Off-Policy Interval Estimation with Lipschitz Value Iteration

TL;DR

This paper introduces a provably correct method for off-policy evaluation that provides reliable reward bounds using Lipschitz value iteration, crucial for high-stakes decision-making scenarios.

Contribution

It proposes a novel Lipschitz value iteration approach to compute tight reward bounds in off-policy evaluation, ensuring correctness and efficiency in continuous settings.

Findings

Method produces valid reward bounds in high-stakes scenarios

Lipschitz value iteration converges monotonically and efficiently

Demonstrated effectiveness on various benchmark problems

Abstract

Off-policy evaluation provides an essential tool for evaluating the effects of different policies or treatments using only observed data. When applied to high-stakes scenarios such as medical diagnosis or financial decision-making, it is crucial to provide provably correct upper and lower bounds of the expected reward, not just a classical single point estimate, to the end-users, as executing a poor policy can be very costly. In this work, we propose a provably correct method for obtaining interval bounds for off-policy evaluation in a general continuous setting. The idea is to search for the maximum and minimum values of the expected reward among all the Lipschitz Q-functions that are consistent with the observations, which amounts to solving a constrained optimization problem on a Lipschitz function space. We go on to introduce a Lipschitz value iteration method to monotonically tighten the interval, which is simple yet efficient and provably convergent. We demonstrate the practical efficiency of our method on a range of benchmarks.