A theoretical deepening of mean performance optimization in finite Markov decision processes and its application in information theory

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K11674
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60010:Theory of informatics-related
• Research Institution: University of Fukui
• Principal Investigator: Iwata Ken-ichi 福井大学, 学術研究院工学系部門, 教授 (80284313)
• Co-Investigator(Kenkyū-buntansha): 山本 博資 東京大学, 大学院新領域創成科学研究科, 名誉教授 (30136212)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 情報理論 / 情報源符号 / 平均符号長 / マルコフ決定過程 / 準瞬時符号 / AIFV符号

Outline of Final Research Achievements

This research considers optimizing performance in Markov chains satisfying conditions (a) and (b), and we apply the optimization to source coding. (a) The performance in each state s_i of the Markov chain is determined by the performance function f_i(t_i), i=0, 1, ... , m-1, and we choose each state's variable t_i. (b) The variable t_i determines the transition probability p_i (s_j | s_i, t_i) from state s_i to state s_j and the pair of variables t = (t_i, i =0, 1, ... , m-1) uniquely determines the stationary distribution Q_i of the states s_i in the Markov chain. The optimizing method for average performance under (a) and (b) was applied to the almost instantaneous source coding.

Free Research Field

情報理論

Academic Significance and Societal Importance of the Research Achievements

無歪み情報源符号(データ圧縮)における準瞬時符号は，2015年の"Almost Instantaneous Fixed-to-Variable Length Codes"により提案された符号である．準瞬時符号のクラスにおいて平均符号長を最小にする符号構成法は未解決であった．本研究はマルコフ決定課程における平均性能最適化を検討し，準瞬時符号のクラスにおいて平均符号長を最小にする符号構成法にある種の一般的な手法を提案した．