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In this paper, we provide a general framework for studying multi-agent onlinelearning problems in the presence of delays and asynchronicities. Specifically,we propose and analyze a class of adaptive dual averaging schemes in whichagents only need to accumulate gradient feedback received from the wholesystem, without requiring any between-agent coordination. In the single-agentcase, the adaptivity of the proposed method allows us to extend a range ofexisting results to problems with potentially unbounded delays between playingan action and receiving the corresponding feedback. In the multi-agent case,the situation is significantly more complicated because agents may not haveaccess to a global clock to use as a reference point; to overcome this, wefocus on the information that is available for producing each prediction ratherthan the actual delay associated with each feedback. This allows us to deriveadaptive learning strategies with optimal regret bounds, even in a fullydecentralized, asynchronous environment. Finally, we also analyze an"optimistic" variant of the proposed algorithm which is capable of exploitingthe predictability of problems with a slower variation and leads to improvedregret bounds.

Multi-Agent Online Optimization with Delays: Asynchronicity, Adaptivity, and Optimism