How do cost functions behave in distributed training systems?

In distributed training, the cost function is decomposed across workers and aggregated through synchronization strategies.

In distributed learning, each worker computes gradients on a subset of data, effectively optimizing a local approximation of the global cost function. The global objective remains unchanged, but synchronization methods like AllReduce ensure gradient consistency. Challenges include stale gradients, communication overhead, and gradient variance between nodes. The cost function itself remains mathematically identical, but its optimization path becomes asynchronous and noisy due to system constraints.