A decentralised forward-backward-type algorithm with network-independent heterogenous agent step sizes

Consider the problem of finding a zero of a finite sum of maximally monotone operators, where some operators are Lipschitz continuous and the rest are potentially set-valued. We propose a forward-backward-type algorithm for this problem suitable for decentralised implementation. In each iteration, agents evaluate a Lipschitz continuous operator and the resolvent of a potentially set-valued operator, and then communicate with neighbouring agents. Agents choose their step sizes independently using only local information, and the step size upper bound has no dependence on the communication graph. We demonstrate the potential advantages of the proposed algorithm with numerical results for min-max problems and aggregative games.