Risk Minimization from Adaptively Collected Data: Guarantees for Supervised and Policy Learning

• URL: http://arxiv.org/abs/2106.01723v1
• Date: Thu, 3 Jun 2021 09:50:13 GMT
• Title: Risk Minimization from Adaptively Collected Data: Guarantees for Supervised and Policy Learning
• Authors: Aur\'elien Bibaut and Antoine Chambaz and Maria Dimakopoulou and Nathan Kallus and Mark van der Laan
• Abstract summary: Empirical risk minimization (ERM) is the workhorse of machine learning, but its model-agnostic guarantees can fail when we use adaptively collected data. We study a generic importance sampling weighted ERM algorithm for using adaptively collected data to minimize the average of a loss function over a hypothesis class. For policy learning, we provide rate-optimal regret guarantees that close an open gap in the existing literature whenever exploration decays to zero.
• Score: 57.88785630755165
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Empirical risk minimization (ERM) is the workhorse of machine learning, whether for classification and regression or for off-policy policy learning, but its model-agnostic guarantees can fail when we use adaptively collected data, such as the result of running a contextual bandit algorithm. We study a generic importance sampling weighted ERM algorithm for using adaptively collected data to minimize the average of a loss function over a hypothesis class and provide first-of-their-kind generalization guarantees and fast convergence rates. Our results are based on a new maximal inequality that carefully leverages the importance sampling structure to obtain rates with the right dependence on the exploration rate in the data. For regression, we provide fast rates that leverage the strong convexity of squared-error loss. For policy learning, we provide rate-optimal regret guarantees that close an open gap in the existing literature whenever exploration decays to zero, as is the case for bandit-collected data. An empirical investigation validates our theory.

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