unbiased gradient estimation

Statistical inference for the value function of optimal treatment regimes is challenging due to its inherent non-differentiability. Method: We propose a Softmax-based smoothing estimator to construct valid confidence intervals, circumventing reliance on parametric assumptions, stringent boundary conditions, or high-dimensional kernel density estimation. Under mild regularity conditions, the estimator achieves √n-consistency and asymptotic normality. First-order bias correction and tight control of second-order remainder terms ensure both computational efficiency and statistical robustness, even in confounded causal optimization settings. Contribution/Results: Our key innovation lies in embedding Softmax smoothing within a nonparametric causal inference framework—enabling, for the first time, accurate and generalizable inference for non-differentiable optimal value functions without imposing smoothness assumptions. This substantially enhances the reliability and practical applicability of personalized treatment strategy evaluation.

This study addresses the challenge of parameter inference in discrete stochastic dynamical models—such as those simulated via the Gillespie algorithm—where non-differentiability impedes gradient-based learning. The authors systematically introduce and compare three gradient estimators: Gumbel-Softmax Straight-Through (GS-ST), Score Function, and Alternative Path. Evaluated on stochastic biochemical systems exhibiting relaxation or oscillatory dynamics, GS-ST performs well in many settings but suffers from substantially increased variance in complex parameter regimes. In contrast, the Score Function and Alternative Path estimators demonstrate consistently lower variance and greater robustness, enabling accurate parameter inference. This work provides a practical framework and empirical guidance for differentiable modeling of discrete stochastic systems.

It has been frequently observed that Neyman orthogonality, the central device underlying double/debiased machine learning (Chernozhukov et al., 2018), and pathwise differentiability, a cornerstone concept from semiparametric theory, often lead to the same debiased estimators in practice. Despite the widespread adoption of both ideas, the precise nature of this equivalence has remained elusive, with the two concepts having been developed in largely separate traditions. In this work, we revisit the semiparametric framework of van der Laan and Robins (2003) and identify an implicit regularity assumption on the relationship between target and nuisance parameters -- a local product structure -- that allows us to establish a formal equivalence between Neyman orthogonality and pathwise differentiability. We demonstrate that the two directions of this equivalence impose fundamentally different structural requirements, and illustrate the theory through a concrete example of estimating the average treatment effect. This helps clarify the relationship between these two foundational frameworks and provides a useful reference for practitioners working at their intersection.

For stochastic simulation models with intractable likelihoods, existing score estimators based on noisy Monte Carlo ratio estimators suffer from bias and instability. Method: We propose the first gradient-based simulation parameter estimation framework, which eliminates ratio bias via a multi-timescale stochastic approximation algorithm, incorporates a nested simulation optimization architecture, and extends— for the first time—to neural network training. The method integrates stochastic approximation, multiscale optimization, nested Monte Carlo estimation, and asymptotic statistical analysis. Contributions/Results: We rigorously establish strong consistency, asymptotic normality, optimal convergence rate, and an optimal budget allocation strategy for the estimator. Numerical experiments demonstrate substantial improvements in estimation accuracy and significant reductions in computational cost.

This work addresses the structural identifiability of parameters in stochastic differential equation (SDE) models under multiple interventions—i.e., whether SDE parameters can be uniquely recovered from samples of post-intervention stationary distributions. Theoretically, we establish the first uniqueness guarantee for SDE parameter recovery under multi-intervention settings; for linear SDEs, we derive a tight lower bound on the minimum number of required interventions; for weak-noise nonlinear SDEs, we obtain an upper bound on identifiability. Methodologically, we propose a parametric framework featuring learnable activation functions, integrating intervention modeling, stationary distribution analysis, and weak-noise asymptotic theory. Experiments on synthetic data demonstrate that our approach accurately recovers ground-truth parameters, and the theory-guided learnable architecture significantly improves both estimation accuracy and robustness.

This work addresses the computationally expensive inverse problem of parameter estimation for stochastic differential equations (SDEs) by proposing an efficient solution framework that, for the first time, integrates Wiener chaos expansion (WCE) with stochastic gradient descent (SGD). By projecting the stochastic solution onto a deterministic system of propagators via an orthogonal Hermite polynomial basis, the method constructs a regularized discrepancy functional amenable to SGD optimization. This transformation effectively converts the original stochastic inverse problem into a deterministic optimization task, substantially reducing computational complexity and data requirements. Numerical experiments on several nonlinear SDE models—including a biological individual growth model—demonstrate that the approach accurately and robustly recovers parameters even from sparse and noisy observational data, exhibiting strong scalability and practical promise.

This study addresses sensitivity analysis and intervention optimization for discrete-time stochastic epidemic models under parameter uncertainty. The authors propose an unbiased gradient estimator tailored to posterior parameter distributions obtained via Bayesian calibration, enabling quantification of how vaccination coverage and contact rates influence the total number of infections over a finite time horizon. By integrating stochastic simulation with gradient estimation, the method achieves low variance—particularly outperforming finite-difference approaches in estimating derivatives with respect to contact rates—and reveals substantial discrepancies in sensitivity between the stochastic model and its deterministic limit. The findings indicate that parameter uncertainty attenuates indirect effects such as herd immunity, leading to more conservative optimal intervention strategies and an overall reduction in sensitivity.

This work addresses the limitation of classical stochastic optimization theory, which relies on the uniform escape (UE) assumption to avoid strict saddle points—a condition often violated in over-parameterized, interpolation, or finite-sum settings. The authors establish a stochastic recursive almost sure saddle avoidance theorem without requiring the UE assumption. By introducing a path-dependent variable transformation and a pathwise Lyapunov–Perron method, they extend the center-stable manifold framework to sequences of random mappings lacking common fixed points, under assumptions of local smoothness, finite moment conditions, and without-replacement sampling structure. This unified framework applies to stochastic mirror descent (including SGD), stochastic reshuffling, and proximal stochastic gradient methods for nonsmooth composite objectives, proving their almost sure convergence to local minima by first avoiding strict saddle points and then ensuring iterative convergence.

This paper investigates the minimax optimal error lower bounds for structure-agnostic (i.e., model-agnostic) nonparametric functional estimation, focusing on causal parameters such as the average treatment effect (ATE) and general functional targets. Methodologically, it integrates double machine learning (DML), first-order debiasing, double robustness analysis, and minimax lower bound theory. The key contributions are: (i) the first systematic characterization of structure-agnostic optimal convergence rates under both doubly robust and non-doubly robust settings; (ii) a rigorous proof that DML achieves the theoretical minimax optimal rate across all structure-agnostic scenarios, with explicit closed-form expressions for the optimal rates; and (iii) unification and generalization of existing ATE lower bound results, thereby establishing the universal minimax optimality of DML in this framework. These findings provide foundational theoretical support for model-free causal and statistical inference.

This work addresses stochastic composite inclusion problems that may be non-monotone, particularly tackling the challenge of lacking effective variance reduction methods under biased estimators. The authors propose a unified framework that, for the first time, introduces biased variance-reduced estimators to inclusion and fixed-point problems, designing a new class of estimators tailored for the forward-reflected-backward splitting algorithm and providing a unified analysis covering both unbiased and biased settings. By integrating variance reduction techniques such as loopless-SVRG and SAGA, the method achieves an expected residual convergence rate of O(1/k) and almost sure convergence in the unbiased case, with oracle complexities of O(n^{2/3}ε^{-2}) and O(ε^{-10/3}), respectively. In the biased setting, the corresponding complexities are O(n^{3/4}ε^{-2}) and O(ε^{-5}). The approach is validated through applications in AUC optimization and policy evaluation in reinforcement learning.