Proof of convergence for multi-objective optimization using inverse reinforcement learning.
problem Proving convergence in multi-objective optimization problems.
method Wasserstein inverse reinforcement learning with projective subgradient method and gradient descent.
result Convergence of inverse reinforcement learning for multi-objective optimization.
New method uses FY loss for better inverse optimization.
problem Estimating unknown parameters from noisy and suboptimal solutions.
method Fenchel-Young loss approach for efficient gradient-based optimization.
result Significant improvement in parameter estimation accuracy and computational speed.
Given a set of observations generated by an optimization process, the goal of inverse optimization is to determine likely parameters of that process. We cast inverse optimization as a form of deep learning. Our method, called deep inverse optimization, is to unroll an iterative optimization process and then use backpro…
Proof shows imitation of expert's reward and solutions in multi-objective optimization.
problem Multi-objective optimization with reward and solution imitation.
method Wasserstein inverse reinforcement learning.
result Wasserstein inverse reinforcement learning enables imitation of expert's reward and solutions in multi-objective optimization.
Researchers analyze inverse optimal transport, deriving theoretical and empirical insights.
problem Understanding the inverse problem of inferring cost matrices from optimal couplings.
method Formalized and analyzed using entropy-regularized optimal transport, with theoretical and empirical contributions.
result Characterization of the manifold of cross-ratio equivalent costs and derivation of an MCMC sampler.
Enhances inverse design optimization with machine learning and reduced fidelity simulations.
problem Limited compute resources in inverse design optimization.
method Synergy of multi-fidelity simulations, machine learning, and search space reduction.
result Significant computational resource savings and improved optimization performance.
Inverse optimal control, also known as inverse reinforcement learning, is the problem of recovering an unknown reward function in a Markov decision process from expert demonstrations of the optimal policy. We introduce a probabilistic inverse optimal control algorithm that scales gracefully with task dimensionality, an…
Paper solves inverse optimal transport problem with convex optimization and neural network.
problem Learning the cost function for optimal transport from observed data.
method Unconstrained convex optimization, Sinkhorn-Knopp algorithm, and deep neural network parameterization.
result Novel framework avoids repeated OT solving, demonstrating efficiency and accuracy.
Paper explores stability, regularization, and gradient flows for stochastic inverse problems.
problem Recovering random probability distributions from measurements.
method Direct inversion, variational formulation with regularization, and optimization via gradient flows.
result The choice of metric impacts stability and properties of the optimizer.
We study the inverse optimal control problem in social sciences: we aim at learning a user's true cost function from the observed temporal behavior. In contrast to traditional phenomenological works that aim to learn a generative model to fit the behavioral data, we propose a novel variational principle and treat user …
Proposes a method to learn both constraints and objective functions from data.
problem Data-driven inverse optimization for mixed-integer linear programs (MILPs).
method Two-stage approach: first learns constraints, then estimates objective-function weights conditioned on learned constraints.
result Proposes and validates a method for learning both objective functions and constraints from data.
Optimal insurance minimizes ruin probability with non-decreasing functions.
problem Minimizing ruin probability with insurance premiums and non-decreasing functions.
method Reformulated problem with inverse survival function as control variable.
result Deductible insurance with maximum limit is optimal.
Stochastic optimization is key to efficient inversion in PDE-constrained optimization. Using 'simultaneous shots', or random superposition of source terms, works very well in simple acquisition geometries where all sources see all receivers, but this rarely occurs in practice. We develop an approach that interpolates d…
New methods tackle complex inverse problems with scalable optimization-based MCMC.
problem Estimating high-dimensional model parameters and hyperparameters in nonlinear hierarchical statistical inverse problems.
method Optimization-based Markov chain Monte Carlo (MCMC) methods using RTO and pseudo-marginal MCMC.
result Efficient sampling tools for hierarchical Bayesian inversion with robust performance to model parameter dimensions.
This paper tackles regularization parameter learning in inverse problems using data-driven bilevel optimization.
problem Finding optimal regularization parameters in inverse problems.
method Data-driven bilevel optimization approach, analyzing performance in large data samples.
result The approach can reduce computational cost through online numerical schemes based on stochastic gradient descent.
