Reinforcement Learning Trees

Abstract

In this article, we introduce a new type of tree-based method, reinforcement learning trees (RLT), which exhibits significantly improved performance over traditional methods such as random forests (Breiman 2001) under high-dimensional settings. The innovations are three-fold. First, the new method implements reinforcement learning at each selection of a splitting variable during the tree construction processes. By splitting on the variable that brings the greatest future improvement in later splits, rather than choosing the one with largest marginal effect from the immediate split, the constructed tree uses the available samples in a more efficient way. Moreover, such an approach enables linear combination cuts at little extra computational cost. Second, we propose a variable muting procedure that progressively eliminates noise variables during the construction of each individual tree. The muting procedure also takes advantage of reinforcement learning and prevents noise variables from being considered in the search for splitting rules, so that toward terminal nodes, where the sample size is small, the splitting rules are still constructed from only strong variables. Last, we investigate asymptotic properties of the proposed method under basic assumptions and discuss rationale in general settings. Supplementary materials for this article are available online.

• Consistency
• Error bound
• Random forests
• Reinforcement learning
• Trees

Additional information

Notes on contributors

Ruoqing Zhu

R. Zhu (E-mail: [email protected]) is a student, D. Zeng (E-mail: [email protected]) is Professor, and M. R. Kosorok (E-mail: [email protected]) is W. R. Kenan, Jr. Distinguished Professor and Chair, Department of Biostatistics, CB#7420, University of North Carolina, Chapel Hill, NC 27599-7420. The authors thank the editors and reviewers for their careful review and thoughtful suggestions, which led to a significantly improved article. The authors were funded in part by grants P01 CA142538 from the National Cancer Institute and U01 NS082062 from the National Institute of Neurological Disorders and Stroke.

Donglin Zeng

R. Zhu (E-mail: [email protected]) is a student, D. Zeng (E-mail: [email protected]) is Professor, and M. R. Kosorok (E-mail: [email protected]) is W. R. Kenan, Jr. Distinguished Professor and Chair, Department of Biostatistics, CB#7420, University of North Carolina, Chapel Hill, NC 27599-7420. The authors thank the editors and reviewers for their careful review and thoughtful suggestions, which led to a significantly improved article. The authors were funded in part by grants P01 CA142538 from the National Cancer Institute and U01 NS082062 from the National Institute of Neurological Disorders and Stroke.

Michael R. Kosorok

R. Zhu (E-mail: [email protected]) is a student, D. Zeng (E-mail: [email protected]) is Professor, and M. R. Kosorok (E-mail: [email protected]) is W. R. Kenan, Jr. Distinguished Professor and Chair, Department of Biostatistics, CB#7420, University of North Carolina, Chapel Hill, NC 27599-7420. The authors thank the editors and reviewers for their careful review and thoughtful suggestions, which led to a significantly improved article. The authors were funded in part by grants P01 CA142538 from the National Cancer Institute and U01 NS082062 from the National Institute of Neurological Disorders and Stroke.