David Bruns-Smith

David Bruns-Smith, Oliver Dukes, Avi Feller et al.

We provide a novel characterization of augmented balancing weights, also known as automatic debiased machine learning (AutoDML). These popular doubly robust or de-biased machine learning estimators combine outcome modeling with balancing weights - weights that achieve covariate balance directly in lieu of estimating and inverting the propensity score. When the outcome and weighting models are both linear in some (possibly infinite) basis, we show that the augmented estimator is equivalent to a single linear model with coefficients that combine the coefficients from the original outcome model and coefficients from an unpenalized ordinary least squares (OLS) fit on the same data. We see that, under certain choices of regularization parameters, the augmented estimator often collapses to the OLS estimator alone; this occurs for example in a re-analysis of the Lalonde 1986 dataset. We then extend these results to specific choices of outcome and weighting models. We first show that the augmented estimator that uses (kernel) ridge regression for both outcome and weighting models is equivalent to a single, undersmoothed (kernel) ridge regression. This holds numerically in finite samples and lays the groundwork for a novel analysis of undersmoothing and asymptotic rates of convergence. When the weighting model is instead lasso-penalized regression, we give closed-form expressions for special cases and demonstrate a ``double selection'' property. Our framework opens the black box on this increasingly popular class of estimators, bridges the gap between existing results on the semiparametric efficiency of undersmoothed and doubly robust estimators, and provides new insights into the performance of augmented balancing weights.

David Bruns-Smith, Avi Feller

We study balancing weight estimators, which reweight outcomes from a source population to estimate missing outcomes in a target population. These estimators minimize the worst-case error by making an assumption about the outcome model. In this paper, we show that this outcome assumption has two immediate implications. First, we can replace the minimax optimization problem for balancing weights with a simple convex loss over the assumed outcome function class. Second, we can replace the commonly-made overlap assumption with a more appropriate quantitative measure, the minimum worst-case bias. Finally, we show conditions under which the weights remain robust when our assumptions on the outcomes are wrong.

David Bruns-Smith, Angela Zhou

Offline reinforcement learning is important in domains such as medicine, economics, and e-commerce where online experimentation is costly, dangerous or unethical, and where the true model is unknown. However, most methods assume all covariates used in the behavior policy's action decisions are observed. Though this assumption, sequential ignorability/unconfoundedness, likely does not hold in observational data, most of the data that accounts for selection into treatment may be observed, motivating sensitivity analysis. We study robust policy evaluation and policy optimization in the presence of sequentially-exogenous unobserved confounders under a sensitivity model. We propose and analyze orthogonalized robust fitted-Q-iteration that uses closed-form solutions of the robust Bellman operator to derive a loss minimization problem for the robust Q function, and adds a bias-correction to quantile estimation. Our algorithm enjoys the computational ease of fitted-Q-iteration and statistical improvements (reduced dependence on quantile estimation error) from orthogonalization. We provide sample complexity bounds, insights, and show effectiveness both in simulations and on real-world longitudinal healthcare data of treating sepsis. In particular, our model of sequential unobserved confounders yields an online Markov decision process, rather than partially observed Markov decision process: we illustrate how this can enable warm-starting optimistic reinforcement learning algorithms with valid robust bounds from observational data.

David Bruns-Smith

When decision-makers can directly intervene, policy evaluation algorithms give valid causal estimates. In off-policy evaluation (OPE), there may exist unobserved variables that both impact the dynamics and are used by the unknown behavior policy. These "confounders" will introduce spurious correlations and naive estimates for a new policy will be biased. We develop worst-case bounds to assess sensitivity to these unobserved confounders in finite horizons when confounders are drawn iid each period. We demonstrate that a model-based approach with robust MDPs gives sharper lower bounds by exploiting domain knowledge about the dynamics. Finally, we show that when unobserved confounders are persistent over time, OPE is far more difficult and existing techniques produce extremely conservative bounds.

Oscar Clivio, Alexander D'Amour, Alexander Franks et al.

Overlap, also known as positivity, is a key condition for causal treatment effect estimation. Many popular estimators suffer from high variance and become brittle when features differ strongly across treatment groups. This is especially challenging in high dimensions: the curse of dimensionality can make overlap implausible. To address this, we propose a class of feature representations called deconfounding scores, which preserve both identification and the target of estimation; the classical propensity and prognostic scores are two special cases. We characterize the problem of finding a representation with better overlap as minimizing an overlap divergence under a deconfounding score constraint. We then derive closed-form expressions for a class of deconfounding scores under a broad family of generalized linear models with Gaussian features and show that prognostic scores are overlap-optimal within this class. We conduct extensive experiments to assess this behavior empirically.