On the Benefits of Multiple Gossip Steps in Communication-Constrained Decentralized Optimization
This work addresses communication constraints in training large-scale machine learning models in decentralized settings, offering a novel algorithmic approach with theoretical guarantees.
The paper tackles the problem of decentralized optimization with lossy compressed communication, showing that using multiple gossip steps between gradient iterations enables convergence to within ε of the optimal value for smooth non-convex objectives satisfying the Polyak-Łojasiewicz condition, with O(log(1/ε)) gradient and gossip steps.
In decentralized optimization, it is common algorithmic practice to have nodes interleave (local) gradient descent iterations with gossip (i.e. averaging over the network) steps. Motivated by the training of large-scale machine learning models, it is also increasingly common to require that messages be {\em lossy compressed} versions of the local parameters. In this paper, we show that, in such compressed decentralized optimization settings, there are benefits to having {\em multiple} gossip steps between subsequent gradient iterations, even when the cost of doing so is appropriately accounted for e.g. by means of reducing the precision of compressed information. In particular, we show that having $O(\log\frac{1}ε)$ gradient iterations {with constant step size} - and $O(\log\frac{1}ε)$ gossip steps between every pair of these iterations - enables convergence to within $ε$ of the optimal value for smooth non-convex objectives satisfying Polyak-Łojasiewicz condition. This result also holds for smooth strongly convex objectives. To our knowledge, this is the first work that derives convergence results for nonconvex optimization under arbitrary communication compression.