BISTRO: An Efficient Relaxation-Based Method for Contextual Bandits

TL;DR

This paper introduces BISTRO, an efficient relaxation-based algorithm for contextual bandits that leverages unlabeled data and approximation algorithms to handle computational hardness, providing theoretical guarantees for both stochastic and adversarial settings.

Contribution

The paper proposes BISTRO, a novel relaxation-based method that efficiently solves contextual bandits using ERM oracles and extends to adversarial cases with theoretical regret bounds.

Findings

BISTRO requires only d ERM calls per round, where d is the number of actions.

The approach effectively uses unlabeled data to simplify computation.

The adversarial bandit problem is shown to be learnable when full-information online learning has non-trivial regret.

Abstract

We present efficient algorithms for the problem of contextual bandits with i.i.d. covariates, an arbitrary sequence of rewards, and an arbitrary class of policies. Our algorithm BISTRO requires d calls to the empirical risk minimization (ERM) oracle per round, where d is the number of actions. The method uses unlabeled data to make the problem computationally simple. When the ERM problem itself is computationally hard, we extend the approach by employing multiplicative approximation algorithms for the ERM. The integrality gap of the relaxation only enters in the regret bound rather than the benchmark. Finally, we show that the adversarial version of the contextual bandit problem is learnable (and efficient) whenever the full-information supervised online learning problem has a non-trivial regret guarantee (and efficient).