Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems

• URL: http://arxiv.org/abs/2408.17387v1
• Date: Fri, 30 Aug 2024 16:26:31 GMT
• Title: Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems
• Authors: Jack M. Buckingham, Ivo Couckuyt, Juergen Branke,
• Abstract summary: We formulate a knowledgeient-based acquisition function to jointly optimize the first and second-stage variables. We show that differences in the dimension and length scales between the variable types can lead to inefficiencies of the twostep algorithm.
• Score: 2.9016548477524156
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bayesian optimization is a sample-efficient method for solving expensive, black-box optimization problems. Stochastic programming concerns optimization under uncertainty where, typically, average performance is the quantity of interest. In the first stage of a two-stage problem, here-and-now decisions must be made in the face of this uncertainty, while in the second stage, wait-and-see decisions are made after the uncertainty has been resolved. Many methods in stochastic programming assume that the objective is cheap to evaluate and linear or convex. In this work, we apply Bayesian optimization to solve non-convex, two-stage stochastic programs which are expensive to evaluate. We formulate a knowledge-gradient-based acquisition function to jointly optimize the first- and second-stage variables, establish a guarantee of asymptotic consistency and provide a computationally efficient approximation. We demonstrate comparable empirical results to an alternative we formulate which alternates its focus between the two variable types, and superior empirical results over the standard, naive, two-step benchmark. We show that differences in the dimension and length scales between the variable types can lead to inefficiencies of the two-step algorithm, while the joint and alternating acquisition functions perform well in all problems tested. Experiments are conducted on both synthetic and real-world examples.

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)
• Numerical Methods for Convex Multistage Stochastic Optimization [86.45244607927732]
  We focus on optimisation programming (SP), Optimal Control (SOC) and Decision Processes (MDP) Recent progress in solving convex multistage Markov problems is based on cutting planes approximations of the cost-to-go functions of dynamic programming equations. Cutting plane type methods can handle multistage problems with a large number of stages, but a relatively smaller number of state (decision) variables.
  arXiv  Detail & Related papers  (2023-03-28T01:30:40Z)
• Generalizing Bayesian Optimization with Decision-theoretic Entropies [102.82152945324381]
  We consider a generalization of Shannon entropy from work in statistical decision theory. We first show that special cases of this entropy lead to popular acquisition functions used in BO procedures. We then show how alternative choices for the loss yield a flexible family of acquisition functions.
  arXiv  Detail & Related papers  (2022-10-04T04:43:58Z)
• Accelerating Stochastic Probabilistic Inference [1.599072005190786]
  Variational Inference (SVI) has been increasingly attractive thanks to its ability to find good posterior approximations of probabilistic models. Almost all the state-of-the-art SVI algorithms are based on first-order optimization and often suffer from poor convergence rate. We bridge the gap between second-order methods and variational inference by proposing a second-order based variational inference approach.
  arXiv  Detail & Related papers  (2022-03-15T01:19:12Z)
• High Probability Complexity Bounds for Non-Smooth Stochastic Optimization with Heavy-Tailed Noise [51.31435087414348]
  It is essential to theoretically guarantee that algorithms provide small objective residual with high probability. Existing methods for non-smooth convex optimization have complexity bounds with dependence on confidence level. We propose novel stepsize rules for two methods with gradient clipping.
  arXiv  Detail & Related papers  (2021-06-10T17:54:21Z)
• Bilevel Optimization: Convergence Analysis and Enhanced Design [63.64636047748605]
  Bilevel optimization is a tool for many machine learning problems. We propose a novel stoc-efficientgradient estimator named stoc-BiO.
  arXiv  Detail & Related papers  (2020-10-15T18:09:48Z)
• Robust, Accurate Stochastic Optimization for Variational Inference [68.83746081733464]
  We show that common optimization methods lead to poor variational approximations if the problem is moderately large. Motivated by these findings, we develop a more robust and accurate optimization framework by viewing the underlying algorithm as producing a Markov chain.
  arXiv  Detail & Related papers  (2020-09-01T19:12:11Z)
• 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)
• Adaptive First-and Zeroth-order Methods for Weakly Convex Stochastic Optimization Problems [12.010310883787911]
  We analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) optimization problems. Experimental results indicate how the proposed algorithms empirically outperform its zerothorder gradient descent and its design variant.
  arXiv  Detail & Related papers  (2020-05-19T07:44:52Z)

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.