[Paper Review] Reinforcement Learning with Heterogeneous Data: Estimation and Inference

Elynn Chen, Rui Song+1 more|arXiv (Cornell University)|Jan 31, 2022

Software Reliability and Analysis Research4 citations

TL;DR

This paper proposes a novel framework, the K-Heterogeneous Markov Decision Process (K-Hetero MDP), to model sequential decision-making in heterogeneous populations. It introduces Auto-Clustered Policy Evaluation (ACPE) and Auto-Clustered Policy Iteration (ACPI) that automatically detect sub-populations and estimate distinct Q-functions and optimal policies for each, achieving improved estimation accuracy and valid confidence intervals in both synthetic and real-world MIMIC-III ICU data.

ABSTRACT

Reinforcement Learning (RL) has the promise of providing data-driven support for decision-making in a wide range of problems in healthcare, education, business, and other domains. Classical RL methods focus on the mean of the total return and, thus, may provide misleading results in the setting of the heterogeneous populations that commonly underlie large-scale datasets. We introduce the K-Heterogeneous Markov Decision Process (K-Hetero MDP) to address sequential decision problems with population heterogeneity. We propose the Auto-Clustered Policy Evaluation (ACPE) for estimating the value of a given policy, and the Auto-Clustered Policy Iteration (ACPI) for estimating the optimal policy in a given policy class. Our auto-clustered algorithms can automatically detect and identify homogeneous sub-populations, while estimating the Q function and the optimal policy for each sub-population. We establish convergence rates and construct confidence intervals for the estimators obtained by the ACPE and ACPI. We present simulations to support our theoretical findings, and we conduct an empirical study on the standard MIMIC-III dataset. The latter analysis shows evidence of value heterogeneity and confirms the advantages of our new method.

Motivation & Objective

• To address the limitations of classical mean-value-based reinforcement learning in heterogeneous populations where aggregated data masks sub-population differences.
• To develop a method that automatically detects and estimates distinct policies and value functions for homogeneous sub-populations within a single dataset.
• To provide statistical guarantees, including convergence rates and valid confidence intervals, under a flexible bidirectional asymptotic framework.
• To validate the method’s superiority over standard RL approaches in capturing heterogeneity and improving prediction accuracy on real-world healthcare data.
• To offer theoretical guidance for tuning parameters in the ACPI algorithm for practical deployment.

Proposed method

• Proposes the K-Heterogeneous MDP (K-Hetero MDP) as a formal model for sequential decision-making with multiple sub-populations, each with distinct state-action-reward dynamics.
• Introduces Auto-Clustered Policy Evaluation (ACPE), a two-stage algorithm that clusters trajectories and estimates sub-population-specific Q-functions using penalized temporal difference learning.
• Develops Auto-Clustered Policy Iteration (ACPI), which extends ACPE by iteratively refining policy estimates within each cluster to converge to an optimal policy per sub-population.
• Uses a bidirectional asymptotic framework where either the number of trajectories (N) or the trajectory length (T) can diverge to infinity, enabling valid inference.
• Derives convergence rates and constructs confidence intervals for estimated parameters and value functions using infinity norm analysis of the temporal difference error.
• Applies multivariate nearest-neighbor imputation and time-limited sample-and-hold interpolation to handle irregularly sampled ICU data in the MIMIC-III dataset.

Experimental results

Research questions

• RQ1 Can a reinforcement learning framework detect and model sub-population heterogeneity in large-scale sequential decision-making data?
• RQ2 Does the proposed ACPI algorithm improve estimation accuracy and policy performance compared to standard mean-value-based RL in heterogeneous datasets?
• RQ3 Are the confidence intervals constructed for the estimated value functions and parameters valid under a flexible asymptotic regime where either N or T diverges?
• RQ4 How does the method perform on real-world clinical data with known heterogeneity, such as the MIMIC-III sepsis cohort?
• RQ5 What is the optimal tuning strategy for the clustering and penalization parameters in ACPI, and how does it affect estimation stability?

Key findings

• The ACPE and ACPI algorithms successfully detect two distinct sub-populations in the MIMIC-III sepsis dataset, as evidenced by residual distributions shifting from bimodal to unimodal after clustering.
• The ACPI method reduces prediction error and produces residuals centered at zero with a bell-shaped distribution, indicating better model fit compared to standard linear Q-learning.
• Theoretical analysis confirms convergence rates for the estimators and constructs valid confidence intervals under a bidirectional asymptotic framework, where either N or T diverges to infinity.
• Empirical results on MIMIC-III show evidence of value heterogeneity, with distinct optimal treatment policies emerging for different patient subgroups.
• The method outperforms standard RL in both synthetic and real-world settings, particularly when sub-population sizes are small.
• Theoretical guidance is provided for tuning parameters in ACPI, enhancing its practical usability in high-stakes domains like healthcare.