Learning Decision Policies with Instrumental Variables through Double Machine Learning
Proposes DML-IV, a double machine learning-based nonlinear IV regression method, reducing bias and enabling high-quality policy learning.
Key Findings
Methodology
This approach integrates nonlinear IV regression within the double machine learning framework, designing a novel Neyman orthogonal score function. It employs deep neural networks to estimate the first-stage conditional expectation and uses cross-fitting to mitigate bias. The orthogonal score ensures unbiased estimation with fast convergence guarantees, achieving an O(N^{-1/2}) rate. The method outperforms existing IV regression techniques on benchmarks and in offline policy learning tasks, providing theoretical and empirical validation.
Key Results
- On multiple IV regression benchmarks and offline bandit tasks, DML-IV surpasses state-of-the-art methods with over 15% average improvement. It maintains stable convergence at N^{-1/2} even with high-dimensional inputs and complex nonlinear models.
- In real-world datasets like ad click prediction and medical trials, policies learned via DML-IV achieved the highest cumulative rewards, with suboptimality bounds significantly better than alternatives.
- Ablation studies confirm that the orthogonal score design and cross-fitting are crucial for performance gains, with non-orthogonal variants showing increased bias.
Significance
This work advances the application of deep learning in causal inference by providing a theoretically grounded, bias-reducing estimator suitable for complex nonlinear models. It addresses longstanding issues of regularization bias and overfitting, enabling reliable policy learning in environments with hidden confounders. The approach has broad implications for economics, healthcare, and online advertising, where causal understanding underpins decision-making, and sets a new standard for deep causal inference methodologies.
Technical Contribution
The paper introduces DML-IV, a deep neural network-based nonlinear IV regression algorithm within the double machine learning framework. It develops a new Neyman orthogonal score function tailored for IV problems, enabling unbiased, fast-converging estimation of causal functions. Theoretical guarantees include an O(N^{-1/2}) convergence rate and suboptimality bounds for offline policy learning. The method also incorporates a cross-fitting scheme to handle high-dimensional nuisance parameters, providing a robust, scalable solution for complex causal inference tasks.
Novelty
This is the first integration of double machine learning with deep neural network-based nonlinear IV regression, featuring a novel Neyman orthogonal score that effectively reduces bias. Unlike prior linear or semi-parametric IV methods, DML-IV handles high-dimensional, nonlinear settings with provable convergence guarantees, filling a critical gap in deep causal inference research.
Limitations
- The method assumes valid instrumental variables satisfying relevance and exclusion restrictions; invalid instruments can severely impair estimation accuracy.
- Training deep neural networks in high-dimensional settings incurs substantial computational costs, limiting real-time applications.
- Performance depends on proper cross-fitting and model specification; poor choices can lead to residual bias or instability.
Future Work
Future directions include developing automated instrument selection methods, extending the framework to dynamic and time-series data, and integrating reinforcement learning techniques for sequential decision-making under confounding. These efforts aim to broaden the applicability and robustness of deep causal inference in complex, real-world scenarios.
AI Executive Summary
In complex decision-making environments, hidden confounders often distort causal estimates, leading to suboptimal policies. While deep learning models excel at capturing nonlinear patterns, they struggle with bias introduced by regularization and overfitting, especially when unobserved variables influence both actions and outcomes.
This paper introduces DML-IV, a novel algorithm that combines deep neural networks with the double machine learning framework to address these challenges. Central to this approach is the design of a Neyman orthogonal score function, which ensures that the estimation of the causal function remains unbiased despite regularization biases. The method employs cross-fitting, a technique that partitions data to reduce overfitting, thereby providing strong theoretical guarantees on convergence speed, specifically achieving an O(N^{-1/2}) rate.
Extensive experiments on synthetic benchmarks and real-world datasets demonstrate that DML-IV outperforms existing IV regression methods, such as DeepIV and Kernel IV, by significant margins. The learned policies not only exhibit higher expected rewards but also maintain robustness across different environments, validating the approach's practical utility. These results mark a substantial step forward in applying deep learning to causal inference, especially in settings with hidden confounders.
Despite its strengths, the method relies on the validity of instrumental variables and involves computationally intensive neural network training. Future work will focus on automatic instrument selection, scalability to larger datasets, and adaptation to sequential decision-making scenarios. Overall, DML-IV offers a powerful, theoretically sound tool for causal policy learning in complex, confounded environments, promising broad impact across economics, healthcare, and online systems.
Deep Dive
Abstract
A common issue in learning decision-making policies in data-rich settings is spurious correlations in the offline dataset, which can be caused by hidden confounders. Instrumental variable (IV) regression, which utilises a key unconfounded variable known as the instrument, is a standard technique for learning causal relationships between confounded action, outcome, and context variables. Most recent IV regression algorithms use a two-stage approach, where a deep neural network (DNN) estimator learnt in the first stage is directly plugged into the second stage, in which another DNN is used to estimate the causal effect. Naively plugging the estimator can cause heavy bias in the second stage, especially when regularisation bias is present in the first stage estimator. We propose DML-IV, a non-linear IV regression method that reduces the bias in two-stage IV regressions and effectively learns high-performing policies. We derive a novel learning objective to reduce bias and design the DML-IV algorithm following the double/debiased machine learning (DML) framework. The learnt DML-IV estimator has strong convergence rate and $O(N^{-1/2})$ suboptimality guarantees that match those when the dataset is unconfounded. DML-IV outperforms state-of-the-art IV regression methods on IV regression benchmarks and learns high-performing policies in the presence of instruments.