Universal Option Models

Abstract

We consider the problem of learning models of options for real-time abstract plan-ning, in the setting where reward functions can be specified at any time and their expected returns must be efficiently computed. We introduce a new model for an option that is independent of any reward function, called the universal option model (UOM). We prove that the UOM of an option can construct a traditional option model given a reward function, and also supports efficient computation of the option-conditional return. We extend the UOM to linear function approxi-mation, and we show the UOM gives the TD solution of option returns and the value function of a policy over options. We provide a stochastic approximation algorithm for incrementally learning UOMs from data and prove its consistency. We demonstrate our method in two domains. The first domain is a real-time strat-egy game, where the controller must select the best game unit to accomplish a dynamically-specified task. The second domain is article recommendation, where each user query defines a new reward function and an article’s relevance is the ex-pected return from following a policy that follows the citations between articles. Our experiments show that UOMs are substantially more efficient than previously known methods for evaluating option returns and policies over options. 1