Nonlinear equalization (NLE) is essential for guaranteeing the performance of an optical network (ON). Effective NLE implementation relies on key parameters of the transmission link, including the modulation format (MF) and the launch power. As ONs become more agile, the parameters of fiber optical transmission need to be adaptive and relevant to the routing condition. Therefore, successful NLE implementation relies on the realization of transmission awareness (TA). Although machine learning-enabled optical performance monitoring (OPM) has been extensively investigated in the past few years, current NLE algorithms cannot autonomously perceive transmission parameters. Furthermore, current TA implementation still needs human intervention to guide the NLE. In addition, existing ML-based OPM and NLE cannot be trained autonomously, leading to the incapability of environmental change and mislabeling. Here, we propose cognitive learning (CL) for TA-guided NLE in agile ONs. We perform an experiment involving 32 Gbaud polarization-division-multiplexed (PDM)-quadrature phase shift keying (QPSK)/16-quadrature amplitude modulation (QAM) transmission over 1500 km of standard single-mode fiber (SSMF) with a variable launch power from 0 to 3 dBm. When a deep neural network (DNN) with amplitude histograms (AHs) as inputs and one step per span-learned digital back-propagation (1stps-LDBP) are developed, the CL simultaneously enables both TA and NLE, with the capability of self-learning, mislabeling resistance, and dynamic adaptation. The proof-of-concept experimental results indicate that both the accuracy of TA and the Q-factor of PDM-16QAM can be improved by 34.8% and 0.84 dB, respectively, when the launch power is 3 dBm. Moreover, the accuracy of TA is enhanced by 35.3%, even when the used data has 30% mislabeling. Therefore, the CL framework can be customized to satisfy various NLE implementations, thereby supporting the adaptive transmission of agile ONs.