Propose a strategy for efficiently evaluating and selecting the best deep neural network architecture for your product recommender system. Explain how you would balance competing constraints such as computational resources, deadlines, and model performance.

First, use random filters in the convolutional layers to quickly evaluate multiple architectures and select the top performers. This approach allows us to efficiently explore the design space without investing too much time or resources upfront. Once we have narrowed down our options, we can fine-tune each of these architectures using more expensive methods such as gradient descent.