Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithms

• URL: http://arxiv.org/abs/2305.07730v2
• Date: Tue, 23 Jan 2024 21:44:40 GMT
• Title: Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithms
• Authors: Pedro Zattoni Scroccaro, Bilge Atasoy, Peyman Mohajerin Esfahani
• Abstract summary: We introduce the "incenter" concept, a new notion akin to circumcenter recently proposed by Besbes et al. We propose a novel loss function called Augmented Suboptimality Loss (ASL), a relaxation of the incenter concept for problems with inconsistent data. This algorithm combines approximate subgradient evaluations, together with mirror descent update steps, which is provably efficient for the IO problems with discrete feasible sets with high cardinality.
• Score: 4.0295993947651025
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In Inverse Optimization (IO), an expert agent solves an optimization problem parametric in an exogenous signal. From a learning perspective, the goal is to learn the expert's cost function given a dataset of signals and corresponding optimal actions. Motivated by the geometry of the IO set of consistent cost vectors, we introduce the "incenter" concept, a new notion akin to circumcenter recently proposed by Besbes et al. (2023). Discussing the geometric and robustness interpretation of the incenter cost vector, we develop corresponding tractable convex reformulations, which are in contrast with the circumcenter, which we show is equivalent to an intractable optimization program. We further propose a novel loss function called Augmented Suboptimality Loss (ASL), a relaxation of the incenter concept for problems with inconsistent data. Exploiting the structure of the ASL, we propose a novel first-order algorithm, which we name Stochastic Approximate Mirror Descent. This algorithm combines stochastic and approximate subgradient evaluations, together with mirror descent update steps, which is provably efficient for the IO problems with discrete feasible sets with high cardinality. We implement the IO approaches developed in this paper as a Python package called InvOpt. Our numerical experiments are reproducible, and the underlying source code is available as examples in the InvOpt package.

Related papers

• A Sample Efficient Alternating Minimization-based Algorithm For Robust Phase Retrieval [56.67706781191521]
  In this work, we present a robust phase retrieval problem where the task is to recover an unknown signal. Our proposed oracle avoids the need for computationally spectral descent, using a simple gradient step and outliers.
  arXiv  Detail & Related papers  (2024-09-07T06:37:23Z)
• Sparsity-Constraint Optimization via Splicing Iteration [1.3622424109977902]
  We develop an algorithm named Sparsity-Constraint Optimization via sPlicing itEration (SCOPE) SCOPE converges effectively without tuning parameters. We apply SCOPE to solve quadratic optimization, learn sparse classifiers, and recover sparse Markov networks for binary variables. Our open-source Python package skscope based on C++ implementation is publicly available on GitHub.
  arXiv  Detail & Related papers  (2024-06-17T18:34:51Z)
• Robust expected improvement for Bayesian optimization [1.8130068086063336]
  We propose a surrogate modeling and active learning technique called robust expected improvement (REI) that ports adversarial methodology into the BO/GP framework. We illustrate and draw comparisons to several competitors on benchmark synthetic exercises and real problems of varying complexity.
  arXiv  Detail & Related papers  (2023-02-16T22:34:28Z)
• Adaptive Zeroth-Order Optimisation of Nonconvex Composite Objectives [1.7640556247739623]
  We analyze algorithms for zeroth-order entropy composite objectives, focusing on dependence on dimensionality. This is achieved by exploiting low dimensional structure of the decision set using the mirror descent method with an estimation alike function. To improve the gradient, we replace the classic sampling method based on Rademacher and show that the mini-batch method copes with non-Eucli geometry.
  arXiv  Detail & Related papers  (2022-08-09T07:36:25Z)
• Outlier-Robust Sparse Estimation via Non-Convex Optimization [73.18654719887205]
  We explore the connection between high-dimensional statistics and non-robust optimization in the presence of sparsity constraints. We develop novel and simple optimization formulations for these problems. As a corollary, we obtain that any first-order method that efficiently converges to station yields an efficient algorithm for these tasks.
  arXiv  Detail & Related papers  (2021-09-23T17:38:24Z)
• Momentum Accelerates the Convergence of Stochastic AUPRC Maximization [80.8226518642952]
  We study optimization of areas under precision-recall curves (AUPRC), which is widely used for imbalanced tasks. We develop novel momentum methods with a better iteration of $O (1/epsilon4)$ for finding an $epsilon$stationary solution. We also design a novel family of adaptive methods with the same complexity of $O (1/epsilon4)$, which enjoy faster convergence in practice.
  arXiv  Detail & Related papers  (2021-07-02T16:21:52Z)
• Convergence Analysis of Nonconvex Distributed Stochastic Zeroth-order Coordinate Method [3.860616339202303]
  This paper investigates the distributed non optimization problem of minimizing a global cost function formed by the summation of $ZOn$ local cost functions. Agents approximate their own ZO coordinate method to solve the problem.
  arXiv  Detail & Related papers  (2021-03-24T03:07:46Z)
• Parallel Stochastic Mirror Descent for MDPs [72.75921150912556]
  We consider the problem of learning the optimal policy for infinite-horizon Markov decision processes (MDPs) Some variant of Mirror Descent is proposed for convex programming problems with Lipschitz-continuous functionals. We analyze this algorithm in a general case and obtain an estimate of the convergence rate that does not accumulate errors during the operation of the method.
  arXiv  Detail & Related papers  (2021-02-27T19:28:39Z)
• Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box Optimization Framework [100.36569795440889]
  This work is on the iteration of zero-th-order (ZO) optimization which does not require first-order information. We show that with a graceful design in coordinate importance sampling, the proposed ZO optimization method is efficient both in terms of complexity as well as as function query cost.
  arXiv  Detail & Related papers  (2020-12-21T17:29:58Z)
• Accelerated Algorithms for Convex and Non-Convex Optimization on Manifolds [9.632674803757475]
  We propose a scheme for solving convex and non- optimization problems on distance. Our proposed algorithm adapts to the level of complexity in the objective function.
  arXiv  Detail & Related papers  (2020-10-18T02:48:22Z)
• A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic [142.1492359556374]
  Bilevel optimization is a class of problems which exhibit a two-level structure. We propose a two-timescale approximation (TTSA) algorithm for tackling such a bilevel problem. We show that a two-timescale natural actor-critic policy optimization algorithm can be viewed as a special case of our TTSA framework.
  arXiv  Detail & Related papers  (2020-07-10T05:20:02Z)

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.