Convergence Rate of a Functional Learning Method for Contextual Stochastic Optimization

• URL: http://arxiv.org/abs/2603.13048v1
• Date: Fri, 13 Mar 2026 14:53:35 GMT
• Title: Convergence Rate of a Functional Learning Method for Contextual Stochastic Optimization
• Abstract summary: We analyze a simultaneous learning-and-optimization algorithm that jointly estimates the conditional expectation and optimize the outer objective.<n>We establish that the method achieves a convergence rate of order $mathcalObig (1/sqrtNbig)$, where $N$ denotes the number of observed pairs.
• Score: 0.6015898117103067
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a stochastic optimization problem involving two random variables: a context variable $X$ and a dependent variable $Y$. The objective is to minimize the expected value of a nonlinear loss functional applied to the conditional expectation $\mathbb{E}[f(X, Y,β) \mid X]$, where $f$ is a nonlinear function and $β$ represents the decision variables. We focus on the practically important setting in which direct sampling from the conditional distribution of $Y \mid X$ is infeasible, and only a stream of i.i.d.\ observation pairs $\{(X^k, Y^k)\}_{k=0,1,2,\ldots}$ is available. In our approach, the conditional expectation is approximated within a prespecified parametric function class. We analyze a simultaneous learning-and-optimization algorithm that jointly estimates the conditional expectation and optimizes the outer objective, and establish that the method achieves a convergence rate of order $\mathcal{O}\big(1/\sqrt{N}\big)$, where $N$ denotes the number of observed pairs.

Related papers

• Stochastic Compositional Optimization via Hybrid Momentum Frank--Wolfe [1.3537117504260623]
  We develop an algorithm that drops the assumption on $min_bmx in mathcalX.<n>The analysis extends to heavy-tailed noise oracles with bounded moments for $r$in (1, 2]$ and recovers the rates of the noise as the noise.
  arXiv  Detail & Related papers  (2026-05-14T19:20:22Z)
• Allocating Variance to Maximize Expectation [2.25491649634702]
  We design efficient approximation algorithms for maximizing the expectation of the supremum of families of Gaussian random variables.<n>Such expectation problems occur in diverse applications, ranging from utility auctions to learning mixture models in quantitative genetics.
  arXiv  Detail & Related papers  (2025-02-25T18:59:46Z)
• Beyond likelihood ratio bias: Nested multi-time-scale stochastic approximation for likelihood-free parameter estimation [49.78792404811239]
  We study inference in simulation-based models where the analytical form of the likelihood is unknown.<n>We use a ratio-free nested multi-time-scale approximation (SA) method that simultaneously tracks the score and drives the parameter update.<n>We show that our algorithm can eliminate the original bias $Obig(sqrtfrac1Nbig)$ and accelerate the convergence rate from $Obig(beta_k+sqrtfracalpha_kNbig)$.
  arXiv  Detail & Related papers  (2024-11-20T02:46:15Z)
• Revisiting Step-Size Assumptions in Stochastic Approximation [1.3654846342364308]
  It is shown for the first time that this assumption is not required for convergence and finer results.<n>Rates of convergence are obtained for the standard algorithm and for estimates obtained via the averaging technique of Polyak and Ruppert.<n>Results from numerical experiments illustrate that $beta_theta$ may be large due to a combination of multiplicative noise and Markovian memory.
  arXiv  Detail & Related papers  (2024-05-28T05:11:05Z)
• $L^1$ Estimation: On the Optimality of Linear Estimators [64.76492306585168]
  This work shows that the only prior distribution on $X$ that induces linearity in the conditional median is Gaussian. In particular, it is demonstrated that if the conditional distribution $P_X|Y=y$ is symmetric for all $y$, then $X$ must follow a Gaussian distribution.
  arXiv  Detail & Related papers  (2023-09-17T01:45:13Z)
• Policy Gradient Optimal Correlation Search for Variance Reduction in Monte Carlo simulation and Maximum Optimal Transport [0.0]
  We propose a new algorithm for variance reduction when estimating $f(X_T)$ where $X$ is the solution to some differential equation and $f$ is a test function. The new estimator is $(f(XT) + f(X2_T))/2$, where $X1$ and $X2$ have same marginal law as $X2$ but are pathwise correlated so that to reduce the variance.
  arXiv  Detail & Related papers  (2023-07-24T11:37:02Z)
• Oblivious Stochastic Composite Optimization [47.48197617884748]
  We show that our algorithms converge without any prior knowledge on the parameters of the problem.<n>All three algorithms work without prior knowledge of the diameter of the feasible set, the Lipschitz constant or smoothness of the objective function.<n>We extend our framework to relative scale and demonstrate the efficiency and robustness of our methods on large-scale semidefinite programs.
  arXiv  Detail & Related papers  (2023-06-30T08:34:29Z)
• Estimating the minimizer and the minimum value of a regression function under passive design [72.85024381807466]
  We propose a new method for estimating the minimizer $boldsymbolx*$ and the minimum value $f*$ of a smooth and strongly convex regression function $f$. We derive non-asymptotic upper bounds for the quadratic risk and optimization error of $boldsymbolz_n$, and for the risk of estimating $f*$.
  arXiv  Detail & Related papers  (2022-11-29T18:38:40Z)
• Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization [52.25843977506935]
  We propose an adaptive variance method, called AdaSpider, for $L$-smooth, non-reduction functions with a finitesum structure. In doing so, we are able to compute an $epsilon-stationary point with $tildeOleft + st/epsilon calls.
  arXiv  Detail & Related papers  (2022-11-03T14:41:46Z)
• Statistical Inference of Constrained Stochastic Optimization via Sketched Sequential Quadratic Programming [53.63469275932989]
  We consider online statistical inference of constrained nonlinear optimization problems.<n>We apply the Sequential Quadratic Programming (StoSQP) method to solve these problems.
  arXiv  Detail & Related papers  (2022-05-27T00:34:03Z)
• Localization in 1D non-parametric latent space models from pairwise affinities [6.982738885923206]
  We consider the problem of estimating latent positions in a one-dimensional torus from pairwise affinities. We introduce an estimation procedure that provably localizes all the latent positions with a maximum error of the order of $sqrtlog(n)/n$, with high-probability.
  arXiv  Detail & Related papers  (2021-08-06T13:05:30Z)
• Finding Global Minima via Kernel Approximations [90.42048080064849]
  We consider the global minimization of smooth functions based solely on function evaluations. In this paper, we consider an approach that jointly models the function to approximate and finds a global minimum.
  arXiv  Detail & Related papers  (2020-12-22T12:59:30Z)
• Accelerating Optimization and Reinforcement Learning with Quasi-Stochastic Approximation [2.294014185517203]
  This paper sets out to extend convergence theory to quasi-stochastic approximations. It is illustrated with applications to gradient-free optimization and policy gradient algorithms for reinforcement learning.
  arXiv  Detail & Related papers  (2020-09-30T04:44:45Z)
• Optimal Robust Linear Regression in Nearly Linear Time [97.11565882347772]
  We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = langle X,w* rangle + epsilon$ We propose estimators for this problem under two settings: (i) $X$ is L4-L2 hypercontractive, $mathbbE [XXtop]$ has bounded condition number and $epsilon$ has bounded variance and (ii) $X$ is sub-Gaussian with identity second moment and $epsilon$ is
  arXiv  Detail & Related papers  (2020-07-16T06:44:44Z)

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.