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Sensitive discount optimality Unifying discounted and average reward reinforcement learning.pdf

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Sensitive discount optimality Unifying discounted and average reward reinforcement learning

Sensitive Discount Optimality: Unifying Discounted andAverage Reward Reinforcement LearningSridhar Mahadevan Department of Computer Science and EngineeringUniversity of South FloridaTampa, Florida 33620Tel: (813) 974-3260mahadeva@csee.usf.eduMarch 12, 1996AbstractResearch in reinforcement learning (RL) has thus far concentrated on two optimalitycriteria: the discounted framework, which has been very well-studied, and the average-reward framework, in which interest is rapidly increasing. In this paper, we present aframework called sensitive discount optimality which oers an elegant way of linkingthese two paradigms. Although sensitive discount optimality has been well studied indynamic programming, with several provably convergent algorithms, it has not receivedany attention in RL. This framework is based on studying the properties of the expectedcumulative discounted reward, as discounting tends to 1. Under these conditions, thecumulative discounted reward can be expanded using a Laurent series expansion toyields a sequence of terms, the rst of which is the average reward, the second involvesthe average adjusted sum of rewards (or bias), etc. We use the sensitive discountoptimality framework to derive a new model-free average reward technique, which isrelated to Q-learning type methods proposed by Bertsekas, Schwartz, and Singh, butwhich unlike these previous methods, optimizes both the rst and second terms in theLaurent series (average reward and bias values).Keywords: Reinforcement learning, Average Reward.Statement: This paper has not been submitted to any other conference.This research is supported by a National Science Foundation CAREER Award Grant No. IRI-9501852.This paper is to appear in the 13th International Conference on Machine Learning (IMLC-96), Bari, Italy,July 3rd-6th. 1 1 MotivationReinforcement learning (RL) has become one of the most actively studied areas in machinelearning [7, 20]. Thus far, the work in RL has concentrated on one of two opt