Competing With Strategies
Wei Han, Alexander Rakhlin, Karthik Sridharan

TL;DR
This paper introduces new tools for online learning that enable regret minimization against a set of strategies, including autoregressive and statistical model-based strategies, with some algorithms being computationally efficient.
Contribution
The paper develops a framework for analyzing minimax rates and designing regret-minimization algorithms against strategy sets, extending beyond standard regret measures.
Findings
Existence of regret-minimization methods for strategy sets
Development of efficient algorithms for certain strategy classes
Analysis of minimax rates for strategy-based regret
Abstract
We study the problem of online learning with a notion of regret defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and for deriving regret-minimization algorithms in this scenario. While the standard methods for minimizing the usual notion of regret fail, through our analysis we demonstrate existence of regret-minimization methods that compete with such sets of strategies as: autoregressive algorithms, strategies based on statistical models, regularized least squares, and follow the regularized leader strategies. In several cases we also derive efficient learning algorithms.
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Machine Learning and Algorithms · Distributed Sensor Networks and Detection Algorithms
