Adversarial Delays in Online Strongly-Convex Optimization


Abstract in English

We consider the problem of strongly-convex online optimization in presence of adversarial delays; in a T-iteration online game, the feedback of the players query at time t is arbitrarily delayed by an adversary for d_t rounds and delivered before the game ends, at iteration t+d_t-1. Specifically for algo{online-gradient-descent} algorithm we show it has a simple regret bound of Oh{sum_{t=1}^T log (1+ frac{d_t}{t})}. This gives a clear and simple bound without resorting any distributional and limiting assumptions on the delays. We further show how this result encompasses and generalizes several of the existing known results in the literature. Specifically it matches the celebrated logarithmic regret Oh{log T} when there are no delays (i.e. d_t = 1) and regret bound of Oh{tau log T} for constant delays d_t = tau.

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