden premise that observations of the system behaviour in the form of sample trajectories can be obtained with ease from the model. In this paper, we consider a modified version, where the cost function is the expectation of a non-convex function of the value function without access to the generative model. Rather, we assume that a sample trajectory generated using a priori chosen behaviour policy is made available. In this restricted setting, we solve the modified control problem in its true sense, i.e., to find the best possible policy given this limited information. We propose a stochastic approximation algorithm based on the well-known cross entropy method which is data (sample trajectory) efficient, stable, robust as well as computationally and storage efficient. We provide a proof of convergence of our algorithm to a policy which is globally optimal relative to the behaviour policy. We also present experimental results to corroborate our claims and we demonstrate the superiority of the solution produced by our algorithm compared to the state-of-the-art algorithms under appropriately chosen behaviour policy.