Worst-case Performance of Greedy Policies in Bandits with Imperfect Context Observations

TL;DR

This paper analyzes the worst-case performance of greedy policies in contextual bandits with imperfect context observations, showing they have poly-logarithmic regret growth over time and linear dependence on the number of arms.

Contribution

It introduces a non-asymptotic analysis of greedy policies in imperfect contextual bandits, revealing their regret bounds and efficiency in such settings.

Findings

Regret grows poly-logarithmically with time horizon.

Regret scales linearly with the number of arms.

Numerical results confirm theoretical efficiency.

Abstract

Contextual bandits are canonical models for sequential decision-making under uncertainty in environments with time-varying components. In this setting, the expected reward of each bandit arm consists of the inner product of an unknown parameter with the context vector of that arm. The classical bandit settings heavily rely on assuming that the contexts are fully observed, while study of the richer model of imperfectly observed contextual bandits is immature. This work considers Greedy reinforcement learning policies that take actions as if the current estimates of the parameter and of the unobserved contexts coincide with the corresponding true values. We establish that the non-asymptotic worst-case regret grows poly-logarithmically with the time horizon and the failure probability, while it scales linearly with the number of arms. Numerical analysis showcasing the above efficiency of Greedy policies is also provided.