Learning from samples: inverse problems over measures
INRIA (PreMeDICaL & HeKA)（法国国家信息与自动化研究所（PreMeDICaL & HeKA））；CNRS and ENS, PSL Université（法国国家科学研究中心与巴黎高等师范学院，PSL大学）；Mathematics Institute, University of Warwick（华威大学数学研究所）
We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle. Such problems arise in learning costs, energies, and dynamics from distributional data, but the associated forward solution map is typically nonlinear and implicit. We show that its optimality gap nevertheless yields convex empirical objectives for finite-dimensional potential classes, and we introduce sharpened Fenchel--Young losses that add a data-dependent discrepancy inside the forward problem. This keeps the estimator calibrated while improving the local geometry of the loss. Our main stability theorem separates the inverse error analysis into measurement error, forward perturbation, and empirical curvature. We instantiate this principle for inverse entropic unbalanced optimal transport and for inverse Jordan--Kinderlehrer--Otto (JKO) learning from independent snapshot samples, obtaining high-probability parameter recovery bounds. JKO schemes discretize Wasserstein gradient flows through a sequence of variational problems over measures, making them a natural language for population dynamics observed through snapshots. In this JKO case, the sharpened objective reduces to an unbalanced transport problem, which also clarifies the connection between variational gap losses and quadratic iJKO\(^\star\) surrogates. Numerical experiments illustrate the conditioning effect of sharpening and its benefits for sparse inverse-gradient-flow recovery.
On the Sample Complexity of Learning for Blind Inverse Problems
MaLGa - DIBRIS - Università degli studi di Genova（MaLGa - DIBRIS - 旧金山大学）；MaLGa - DIMA - Università degli studi di Genova（MaLGa - DIMA - 旧金山大学）；Italian Institute of Technology（意大利理工学院）
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 formulation of the IRL problem motivated by the geometric analysis is then proposed with the basic objective of the inverse reinforcement problem in mind: to find a reward function that generates a specified optimal policy. The paper further analyzes the proposed formulation of inverse …
Inverse reinforcement learning (IRL) is the task of finding a reward function that generates a desired optimal policy for a given Markov Decision Process (MDP). This paper develops an information-theoretic lower bound for the sample complexity of the finite state, finite action IRL problem. A geometric construction of $β$-strict separable IRL problems using spherical codes is considered. Properties of the ensemble size as well as the Kullback-Leibler divergence between the generated trajectories are derived. The resulting ensemble is then used along with Fano's inequality to derive a sample co…
Northwestern University（西北大学）；Allstate Insurance Company（好事达保险公司）；Department of Industrial Engineering and Management Sciences（工业工程与管理科学系）；Data, Discovery and Decision Science（数据、发现与决策科学（部门））
Most recent machine learning research focuses on developing new classifiers for the sake of improving classification accuracy. With many well-performing state-of-the-art classifiers available, there is a growing need for understanding interpretability of a classifier necessitated by practical purposes such as to find the best diet recommendation for a diabetes patient. Inverse classification is a post modeling process to find changes in input features of samples to alter the initially predicted class. It is useful in many business applications to determine how to adjust a sample input data suc…
We present an adversarial active exploration for inverse dynamics model learning, a simple yet effective learning scheme that incentivizes exploration in an environment without any human intervention. Our framework consists of a deep reinforcement learning (DRL) agent and an inverse dynamics model contesting with each other. The former collects training samples for the latter, with an objective to maximize the error of the latter. The latter is trained with samples collected by the former, and generates rewards for the former when it fails to predict the actual action taken by the former. In s…
In this paper, we present an algorithm to efficiently learn socially-compliant navigation policies from observations of human trajectories. As mobile robots come to inhabit and traffic social spaces, they must account for social cues and behave in a socially compliant manner. We focus on learning such cues from examples. We describe an inverse reinforcement learning based algorithm which learns from human trajectory observations without knowing their specific actions. We increase the sample-efficiency of our approach over alternative methods by leveraging the notion of a replay buffer (found i…
