Local Metric Learning for Off-Policy Evaluation in Contextual Bandits with Continuous Actions

TL;DR

This paper introduces a kernel-based local metric learning approach for off-policy evaluation in continuous action contextual bandits, effectively handling deterministic policies and optimizing the kernel metric to minimize mean squared error.

Contribution

It develops a novel kernel metric learning method for off-policy evaluation with continuous actions, extending prior work to vector actions and metric optimization.

Findings

The proposed estimator is consistent.

It significantly reduces mean squared error compared to baselines.

Effective for deterministic policies in continuous action spaces.

Abstract

We consider local kernel metric learning for off-policy evaluation (OPE) of deterministic policies in contextual bandits with continuous action spaces. Our work is motivated by practical scenarios where the target policy needs to be deterministic due to domain requirements, such as prescription of treatment dosage and duration in medicine. Although importance sampling (IS) provides a basic principle for OPE, it is ill-posed for the deterministic target policy with continuous actions. Our main idea is to relax the target policy and pose the problem as kernel-based estimation, where we learn the kernel metric in order to minimize the overall mean squared error (MSE). We present an analytic solution for the optimal metric, based on the analysis of bias and variance. Whereas prior work has been limited to scalar action spaces or kernel bandwidth selection, our work takes a step further being capable of vector action spaces and metric optimization. We show that our estimator is consistent, and significantly reduces the MSE compared to baseline OPE methods through experiments on various domains.