Adversarial Delays in Online Strongly-Convex Optimization
This addresses the challenge of handling arbitrary delays in online optimization for applications like real-time systems, though it is incremental as it builds on known algorithms with a new analysis.
The paper tackles the problem of strongly-convex online optimization with adversarial delays, showing that the online gradient descent algorithm achieves a simple regret bound of O(∑_{t=1}^T log(1 + d_t/t)), which generalizes existing results like logarithmic regret for no delays and O(τ log T) for constant delays.
We consider the problem of strongly-convex online optimization in presence of adversarial delays; in a T-iteration online game, the feedback of the player's 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{τ\log T} for constant delays d_t = τ.