Cordial Learning lets agents exchange only low-dimensional outputs and converge to a global optimum on correlated data

Introduces the cordial (correlated and distributed) learning setting and method for distributed learning tasks where an agent's label depends on other agents' inputs for the same sample and those inputs are also correlated. Existing decentralized methods such as federated learning ignore the structure of the problem and perform poorly on correlated data, while centralized approaches are infeasible due to privacy and communication constraints; cordial learning addresses this gap. The abstract states the problem setting and method positioning, noting that decentralized methods like federated learning perform poorly on correlated data and that centralized approaches are infeasible due to privacy and communication constraints.

The method shares only low-dimensional outputs between agents while training local models to extract informative signals from peers. Unlike sharing model parameters or raw data, communication is compressed to low-dimensional outputs while retaining the ability to exploit peer information. The abstract describes it as 'sharing only low-dimensional outputs between the agents while training local models to extract informative signals from peers'.

The distributed learning is characterized as a game in which the loss function of each agent depends on the models of others. Formalizes distributed training as a game of interdependent agents, providing a framework for convergence analysis. The abstract states it 'induces a game in which the loss function of each agent depends on the models of others'.

Under a linear model assumption, proves convergence with probability one to a globally optimal solution despite the nonconvex global objective, and validates on structured multi-digit MNIST tasks that it remains highly effective in highly nonlinear settings. Provides a probability-one global optimality guarantee under a nonconvex global objective and extends the method from linear analysis to nonlinear experimental settings. The abstract states it 'converges with probability one to a globally optimal solution, despite the nonconvex global objective', with experiments on 'structured multi-digit MNIST tasks' reported as remaining highly effective in highly nonlinear settings.

The work targets distributed learning settings where agents share the same environment, an agent's label depends on other agents' inputs, and those inputs are correlated; it applies when centralized training is infeasible under privacy and communication constraints and sharing raw data or full models is undesirable. The method operates by sharing only low-dimensional outputs and training local models to extract signals from peers. The theoretical guarantee applies under a linear model assumption, and the experimental validation uses structured multi-digit MNIST tasks.

The abstract does not specify the form and dimensionality of the low-dimensional outputs, the number of agents and topology, or communication rounds and overhead, nor does it give quantitative metrics or baseline comparison details for the multi-digit MNIST experiments; how the linear-model convergence proof extends to nonlinear models remains an open question. Readers needing to reproduce results or assess practical communication costs would need the proofs and experimental setup in the full text.