Competing With Strategies

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.