Consensus Distributionally Robust Optimization with Phi-Divergence

Research output: Contribution to journalArticlepeer-review

Abstract

We study an efficient algorithm to solve the distributionally robust optimization (DRO) problem, which has recently attracted attention as a new paradigm for decision making in uncertain situations. In traditional stochastic programming, a decision is sought that minimizes the expected cost over uncertain parameters, given the probability distribution of the unknown parameters. In contrast, in DRO, robust decision making can be derived from data without assuming a probability distribution; thus, it is expected to provide a powerful method for data-driven decision making. However, solutions to DRO problems are computationally challenging and cannot be used for large-scale problems. Therefore, we propose a distributed optimization algorithm for DRO using consensus optimization (CO). CO is a decomposition method for large-scale problems and it is rapid because it decomposes the problem into smaller subproblems to solve. As different subproblems lead to different decisions, a coherence constraint is imposed to ensure agreement, thereby guaranteeing global convergence. We applied the proposed method to linear programming, quadratic programming, and second-order cone programming in numerical experiments and verified its effectiveness.

Original languageEnglish
JournalIEEE Access
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Alternating direction method of multipliers
  • Consensus optimization
  • Decision making
  • Decomposition method
  • Distributionally robust optimization
  • Linear programming
  • Optimization
  • Probability distribution
  • Programming
  • Stochastic processes
  • Stochastic programming
  • Uncertainty

ASJC Scopus subject areas

  • Computer Science(all)
  • Materials Science(all)
  • Engineering(all)

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