Online Information Compression of Finite-valued Networks via Finite Automata Approach and Reinforcement Learning

The storage and transmission of large-scale data are recognized as significant challenges that incur substantial costs due to the massive volume of information involved. Lossless compression offers a potential solution to this problem. In this work, we explore the online lossless state compression (LSC) in finite-valued networks by effectively combining the methods of finite state automata and reinforcement learning. To achieve online lossless compression, the concept of k-step compressed walks (state sequences) is introduced. By constructing a finite state automaton to identify all insertable walks, the recoverability conditions of online lossless compression are presented. For any given compressed walk w’_c, one algorithm is proposed to find a minimal recoverable k_min-step compressed walk, thereby improving the compression ratio. Furthermore, it can be found that if a compressed walk keeps recoverability, adding more states to it would not break this property. Additionally, a model-free reinforcement learning framework based on Q-learning is developed to obtain globally minimal recoverable compressed walks. Finally, a numerical example is given to demonstrate the efficiency of the proposed online lossless compression scheme, achieving a compression ratio of 44.4%.