SPEED: Experimental Design for Policy Evaluation in Linear Heteroscedastic Bandits

TL;DR

This paper introduces SPEED, a novel experimental design method for optimal data collection in linear heteroscedastic bandits, significantly improving policy evaluation accuracy by minimizing mean squared error.

Contribution

It formulates an optimal design for weighted least squares in heteroscedastic linear bandits and develops SPEED, the first algorithm tracking this design for improved policy evaluation.

Findings

SPEED achieves mean squared error comparable to the oracle strategy.

SPEED significantly outperforms naive policy execution in policy evaluation.

The method effectively handles heteroscedastic reward noise in linear bandits.

Abstract

In this paper, we study the problem of optimal data collection for policy evaluation in linear bandits. In policy evaluation, we are given a target policy and asked to estimate the expected reward it will obtain when executed in a multi-armed bandit environment. Our work is the first work that focuses on such optimal data collection strategy for policy evaluation involving heteroscedastic reward noise in the linear bandit setting. We first formulate an optimal design for weighted least squares estimates in the heteroscedastic linear bandit setting that reduces the MSE of the value of the target policy. We then use this formulation to derive the optimal allocation of samples per action during data collection. We then introduce a novel algorithm SPEED (Structured Policy Evaluation Experimental Design) that tracks the optimal design and derive its regret with respect to the optimal design. Finally, we empirically validate that SPEED leads to policy evaluation with mean squared error comparable to the oracle strategy and significantly lower than simply running the target policy.