6 research outputs found
Distributed Online Optimization via Gradient Tracking with Adaptive Momentum
This paper deals with a network of computing agents aiming to solve an online
optimization problem in a distributed fashion, i.e., by means of local
computation and communication, without any central coordinator. We propose the
gradient tracking with adaptive momentum estimation (GTAdam) distributed
algorithm, which combines a gradient tracking mechanism with first and second
order momentum estimates of the gradient. The algorithm is analyzed in the
online setting for strongly convex and smooth cost functions. We prove that the
average dynamic regret is bounded and that the convergence rate is linear. The
algorithm is tested on a time-varying classification problem, on a (moving)
target localization problem and in a stochastic optimization setup from image
classification. In these numerical experiments from multi-agent learning,
GTAdam outperforms state-of-the-art distributed optimization methods
Multi-Agent Online Optimization with Delays: Asynchronicity, Adaptivity, and Optimism
Online learning has been successfully applied to many problems in which data
are revealed over time. In this paper, we provide a general framework for
studying multi-agent online learning problems in the presence of delays and
asynchronicities. Specifically, we propose and analyze a class of adaptive dual
averaging schemes in which agents only need to accumulate gradient feedback
received from the whole system, without requiring any between-agent
coordination. In the single-agent case, the adaptivity of the proposed method
allows us to extend a range of existing results to problems with potentially
unbounded delays between playing an action and receiving the corresponding
feedback. In the multi-agent case, the situation is significantly more
complicated because agents may not have access to a global clock to use as a
reference point; to overcome this, we focus on the information that is
available for producing each prediction rather than the actual delay associated
with each feedback. This allows us to derive adaptive learning strategies with
optimal regret bounds, at both the agent and network levels. Finally, we also
analyze an "optimistic" variant of the proposed algorithm which is capable of
exploiting the predictability of problems with a slower variation and leads to
improved regret bounds