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SPEED: Experimental Design for Policy Evaluation in Linear Heteroscedastic Bandits
Subhojyoti Mukherjee · Qiaomin Xie · Josiah Hanna · Robert Nowak

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in The Many Facets of Preference-Based Learning »
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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.

Author Information

Subhojyoti Mukherjee (University of Wisconsin Madison)

I am a first-year Ph.D. candidate in the Department of Electrical and Computer Engineering (ECE), University of Wisconsin-Madison. I am advised by Dr. Robert Nowak.

Qiaomin Xie (University of Wisconsin - Madison)
Josiah Hanna (University of Wisconsin - Madison)
Josiah Hanna

Josiah Hanna is an assistant professor in the Computer Sciences Department at the University of Wisconsin -- Madison. He received his Ph.D. in the Computer Science Department at the University of Texas at Austin. Prior to attending UT Austin, he completed his B.S. in computer science and mathematics at the University of Kentucky. Before joining UW--Madison, he was a post-doc at the University of Edinburgh and also spent time at FiveAI working on autonomous driving. Josiah is a recipient of the NSF Graduate Research Fellowship and the IBM Ph.D. Fellowship. His research interests lie in artificial intelligence and machine learning, seeking to develop algorithms that allow autonomous agents to learn (efficiently) from experience. In particular, he studies reinforcement learning and methods to increase the data efficiency of reinforcement learning algorithms.

Robert Nowak (University of Wisconsion-Madison)
Robert Nowak

Robert Nowak holds the Nosbusch Professorship in Engineering at the University of Wisconsin-Madison, where his research focuses on signal processing, machine learning, optimization, and statistics.

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