Asynchronous Online Learning in Multi-Agent Systems With Proximity Constraints

We consider the problem of distributed learning from sequential data via online convex optimization. A multi-agent system is considered where each agent has a private objective but is willing to cooperate in order to minimize the network cost, which is the sum of local cost functions. Different from the classical distributed settings, where the agents coordinate through the use of consensus constraints, we allow the neighboring agent actions to be related via a non-linear proximity function. A decentralized saddle point algorithm is proposed that is capable of handling gradient delays arising from computational issues. The proposed online asynchronous algorithm is analyzed under adversarial settings by developing bounds on the regret of O(√T), which measures the cumulative loss incurred by the online algorithm against a clairvoyant, and network discrepancy of O(T
^3/4
), which measures the cumulative constraint violation or agent disagreement. By allowing the agents to utilize stale gradient information, the proposed algorithm embraces the nuances of distributed learning and serves to be the first distributed online algorithm that can handle adversarial delays. A modified saddle point algorithm is also proposed that explicitly forces the agents to agree as per the constraint function resulting in zero network discrepancy while incurring a slightly higher regret. To showcase the efficacy of the proposed asynchronous algorithm, a spatially correlated random field estimation problem is formulated and solved. Additionally, an application of vision-based target localization with moving cameras demonstrates the benefits of this approach in practice.