Bayesian Joint Chance Constrained Optimization: Approximations and Statistical Consistency

• URL: http://arxiv.org/abs/2106.12199v2
• Date: Sat, 26 Jun 2021 17:01:49 GMT
• Title: Bayesian Joint Chance Constrained Optimization: Approximations and Statistical Consistency
• Authors: Prateek Jaiswal, Harsha Honnappa, Vinayak A. Rao
• Abstract summary: We focus on the question of statistical consistency of the optimal value, computed using an approximate posterior distribution. We also prove the feasibility of the approximate optimization problem. We also demonstrate the utility of our approach on an optimal staffing problem for an M/M/c queueing model.
• Score: 10.20554144865699
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems. However, the computation of Bayesian posteriors is typically an intractable problem, and has spawned a large literature on approximate Bayesian computation. Here, in the context of chance-constrained optimization, we focus on the question of statistical consistency (in an appropriate sense) of the optimal value, computed using an approximate posterior distribution. To this end, we rigorously prove a frequentist consistency result demonstrating the convergence of the optimal value to the optimal value of a fixed, parameterized constrained optimization problem. We augment this by also establishing a probabilistic rate of convergence of the optimal value. We also prove the convex feasibility of the approximate Bayesian stochastic optimization problem. Finally, we demonstrate the utility of our approach on an optimal staffing problem for an M/M/c queueing model.

Related papers

• BO4IO: A Bayesian optimization approach to inverse optimization with uncertainty quantification [5.031974232392534]
  This work addresses data-driven inverse optimization (IO) The goal is to estimate unknown parameters in an optimization model from observed decisions that can be assumed to be optimal or near-optimal.
  arXiv  Detail & Related papers  (2024-05-28T06:52:17Z)
• Principled Preferential Bayesian Optimization [22.269732173306192]
  We study the problem of preferential Bayesian optimization (BO) We aim to optimize a black-box function with only preference feedback over a pair of candidate solutions. An optimistic algorithm with an efficient computational method is then developed to solve the problem.
  arXiv  Detail & Related papers  (2024-02-08T02:57:47Z)
• Selection of the Most Probable Best [2.1095005405219815]
  We consider an expected-value ranking and selection (R&S) problem where all k solutions' simulation outputs depend on a common parameter whose uncertainty can be modeled by a distribution. We define the most probable best (MPB) to be the solution that has the largest probability of being optimal with respect to the distribution. We devise a series of algorithms that replace the unknown means in the optimality conditions with their estimates and prove the algorithms' sampling ratios achieve the conditions as the simulation budget increases.
  arXiv  Detail & Related papers  (2022-07-15T15:27:27Z)
• Non-Convex Optimization with Certificates and Fast Rates Through Kernel Sums of Squares [68.8204255655161]
  We consider potentially non- optimized approximation problems. In this paper, we propose an algorithm that achieves close to optimal a priori computational guarantees.
  arXiv  Detail & Related papers  (2022-04-11T09:37:04Z)
• Posterior temperature optimized Bayesian models for inverse problems in medical imaging [59.82184400837329]
  We present an unsupervised Bayesian approach to inverse problems in medical imaging using mean-field variational inference with a fully tempered posterior. We show that an optimized posterior temperature leads to improved accuracy and uncertainty estimation. Our source code is publicly available at calibrated.com/Cardio-AI/mfvi-dip-mia.
  arXiv  Detail & Related papers  (2022-02-02T12:16:33Z)
• Integrated Conditional Estimation-Optimization [6.037383467521294]
  Many real-world optimization problems uncertain parameters with probability can be estimated using contextual feature information. In contrast to the standard approach of estimating the distribution of uncertain parameters, we propose an integrated conditional estimation approach. We show that our ICEO approach is theally consistent under moderate conditions.
  arXiv  Detail & Related papers  (2021-10-24T04:49:35Z)
• Outlier-Robust Sparse Estimation via Non-Convex Optimization [73.18654719887205]
  We explore the connection between high-dimensional statistics and non-robust optimization in the presence of sparsity constraints. We develop novel and simple optimization formulations for these problems. As a corollary, we obtain that any first-order method that efficiently converges to station yields an efficient algorithm for these tasks.
  arXiv  Detail & Related papers  (2021-09-23T17:38:24Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)
• Incorporating Expert Prior in Bayesian Optimisation via Space Warping [54.412024556499254]
  In big search spaces the algorithm goes through several low function value regions before reaching the optimum of the function. One approach to subside this cold start phase is to use prior knowledge that can accelerate the optimisation. In this paper, we represent the prior knowledge about the function optimum through a prior distribution. The prior distribution is then used to warp the search space in such a way that space gets expanded around the high probability region of function optimum and shrinks around low probability region of optimum.
  arXiv  Detail & Related papers  (2020-03-27T06:18:49Z)
• 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.