We propose a new method for training convolutional neural networks which integrates reinforcement learning along with supervised learning and use ti for transfer learning for classification of glaucoma from colored fundus images. The training method uses hill climbing techniques via two different climber types, viz "random movment" and "random detection" integrated with supervised learning model though stochastic gradient descent with momentum (SGDM) model. The model was trained and tested using the Drishti GS and RIM-ONE-r2 datasets having glaucomatous and normal fundus images. The performance metrics for prediction was tested by transfer learning on five CNN architectures, namely GoogLenet, DesnseNet-201, NASNet, VGG-19 and Inception-resnet-v2. A fivefold classification was used for evaluating the perfroamnace and high sensitivities while high maintaining high accuracies were achieved. Of the models tested, the denseNet-201 architecture performed the best in terms of sensitivity and area under the curve (AUC). This method of training allows transfer learning on small datasets and can be applied for tele-ophthalmology applications including training with local datasets.