A Stochastic View of Optimal Regret through Minimax Duality

@article{Abernethy2009ASV,
  title={A Stochastic View of Optimal Regret through Minimax Duality},
  author={Jacob D. Abernethy and Alekh Agarwal and Peter L. Bartlett and Alexander Rakhlin},
  journal={CoRR},
  year={2009},
  volume={abs/0903.5328}
}
We study the regret of optimal strategies for online convex optimization games. Using von Neumann’s minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary’s action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret… CONTINUE READING
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A stochastic view of optimal regret through minimax duality

  • A. Agarwal J. Abernethy, P. L. Bartlett, A. Rakhlin
  • 2009

Convex games in banach spaces (working title)

  • K. Sridharan, A. Tewari
  • 2009
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