Robust personalized pricing under uncertainty of purchase probabilities

• URL: http://arxiv.org/abs/2407.15332v1
• Date: Mon, 22 Jul 2024 02:36:19 GMT
• Title: Robust personalized pricing under uncertainty of purchase probabilities
• Authors: Shunnosuke Ikeda, Naoki Nishimura, Noriyoshi Sukegawa, Yuichi Takano,
• Abstract summary: We propose a robust optimization model for personalized pricing that accounts for the uncertainty of predicted purchase probabilities. We also develop a Lagrangian decomposition algorithm combined with line search to efficiently find high-quality solutions for large-scale optimization problems.
• Score: 2.9061423802698565
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper is concerned with personalized pricing models aimed at maximizing the expected revenues or profits for a single item. While it is essential for personalized pricing to predict the purchase probabilities for each consumer, these predicted values are inherently subject to unavoidable errors that can negatively impact the realized revenues and profits. To address this issue, we focus on robust optimization techniques that yield reliable solutions to optimization problems under uncertainty. Specifically, we propose a robust optimization model for personalized pricing that accounts for the uncertainty of predicted purchase probabilities. This model can be formulated as a mixed-integer linear optimization problem, which can be solved exactly using mathematical optimization solvers. We also develop a Lagrangian decomposition algorithm combined with line search to efficiently find high-quality solutions for large-scale optimization problems. Experimental results demonstrate the effectiveness of our robust optimization model and highlight the utility of our Lagrangian decomposition algorithm in terms of both computational efficiency and solution quality.

Related papers

• Learning Joint Models of Prediction and Optimization [56.04498536842065]
  Predict-Then-Then framework uses machine learning models to predict unknown parameters of an optimization problem from features before solving. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by joint predictive models.
  arXiv  Detail & Related papers  (2024-09-07T19:52:14Z)
• Robust portfolio optimization for recommender systems considering uncertainty of estimated statistics [2.928964540437144]
  We propose a robust portfolio optimization model that copes with the uncertainty of estimated statistics based on the cardinality-based uncertainty sets. Our method has the potential to improve the recommendation quality of various rating prediction algorithms.
  arXiv  Detail & Related papers  (2024-06-09T15:42:54Z)
• End-to-End Learning for Fair Multiobjective Optimization Under Uncertainty [55.04219793298687]
  The Predict-Then-Forecast (PtO) paradigm in machine learning aims to maximize downstream decision quality. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives. It shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.
  arXiv  Detail & Related papers  (2024-02-12T16:33:35Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• Modeling the Second Player in Distributionally Robust Optimization [90.25995710696425]
  We argue for the use of neural generative models to characterize the worst-case distribution. This approach poses a number of implementation and optimization challenges. We find that the proposed approach yields models that are more robust than comparable baselines.
  arXiv  Detail & Related papers  (2021-03-18T14:26:26Z)
• Differentially Private Convex Optimization with Feasibility Guarantees [44.36831037077509]
  This paper develops a novel differentially private framework to solve convex optimization problems. The proposed framework provides a trade-off between the expected optimality loss and the variance of optimization results.
  arXiv  Detail & Related papers  (2020-06-22T15:30:52Z)
• Automatically Learning Compact Quality-aware Surrogates for Optimization Problems [55.94450542785096]
  Solving optimization problems with unknown parameters requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the optimization problem as a layer in a complex training model pipeline results in predictions of iteration of unobserved decision making. We show that we can improve solution quality by learning a low-dimensional surrogate model of a large optimization problem.
  arXiv  Detail & Related papers  (2020-06-18T19:11:54Z)
• Bilevel Optimization for Differentially Private Optimization in Energy Systems [53.806512366696275]
  This paper studies how to apply differential privacy to constrained optimization problems whose inputs are sensitive. The paper shows that, under a natural assumption, a bilevel model can be solved efficiently for large-scale nonlinear optimization problems.
  arXiv  Detail & Related papers  (2020-01-26T20:15:28Z)

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.