Decentralized Online Exp-Concave Optimization

Key points

• While recent work has established near-optimal regret guarantees for convex and strongly convex losses, the case of exp-concave losses remains an open challenge: specifically, whether logarithmic regret is achievable.1
• In this paper, we answer this question affirmatively by proposing Decentralized Online Newton Step (D-ONS), which adapts the idea of blocking and accelerated gossip to the Online Newton Step algorithm in a non-trivial manner.1
• Concretely, our algorithm achieves a regret bound of $O\left(Nd(1-σ2)^{-1/2}\,\log^2(T) \right)$ where $N$ is the number of agents, $d$ is the dimension, $T$ is the horizon, and $1-σ2$ represents the spectral gap of the network.1
• To our knowledge, this is the first logarithmic regret bound for decentralized online exp-concave optimization.1

Sources (1)

• [1]Decentralized Online Exp-Concave Optimization
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 18, 04:56 AM

  Decentralized Online Convex Optimization (D-OCO) is a fundamental framework in which a set of local agents aims to minimize a sequence of global loss functions using only local computations and communications.

  While recent work has established near-optimal regret guarantees for convex and strongly convex losses, the case of exp-concave losses remains an open challenge: specifically, whether logarithmic regret is achievable.

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