Inference on Optimal Policy Values and Other Irregular Functionals via Smoothing

• URL: http://arxiv.org/abs/2507.11780v1
• Date: Tue, 15 Jul 2025 22:38:39 GMT
• Title: Inference on Optimal Policy Values and Other Irregular Functionals via Smoothing
• Authors: Justin Whitehouse, Morgane Austern, Vasilis Syrgkanis,
• Abstract summary: We show that a softmax smoothing-based estimator can be used to estimate parameters that are specified as a maximum of scores involving nuisance components.<n>Our estimator obtains $sqrtn$ convergence rates, avoids parametric restrictions/unrealistic margin assumptions, and is often statistically efficient.
• Score: 24.31381939721388
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Constructing confidence intervals for the value of an optimal treatment policy is an important problem in causal inference. Insight into the optimal policy value can guide the development of reward-maximizing, individualized treatment regimes. However, because the functional that defines the optimal value is non-differentiable, standard semi-parametric approaches for performing inference fail to be directly applicable. Existing approaches for handling this non-differentiability fall roughly into two camps. In one camp are estimators based on constructing smooth approximations of the optimal value. These approaches are computationally lightweight, but typically place unrealistic parametric assumptions on outcome regressions. In another camp are approaches that directly de-bias the non-smooth objective. These approaches don't place parametric assumptions on nuisance functions, but they either require the computation of intractably-many nuisance estimates, assume unrealistic $L^\infty$ nuisance convergence rates, or make strong margin assumptions that prohibit non-response to a treatment. In this paper, we revisit the problem of constructing smooth approximations of non-differentiable functionals. By carefully controlling first-order bias and second-order remainders, we show that a softmax smoothing-based estimator can be used to estimate parameters that are specified as a maximum of scores involving nuisance components. In particular, this includes the value of the optimal treatment policy as a special case. Our estimator obtains $\sqrt{n}$ convergence rates, avoids parametric restrictions/unrealistic margin assumptions, and is often statistically efficient.

Related papers

• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate.<n>We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• C-Learner: Constrained Learning for Causal Inference [5.395560682099634]
  We propose a novel debiasing approach that achieves the best weighting of both worlds, producing stable plug-in estimates.<n>Our constrained learning framework solves for the best plug-in estimator under the constraint that the first-order error with respect to the plugged-in quantity is zero.
  arXiv  Detail & Related papers  (2024-05-15T16:38:28Z)
• Nonparametric estimation of a covariate-adjusted counterfactual treatment regimen response curve [2.7446241148152253]
  Flexible estimation of the mean outcome under a treatment regimen is a key step toward personalized medicine. We propose an inverse probability weighted nonparametrically efficient estimator of the smoothed regimen-response curve function. Some finite-sample properties are explored with simulations.
  arXiv  Detail & Related papers  (2023-09-28T01:46:24Z)
• Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency [53.90687548731265]
  We study optimal procedures for estimating a linear functional based on observational data. For any convex and symmetric function class $mathcalF$, we derive a non-asymptotic local minimax bound on the mean-squared error.
  arXiv  Detail & Related papers  (2023-01-16T02:57:37Z)
• Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiency [59.48096489854697]
  The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We prove non-asymptotic upper bounds on the mean-squared error of such procedures. We establish its instance-dependent optimality in finite samples via matching non-asymptotic local minimax lower bounds.
  arXiv  Detail & Related papers  (2022-09-26T23:50:55Z)
• Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
  We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing. We study the case where probability distributions are not known a priori but need to be estimated from data.
  arXiv  Detail & Related papers  (2022-08-29T16:16:22Z)
• Understanding the Effect of Stochasticity in Policy Optimization [86.7574122154668]
  We show that the preferability of optimization methods depends critically on whether exact gradients are used. Second, to explain these findings we introduce the concept of committal rate for policy optimization. Third, we show that in the absence of external oracle information, there is an inherent trade-off between exploiting geometry to accelerate convergence versus achieving optimality almost surely.
  arXiv  Detail & Related papers  (2021-10-29T06:35:44Z)
• Multiply Robust Causal Mediation Analysis with Continuous Treatments [12.196869756333797]
  We propose an estimator suitable for settings with continuous treatments inspired by the influence function-based estimator of Tchetgen Tchetgen and Shpitser (2012) Our proposed approach employs cross-fitting, relaxing the smoothness requirements on the nuisance functions and allowing them to be estimated at slower rates than the target parameter.
  arXiv  Detail & Related papers  (2021-05-19T16:58:57Z)
• Support recovery and sup-norm convergence rates for sparse pivotal estimation [79.13844065776928]
  In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. We show minimax sup-norm convergence rates for non smoothed and smoothed, single task and multitask square-root Lasso-type estimators.
  arXiv  Detail & Related papers  (2020-01-15T16:11:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.