Conservative Contextual Linear Bandits

TL;DR

This paper introduces CLUCB, a safe and conservative algorithm for contextual linear bandits that guarantees performance above a baseline while minimizing regret, with proven bounds and empirical validation.

Contribution

The paper proposes a novel safe linear bandit algorithm, CLUCB, with theoretical regret bounds and empirical evidence demonstrating safety and effectiveness.

Findings

CLUCB maintains performance above the safety threshold over time.

Regret of CLUCB decomposes into standard UCB regret plus a constant safety loss.

Empirical results confirm the safety and theoretical analysis of CLUCB.

Abstract

Safety is a desirable property that can immensely increase the applicability of learning algorithms in real-world decision-making problems. It is much easier for a company to deploy an algorithm that is safe, i.e., guaranteed to perform at least as well as a baseline. In this paper, we study the issue of safety in contextual linear bandits that have application in many different fields including personalized ad recommendation in online marketing. We formulate a notion of safety for this class of algorithms. We develop a safe contextual linear bandit algorithm, called conservative linear UCB (CLUCB), that simultaneously minimizes its regret and satisfies the safety constraint, i.e., maintains its performance above a fixed percentage of the performance of a baseline strategy, uniformly over time. We prove an upper-bound on the regret of CLUCB and show that it can be decomposed into two terms: 1) an upper-bound for the regret of the standard linear UCB algorithm that grows with the time horizon and 2) a constant (does not grow with the time horizon) term that accounts for the loss of being conservative in order to satisfy the safety constraint. We empirically show that our algorithm is safe and validate our theoretical analysis.