Gradient descent and SGD solve nonlinear inverse problems efficiently.
problem Solving nonlinear inverse problems with random design.
method Gradient descent and SGD with mini-batching, under classical assumptions.
result Achieves optimal convergence rates in RKHS framework.
DO-IQS recovers optimal stopping region from expert trajectories, addressing specific challenges.
problem Recovering optimal stopping region from expert trajectories with unknown gain functions.
method Dynamics-Aware Offline Inverse Q-Learning incorporating temporal information and confidence-based oversampling.
result Demonstrated performance on real and artificial data, including optimal intervention for critical events.
The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. Over the last decade, many applications of the inverse Ising problem have arisen, driven by the advent of large-scale data across different scientific disciplines…
Paper develops a method to learn optimal sparsity-promoting regularizers for linear inverse problems.
problem Solving linear inverse problems with sparse solutions.
method Bilevel optimization framework to select an optimal synthesis operator B. result Established well-posedness and theoretical guarantees for the learning process.
Neural Optimal Design of Experiments improves inverse problem solving efficiency.
problem Optimal experimental design in inverse problems.
method Jointly trains a reconstruction model and design variables in a single loop.
result Significantly reduces computational complexity and improves reconstruction accuracy.
New method solves blind inverse problems by optimizing both operator and image parameters.
problem Solving blind inverse problems with known forward operator.
method Parallel reverse diffusion guided by gradients from intermediate stages.
result State-of-the-art performance on blind deblurring and imaging through turbulence.
Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to compute the inverse or inverse square root of a matrix whose size is quadratic of …
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge, etc. The Bayesian formalism to inverse problems avoids most of the difficulties en…
Paper proposes efficient image inversion and editing using rectified stochastic differential equations.
problem Inversion and editing of real images using generative models.
method Proposes RF inversion using dynamic optimal control and a linear quadratic regulator, extending to stochastic sampler for Flux.
result Allows state-of-the-art performance in zero-shot inversion and editing, outperforming prior works.
Paper develops efficient methods for estimating Hessian inverses in stochastic optimization.
problem Estimating the inverse Hessian for convex function minimization.
method Robbins-Monro procedure for recursive estimation of the inverse Hessian.
result Develops universal stochastic Newton methods with improved efficiency.
CPS solves inverse problems using forward passes and constrained particle seeking.
problem Solving inverse problems with limited forward observation information.
method Gradient-free approach that reformulates inverse problem as constrained optimization.
result CPS achieves results comparable to gradient-based methods while outperforming alternatives.
Paper proposes a robust method for inferring parameters in multiobjective optimization.
problem Uncertainty in hypothetical decision-making problem, data quality, and parameter space.
method Wasserstein distributionally robust approach for inverse multiobjective optimization.
result WRO-IMOP minimizes worst-case expected loss over a Wasserstein ball of distributions.
Efficiently optimizes hyperparameters for PDE and inverse problems using Gaussian processes.
problem Hyperparameter optimization for scientific computing and inference methods.
method Bilevel optimization with Gauss-Newton linearization for efficient hyperparameter updates.
result Significant improvements in accuracy and robustness compared to random initialization.
Study inverse problems with measure samples, improving estimator calibration and recovery.
problem Inverse problems with unknown potentials observed through measure samples.
method Introduced convex empirical objectives and sharpened Fenchel--Young losses for finite-dimensional potential classes.
result High-probability parameter recovery bounds for inverse entropic unbalanced optimal transport and inverse JKO learning.
This study develops a dynamic inverse optimization framework to recover hidden, time-varying preferences from observed allocation trajectories.
problem The gap between classical optimization theory and real-world practice, especially in the presence of drift and shocks.
method Dynamic inverse optimization framework using a drift-aware estimator grounded in convex analysis and online learning theory.
result Sharp static and dynamic regret bounds for the framework, demonstrating its responsiveness to gradual drift and sudden shocks.
New method learns population dynamics from snapshots using JKO scheme and inverse optimization.
problem Recovering underlying process governing particle evolution from discrete time samples.
method Combines JKO scheme with inverse optimization techniques for end-to-end adversarial training.
result Improved performance over prior JKO-based methods with theoretical guarantees.
