Rarely-switching linear bandits: optimization of causal effects for the real world

TL;DR

This paper introduces a conservative linear bandit algorithm that updates policies infrequently, minimizing detrimental changes while maintaining near-optimal regret, suitable for real-world scenarios where policy stability is crucial.

Contribution

It extends linear bandit theory to rarely-switching policies, providing a provably effective method that balances policy stability with learning performance.

Findings

The algorithm achieves similar regret to LinUCB with fewer policy changes.

Simulations demonstrate efficient learning with minimal detrimental updates.

Application to a causal inference dataset shows practical effectiveness.

Abstract

Excessively changing policies in many real world scenarios is difficult, unethical, or expensive. After all, doctor guidelines, tax codes, and price lists can only be reprinted so often. We may thus want to only change a policy when it is probable that the change is beneficial. In cases that a policy is a threshold on contextual variables we can estimate treatment effects for populations lying at the threshold. This allows for a schedule of incremental policy updates that let us optimize a policy while making few detrimental changes. Using this idea, and the theory of linear contextual bandits, we present a conservative policy updating procedure which updates a deterministic policy only when justified. We extend the theory of linear bandits to this rarely-switching case, proving that such procedures share the same regret, up to constant scaling, as the common LinUCB algorithm. However the algorithm makes far fewer changes to its policy and, of those changes, fewer are detrimental. We provide simulations and an analysis of an infant health well-being causal inference dataset, showing the algorithm efficiently learns a good policy with few changes. Our approach allows efficiently solving problems where changes are to be avoided, with potential applications in medicine, economics and beyond.