An Online-Learning Approach to Inverse Optimization

Bärmann, Andreas; Martín, Alexander; Pokutta, Sebastian; Schneider, Oskar

doi:10.48550/arxiv.1810.12997

Cited by 5 publications

(8 citation statements)

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“…The suboptimality loss measures how well the predicted ĉnew explains the realized optimal solution x * new . It is more commonly adopted in the inverse linear programming literature (Mohajerin Esfahani et al, 2018;Bärmann et al, 2018;Chen and Kılınç-Karzan, 2020).…”

Section: Predict-then-optimize/contextual Linear Programmingmentioning

confidence: 99%

Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming

Sun¹,

Liu²,

Li³

2023

Preprint

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In this paper, we study the predict-then-optimize problem where the output of a machine learning prediction task is used as the input of some downstream optimization problem, say, the objective coefficient vector of a linear program. The problem is also known as predictive analytics or contextual linear programming. The existing approaches largely suffer from either (i) optimization intractability (a non-convex objective function)/statistical inefficiency (a suboptimal generalization bound) or (ii) requiring strong condition(s) such as no constraint or loss calibration. We develop a new approach to the problem called maximum optimality margin which designs the machine learning loss function by the optimality condition of the downstream optimization. The max-margin formulation enjoys both computational efficiency and good theoretical properties for the learning procedure. More importantly, our new approach only needs the observations of the optimal solution in the training data rather than the objective function, which makes it a new and natural approach to the inverse linear programming problem under both contextual and context-free settings; we also analyze the proposed method under both offline and online settings, and demonstrate its performance using numerical experiments.

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Section: Predict-then-optimize/contextual Linear Programmingmentioning

confidence: 99%

Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming

Sun¹,

Liu²,

Li³

2023

Preprint

View full text Add to dashboard Cite

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“…The estimand in our project-the acquisition function of a Bayesian optimization-is analogous to the risk preferences estimated in Li's paper. Additionally, the sequential nature of the learning problem we study relates to online learning in inverse optimization (Bärmann et al, 2018;Dong et al, 2018;Dong and Zeng, 2020) and inverse Markov decision processes (Erkin et al, 2010).…”

Section: Related Workmentioning

confidence: 99%

Inverse Bayesian Optimization: Learning Human Acquisition Functions in an Exploration vs Exploitation Search Task

Sandholtz,

Miyamoto,

Bornn

et al. 2021

Preprint

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Bayesian optimization is a popular algorithm for sequential optimization of a latent objective function when sampling from the objective is costly. The search path of the algorithm is governed by the acquisition function, which defines the agent's search strategy. Conceptually, the acquisition function characterizes how the optimizer balances exploration and exploitation when searching for the optimum of the latent objective. In this paper, we explore the inverse problem of Bayesian optimization; we seek to estimate the agent's latent acquisition function based on observed search paths. We introduce a probabilistic solution framework for the inverse problem which provides a principled framework to quantify both the variability with which the agent performs the optimization task as well as the uncertainty around their estimated acquisition function.We illustrate our methods by analyzing human behavior from an experiment which was designed to force subjects to balance exploration and exploitation in search of an invisible target location. We find that while most subjects demonstrate clear trends in their search behavior, there is significant variation around these trends from round to round. A wide range of search strategies are exhibited across the subjects in our study, but upper confidence bound acquisition functions offer the best fit for the majority of subjects. Finally, some subjects do not map well to any of the acquisition functions we initially consider; these subjects tend to exhibit exploration preferences beyond that of standard acquisition functions to capture. Guided by the model discrepancies, we augment the candidate acquisition functions to yield a superior fit to the human behavior in this task.

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“…Saez-Gallego and Morales [2017] jointly learn c and b which are affine functions of u. Bärmann et al [2017Bärmann et al [ , 2020 and Dong et al [2018] study online versions of inverse linear and convex optimization, respectively, learning a sequence of cost functions where the feasible set for each observation are assumed to be fully-specified. Tan et al [2019] proposed a gradient-based approach for learning cost and constraints of a PLP, by 'unrolling' a barrier interior point solver and backpropagating through it.…”

Section: Related Workmentioning

confidence: 99%

Learning Linear Programs from Optimal Decisions

Tan,

Terekhov,

Delong

2020

Preprint

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We propose a flexible gradient-based framework for learning linear programs from optimal decisions. Linear programs are often specified by hand, using prior knowledge of relevant costs and constraints. In some applications, linear programs must instead be learned from observations of optimal decisions. Learning from optimal decisions is a particularly challenging bi-level problem, and much of the related inverse optimization literature is dedicated to special cases. We tackle the general problem, learning all parameters jointly while allowing flexible parametrizations of costs, constraints, and loss functions. We also address challenges specific to learning linear programs, such as empty feasible regions and non-unique optimal decisions. Experiments show that our method successfully learns synthetic linear programs and minimum-cost multi-commodity flow instances for which previous methods are not directly applicable. We also provide a fast batch-mode PyTorch implementation of the homogeneous interior point algorithm, which supports gradients by implicit differentiation or backpropagation.Preprint. Under review.

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An Online-Learning Approach to Inverse Optimization

Cited by 5 publications

References 0 publications

Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming

Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming

Inverse Bayesian Optimization: Learning Human Acquisition Functions in an Exploration vs Exploitation Search Task

Learning Linear Programs from Optimal Decisions

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