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We investigate the fundamental optimization question of minimizing a targetfunction $f$, whose gradients are expensive to compute or have limitedavailability, given access to some auxiliary side function $h$ whose gradientsare cheap or more available. This formulation captures many settings ofpractical relevance, such as i) re-using batches in SGD, ii) transfer learning,iii) federated learning, iv) training with compressed models/dropout, etc. Wepropose two generic new algorithms that apply in all these settings and provethat we can benefit from this framework using only an assumption on the Hessiansimilarity between the target and side information. A benefit is obtained whenthis similarity measure is small, we also show a potential benefit fromstochasticity when the auxiliary noise is correlated with that of the targetfunction.

Optimization with Access to Auxiliary Information