In recent years, deep learning technologies have been actively used in various applications. In particular, networks trained using reinforcement learning (RL) are widely exploited for auxiliary tasks in various multimedia frameworks, including image restoration, image compression, and computer vision. Discrete wavelet transform (DWT) and set partitioning in hierarchical trees (SPIHT) are the representative lightweight compression methods that are most widely used for the purposes of frame memory compression and LCD overdrive. In precedent research, in order to improve the compression efficiency of DWT-SPIHT algorithms, the relative complexity of DWT coefficients is quantified, and when compressing DWT coefficients with the SPIHT algorithm, the compression ratio (CR) is adaptively allocated to the compression block according to the numerically expressed complexity. However, the SPIHT algorithm has the characteristic of resource limitation, resulting in the occurrence of remaining blocks, which cannot take advantage of allocating the adaptive CR. Moreover, since the equation expressing the block complexity that determines the CR of each block is obtained through machine learning-based linear regression, it lacks the capability to deal with a wide range of real-world images. To compensate for these drawbacks, this paper optimizes the compression efficiency of the 1-D DWT-SPIHT algorithm using the RL-based episodic auxiliary task. In detail, the proposed method optimally adjusts the proportion of CRs, which are adaptively selected for each block according to the DWT coefficient, through the episodic model trained with the RL algorithm. Consequently, the proposed method achieves an average improvement in peak signal to noise ratio (PSNR) of 2.18dB compared to the baseline 1-D DWT-SPIHT with the fixed compression ratio and 0.68dB compared to the precedent research.