SPEED: Experimental Design for Policy Evaluation in Linear Heteroscedastic Bandits
This addresses the challenge of efficiently evaluating policies in bandit environments with varying noise levels, representing an incremental advance in experimental design for reinforcement learning.
The paper tackles the problem of optimal data collection for policy evaluation in linear bandits with heteroscedastic reward noise, introducing the SPEED algorithm that achieves mean squared error comparable to an oracle strategy and significantly lower than running the target policy directly.
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.