As a main use case of 5G and Beyond wireless network, the ever-increasing machine type communications (MTC) devices pose critical challenges over MTC network in recent years. It is imperative to support massive MTC devices with limited resources. To this end, Non-orthogonal multiple access (NOMA) based random access network has been deemed as a prospective candidate for MTC network. In this paper, we propose a deep reinforcement learning (RL) based approach for NOMA-based random access network with truncated channel inversion power control. Specifically, each MTC device randomly selects a pre-defined power level with a certain probability for data transmission. Devices are using channel inversion power control yet subject to the upper bound of the transmission power. Due to the stochastic feature of the channel fading and the limited transmission power, devices with different achievable power levels have been categorized as different types of devices. In order to achieve high throughput with considering the fairness between all devices, two objective functions are formulated. One is to maximize the minimum long-term expected throughput of all MTC devices, the other is to maximize the geometric mean of the long-term expected throughput for all MTC devices. A Policy based deep reinforcement learning approach is further applied to tune the transmission probabilities of each device to solve the formulated optimization problems. Extensive simulations are conducted to show the merits of our proposed approach.