Smart Predict-then-Optimize Method with Dependent Data: Risk Bounds and Calibration of Autoregression

• URL: http://arxiv.org/abs/2411.12653v1
• Date: Tue, 19 Nov 2024 17:02:04 GMT
• Title: Smart Predict-then-Optimize Method with Dependent Data: Risk Bounds and Calibration of Autoregression
• Authors: Jixian Liu, Tao Xu, Jianping He, Chongrong Fang,
• Abstract summary: We present an autoregressive SPO method directly targeting the optimization problem at the decision stage. We conduct experiments to demonstrate the effectiveness of the SPO+ surrogate compared to the absolute loss and the least squares loss.
• Score: 7.369846475695131
• License:
• Abstract: The predict-then-optimize (PTO) framework is indispensable for addressing practical stochastic decision-making tasks. It consists of two crucial steps: initially predicting unknown parameters of an optimization model and subsequently solving the problem based on these predictions. Elmachtoub and Grigas [1] introduced the Smart Predict-then-Optimize (SPO) loss for the framework, which gauges the decision error arising from predicted parameters, and a convex surrogate, the SPO+ loss, which incorporates the underlying structure of the optimization model. The consistency of these different loss functions is guaranteed under the assumption of i.i.d. training data. Nevertheless, various types of data are often dependent, such as power load fluctuations over time. This dependent nature can lead to diminished model performance in testing or real-world applications. Motivated to make intelligent predictions for time series data, we present an autoregressive SPO method directly targeting the optimization problem at the decision stage in this paper, where the conditions of consistency are no longer met. Therefore, we first analyze the generalization bounds of the SPO loss within our autoregressive model. Subsequently, the uniform calibration results in Liu and Grigas [2] are extended in the proposed model. Finally, we conduct experiments to empirically demonstrate the effectiveness of the SPO+ surrogate compared to the absolute loss and the least squares loss, especially when the cost vectors are determined by stationary dynamical systems and demonstrate the relationship between normalized regret and mixing coefficients.

Related papers

• 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)
• Decision-focused predictions via pessimistic bilevel optimization: a computational study [0.7499722271664147]
  Uncertainty in optimization parameters is an important and longstanding challenge. We build predictive models that measure a emphregret measure on decisions taken with them. We show various computational techniques to achieve tractability.
  arXiv  Detail & Related papers  (2023-12-29T15:05:00Z)
• Model-Based Reparameterization Policy Gradient Methods: Theory and Practical Algorithms [88.74308282658133]
  Reization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. Recent studies have revealed that, when applied to long-term reinforcement learning problems, model-based RP PGMs may experience chaotic and non-smooth optimization landscapes. We propose a spectral normalization method to mitigate the exploding variance issue caused by long model unrolls.
  arXiv  Detail & Related papers  (2023-10-30T18:43:21Z)
• Structured Radial Basis Function Network: Modelling Diversity for Multiple Hypotheses Prediction [51.82628081279621]
  Multi-modal regression is important in forecasting nonstationary processes or with a complex mixture of distributions. A Structured Radial Basis Function Network is presented as an ensemble of multiple hypotheses predictors for regression problems. It is proved that this structured model can efficiently interpolate this tessellation and approximate the multiple hypotheses target distribution.
  arXiv  Detail & Related papers  (2023-09-02T01:27:53Z)
• Online Contextual Decision-Making with a Smart Predict-then-Optimize Method [4.061135251278187]
  We study an online contextual decision-making problem with resource constraints. We propose an algorithm that mixes a prediction step based on the "Smart Predict-then- (SPO)" method with a dual update step based on mirror descent. We prove regret bounds and demonstrate that the overall convergence rate of our method depends on the $mathcalO(T-1/2)$ convergence of online mirror descent.
  arXiv  Detail & Related papers  (2022-06-15T06:16:13Z)
• Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction [69.81996031777717]
  The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. The application of this approach becomes problematic if the available data is incomplete because some dimensions of smaller scale either missing or unmeasured. We consider a first-order approximation of the Mori-Zwanzig decomposition, state the corresponding optimization problem and solve it with the gradient-based optimization method.
  arXiv  Detail & Related papers  (2022-02-23T11:23:59Z)
• Time varying regression with hidden linear dynamics [74.9914602730208]
  We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates.
  arXiv  Detail & Related papers  (2021-12-29T23:37:06Z)
• Risk Bounds and Calibration for a Smart Predict-then-Optimize Method [2.28438857884398]
  We show that the SPO+ loss can minimize low excess true risk with high probability. We show that the results can be strengthened substantially when the feasible region is a level set of bounds.
  arXiv  Detail & Related papers  (2021-08-19T19:25:46Z)
• Learning MDPs from Features: Predict-Then-Optimize for Sequential Decision Problems by Reinforcement Learning [52.74071439183113]
  We study the predict-then-optimize framework in the context of sequential decision problems (formulated as MDPs) solved via reinforcement learning. Two significant computational challenges arise in applying decision-focused learning to MDPs.
  arXiv  Detail & Related papers  (2021-06-06T23:53:31Z)
• SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks [14.564168076456822]
  We propose a flexible model for survival analysis using neural networks along with scalable optimization algorithms. We demonstrate the effectiveness of the proposed method in comparison to existing state-of-the-art deep learning survival analysis models.
  arXiv  Detail & Related papers  (2020-08-19T19:11:25Z)

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.