Populations evolving in fluctuating environments face the fundamental challenge of balancing adaptation to current conditions against preparation for uncertain futures. Here, we study theoretically microbial evolution in partially predictable environments using proteome allocation models that capture the trade-off between growth rate and lag time during environmental transitions. We show that evolutionary dynamics drive populations toward an evolutionary stable allocation strategy that minimizes resource depletion time, thereby balancing faster growth with shorter adaptation delays. In environments with temporal structure, populations evolve to learn the statistical patterns of environmental transitions through proteome pre-allocation, with the evolved allocations reflecting the transition probabilities between conditions. Our framework reveals how microbial populations can extract and exploit environmental predictability without explicit neural computation, using the proteome as a distributed memory system that encodes environmental patterns. This work shows how information-theoretic principles can govern cellular resource allocation, providing a mechanistic foundation for understanding learning-like behavior in evolving biological systems.