The search for multiple escaping targets is a significant issue of cooperative control in multi-agent systems since targets consciously seek to avoid being captured. Moreover, the assumption of continuous observations in existing works is not always suitable due to the limit of measuring equipment and uncertain movement of targets. Therefore, the problem with searching for escaping targets, which can be more aptly labeled "multiple escaping-targets search with random observation conditions" (MESROC), is difficult to address by conventional methods. Inspired by machine learning and the immune response mechanism of human bodies, a self-learning immune co-evolutionary network (SLICEN) is proposed. The SLICEN consists mainly of an immune cellular network (ICN) and an immune learning algorithm (ILA). The ICN provides feasible solutions to MESROC. Different kinds of network models are introduced to work as an ICN, such as convolutional neural networks, extreme learning machines, and support vector machines. The ILA evaluates the performance of feasible solutions and selects the optimal ones to further strengthen ICN reversely. Solutions are repeatedly improved through the co-evolution of ICN and ILA. An essential distinction to conventional machine learning approaches is that SLICEN works well without training samples. Simulations and comparisons demonstrate that patterns of advanced cooperative behavior among searchers function properly. SLICEN is an efficient method for solving MESROC.