To update or not to update? Delayed Nonparametric Bandits with Randomized Allocation

TL;DR

This paper investigates how delayed reward observations impact randomized strategies in contextual bandits, comparing continuous and delayed update methods for exploration-exploitation balance.

Contribution

It provides a theoretical comparison of two delayed reward update strategies, highlighting their consistency and finite-sample performance differences.

Findings

Both strategies achieve strong consistency in allocation.

Delayed updates are more robust across various scenarios.

Finite sample performance varies with delay severity.

Abstract

Delayed rewards problem in contextual bandits has been of interest in various practical settings. We study randomized allocation strategies and provide an understanding on how the exploration-exploitation tradeoff is affected by delays in observing the rewards. In randomized strategies, the extent of exploration-exploitation is controlled by a user-determined exploration probability sequence. In the presence of delayed rewards, one may choose between using the original exploration sequence that updates at every time point or update the sequence only when a new reward is observed, leading to two competing strategies. In this work, we show that while both strategies may lead to strong consistency in allocation, the property holds for a wider scope of situations for the latter. However, for finite sample performance, we illustrate that both strategies have their own advantages and disadvantages, depending on the severity of the delay and underlying reward generating mechanisms.