As an important application in the power system operation and electricity market clearing, the network-constrained unit commitment (NCUC) problem is usually executed by Independent System Operators (ISO) in an open-looped predict-then-optimize (O-PO) process, in which an upstream prediction (e.g., on renewable energy sources (RES) and loads) and a downstream NCUC are executed in a queue. However, in the O-PO framework, a statistically more accurate prediction may not necessarily lead to a higher NCUC economics against actual RES and load realizations. To this end, we present a closed-loop predict-and-optimize (C-PO) framework for improving the NCUC economics. Specifically, the C-PO leverages structures (i.e., constraints and objective) of the NCUC model and relevant feature data to train a cost-oriented RES prediction model, in which the prediction quality is evaluated via the induced NCUC cost instead of the statistical forecast errors. Therefore, the loop between the prediction and the optimization is closed to deliver a cost-oriented RES power prediction for NCUC optimization.