Paper:

# Reinforcement Learning for Penalty Avoidance in Continuous State Spaces

## Kazuteru Miyazaki^{*} and Shigenobu Kobayashi^{**}

^{*}Department of Assessment and Research for Degree Awarding, National Institution for Academic Degrees and University Evaluation, 1-29-1 Gakuennishimachi, Kodaira-city, Tokyo 187-8587, Japan

^{**}Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, Kanagawa 226-8502, Japan

Reinforcement learning involves learning to adapt to environments through the presentation of rewards – special input – serving as clues. To obtain quick rational policies, profit sharing (PS) [6], rational policy making algorithm (RPM) [7], penalty avoiding rational policy making algorithm (PARP) [8], and PS-r* [9] are used. They are called PS-based methods. When applying reinforcement learning to actual problems, treatment of continuous-valued input is sometimes required. A method [10] based on RPM is proposed as a PS-based method corresponding to the continuous-valued input, but only rewards exist and penalties cannot be suitably handled. We studied the treatment of continuous-valued input suitable for a PS-based method in which the environment includes both rewards and penalties. Specifically, we propose having PARP correspond to continuous-valued input while simultaneously targeting the attainment of rewards and avoiding penalties. We applied our proposal to the pole-cart balancing problem and confirmed its validity.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11, No.6, pp. 668-676, 2007.

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