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- W4301885279 abstract "We consider the fundamental problem of prediction with expert advice where the experts are optimizable: there is a black-box optimization oracle that can be used to compute, in constant time, the leading expert in retrospect at any point in time. In this setting, we give a novel online algorithm that attains vanishing regret with respect to $N$ experts in total $widetilde{O}(sqrt{N})$ computation time. We also give a lower bound showing that this running time cannot be improved (up to log factors) in the oracle model, thereby exhibiting a quadratic speedup as compared to the standard, oracle-free setting where the required time for vanishing regret is $widetilde{Theta}(N)$. These results demonstrate an exponential gap between the power of optimization in online learning and its power in statistical learning: in the latter, an optimization oracle---i.e., an efficient empirical risk minimizer---allows to learn a finite hypothesis class of size $N$ in time $O(log{N})$. We also study the implications of our results to learning in repeated zero-sum games, in a setting where the players have access to oracles that compute, in constant time, their best-response to any mixed strategy of their opponent. We show that the runtime required for approximating the minimax value of the game in this setting is $widetilde{Theta}(sqrt{N})$, yielding again a quadratic improvement upon the oracle-free setting, where $widetilde{Theta}(N)$ is known to be tight." @default.
- W4301885279 created "2022-10-05" @default.
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- W4301885279 date "2015-04-08" @default.
- W4301885279 modified "2023-10-18" @default.
- W4301885279 title "The Computational Power of Optimization in Online Learning" @default.
- W4301885279 doi "https://doi.org/10.48550/arxiv.1504.02089" @default.
- W4301885279 hasPublicationYear "2015" @default.
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