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In the resource-constrained embedded systems, the designing of efficient deep neural networks is a challenging process, due to diversity in the artificial intelligence applications. The quantization in deep neural networks superiorly diminishes the storage and computational time by reducing the bit-width of networks encoding. In order to highlight the problem of accuracy loss, the quantization levels are automatically discovered using Policy Feedback-based Reinforcement Learning Method (PF-RELEQ). In this paper, the Proximal Policy Optimization with Policy Feedback (PPO-PF) technique is proposed to determine the best design decisions by choosing the optimum hyper-parameters. In order to enhance the sensitivity of the value function to the change of policy and to improve the accuracy of value estimation at the early learning stage, a policy update method is devised based on the clipped discount factor. In addition, specifically the loss functions of policy satisfy the unbiased estimation of the trust region. The proposed PF-RELEQ effectively balances quality and speed compared to other deep learning methods like ResNet-1202, ResNet-32, ResNet-110, GoogLeNet and AlexNet. The experimental analysis showed that PF-RELEQ achieved 20% computational work-load reduction compared to the existing deep learning methods on ImageNet, CIFAR-10, CIFAR-100 and tomato leaf disease datasets and achieved approximately 2% of improvisation in the validation accuracy. Additionally, the PF-RELEQ needs only 0.55 Graphics Processing Unit on an NVIDIA GTX-1080Ti to develop DNNs that delivers better accuracy improvement with fewer cycle counts for image classification. [ABSTRACT FROM AUTHOR]