The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk averse optimization problems. Despite its theoretical appeal, the implementation of a convex risk function remains difficult, as there is little guidance regarding ho…
Paper tackles estimating initial conditions of spatio-temporal processes from sparse data.
problem Estimating initial conditions of spatio-temporal advection-diffusion processes from sparse data.
method Regularized convex optimization problem with Alternating Direction Method of Multipliers.
result Efficient solutions for non-uniform and shifted uniform sampling schemes.
Robo-advisor uses ML to optimize investment performance.
problem Maximizing investment performance with historical data.
method Inverse optimization and deep reinforcement learning.
result Robo-advisor consistently outperformed S&P 500.
Inverse reinforcement learning (IRL) is the problem of finding a reward function that generates a given optimal policy for a given Markov Decision Process. This paper looks at an algorithmic-independent geometric analysis of the IRL problem with finite states and actions. A L1-regularized Support Vector Machine formula…
New method tackles video inverse problems using image diffusion models.
problem Spatio-temporal degradation in video inverse problems.
method Leverages image diffusion models to treat time dimension as batch dimension, introduces batch-consistent diffusion sampling.
result Achieves state-of-the-art reconstructions for various spatio-temporal degradations.
New method disentangles perceptual uncertainty and behavioral costs in partially observable systems.
problem Tackles inverse optimal control for non-linear partially observable systems.
method Probabilistic approach using maximum causal entropy formulations and local linearization.
result Disentangles perceptual factors and behavioral costs in sequential decision-making.
In this paper, we address the inverse problem, or the statistical machine learning problem, in Markov random fields with a non-parametric pair-wise energy function with continuous variables. The inverse problem is formulated by maximum likelihood estimation. The exact treatment of maximum likelihood estimation is intra…
Efficiently solves inverse classification problems for logistic and softmax models.
problem Finding instances that change classifier predictions.
method Closed-form solution for logistic regression, iterative optimization for softmax.
result Fast, exact solutions for high-dimensional instances and many classes.
Proposes an online method for high-dimensional streaming data.
problem Increasing variable dimensions with sample size in online kernel sliced inverse regression.
method Introduces approximate linear dependence condition and dictionary variable sets to address the problem. Transforms into online generalized eigen-decomposition problem and uses stochastic optimization for updates.
result Achieves close performance to batch processing kernel sliced inverse regression.
Proposes ICC method for dynamic portfolio optimization.
problem Non-stationarity in market conditions makes traditional portfolio optimization ineffective.
method Inverse Covariance Clustering (ICC) to identify market states and integrate into dynamic optimization.
result ICC-PO generates portfolios with higher Sharpe Ratios and greater robustness.
Unified approach for optimizing predictions in linear programming and inverse problems.
problem Optimizing predictions in linear programming and inverse problems.
method Maximum optimality margin approach.
result Unified approach that balances computational efficiency and theoretical properties.
Bayesian method estimates dynamics from near-optimal trajectories.
problem Estimating dynamics from near-optimal expert trajectories in reinforcement learning.
method Constraint-based Bayesian approach integrating expert near-optimality.
result Significant improvements in decision-making and transfer success.
Inverse optimization is a powerful paradigm for learning preferences and restrictions that explain the behavior of a decision maker, based on a set of external signal and the corresponding decision pairs. However, most inverse optimization algorithms are designed specifically in batch setting, where all the data is ava…
The goal of the inverse reinforcement learning (IRL) problem is to recover the reward functions from expert demonstrations. However, the IRL problem like any ill-posed inverse problem suffers the congenital defect that the policy may be optimal for many reward functions, and expert demonstrations may be optimal for man…
Bias correction improves language model training performance.
problem Stochastic update bias in preconditioned optimizers.
method Cross-fitted preconditioning and variance-corrected inversion.
result Reduces held-out pretraining loss by 0.15 nats.
New methods for parameter estimation in mechanistic models using data-consistent inversion.
problem Parameter estimation bias in Bayesian analysis for mechanistic models.
method Data-consistent inversion methods based on rejection sampling, MCMC, GANs, and constrained optimization.
result Improved parameter estimation without bias from uninformative priors.
We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the cardinality constrained likelihood problem to certifiable optimality. The approa…