In many real-world problems, complex dependencies are present both among samples and among features. The Kronecker sum or the Cartesian product of two graphs, each modeling dependencies across features and across samples, has been used as an inverse covariance matrix for a matrix-variate Gaussian distribution, as an alternative to a Kronecker-product inverse covariance matrix, due to its more intuitive sparse structure. However, the existing methods for sparse Kronecker-sum inverse covariance estimation are limited in that they do not scale to more than a few hundred features and samples and t…
Louisiana State University at Baton Rouge（巴吞鲁日路易斯安那州立大学）；Southern University and A&M College（南方大学及农工学院）
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level, it suffices to continue sampling until the sample sum is no less than a certain bound and then take the average of samples as an estimate for the mean of the bounded random variable. We have developed an explicit formula and a bisection search method for the determination of such bound of sample sum, without any knowledge of the bounded variable. Moreover, …
With the recent success of deep neural networks in computer vision, it is important to understand the internal working of these networks. What does a given neuron represent? The concepts captured by a neuron may be hard to understand or express in simple terms. The approach we propose in this paper is to characterize the region of input space that excites a given neuron to a certain level; we call this the inverse set. This inverse set is a complicated high dimensional object that we explore by an optimization-based sampling approach. Inspection of samples of this set by a human can reveal reg…
University of Basel（巴塞尔大学）；Sharif University of Technology（谢里夫理工大学）；University of Zagreb（萨格勒布大学）
Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and noise can make this single estimate inaccurate or misleading. While deep networks such as conditional normalizing flows can be used to sample posteriors in inverse problems, they often yield low-quality samples and uncertainty estimates. In this paper, we propose U-Flow, a Bayesian U-Net based on conditional normalizing flows, which generates high-quality po…
University of Southern California（南加州大学）；Stanford University（斯坦福大学）
In this work, we train conditional Wasserstein generative adversarial networks to effectively sample from the posterior of physics-based Bayesian inference problems. The generator is constructed using a U-Net architecture, with the latent information injected using conditional instance normalization. The former facilitates a multiscale inverse map, while the latter enables the decoupling of the latent space dimension from the dimension of the measurement, and introduces stochasticity at all scales of the U-Net. We solve PDE-based inverse problems to demonstrate the performance of our approach …
Tokyo Institute of Technology（东京工业大学）；Mitsubishi Electric Corporation（三菱电机株式会社）
Inverse Reinforcement Learning (IRL) is attractive in scenarios where reward engineering can be tedious. However, prior IRL algorithms use on-policy transitions, which require intensive sampling from the current policy for stable and optimal performance. This limits IRL applications in the real world, where environment interactions can become highly expensive. To tackle this problem, we present Off-Policy Inverse Reinforcement Learning (OPIRL), which (1) adopts off-policy data distribution instead of on-policy and enables significant reduction of the number of interactions with the environment…
INESC-ID/Instituto Superior Técnico（INESC-ID/高等技术学院）；INRIA Bordeaux Sud-Ouest（法国国立信息与自动化研究院波尔多西南分院）
This paper addresses the problem of learning a task from demonstration. We adopt the framework of inverse reinforcement learning, where tasks are represented in the form of a reward function. Our contribution is a novel active learning algorithm that enables the learning agent to query the expert for more informative demonstrations, thus leading to more sample-efficient learning. For this novel algorithm (Generalized Binary Search for Inverse Reinforcement Learning, or GBS-IRL), we provide a theoretical bound on sample complexity and illustrate its applicability on several different tasks. To …
DICE: Discrete inverse continuity equation for learning population dynamics
Courant Institute of Mathematical Sciences, New York University（纽约大学Courant数学科学研究所）；Computing and Mathematical Sciences, California Institute of Technology（加州理工学院计算与数学科学学院）
Beyond Accuracy: Evaluating Posterior Fidelity of Diffusion Inverse Solvers
Department of Statistics, University of Michigan（密歇根大学统计学系）；Department of EECS, University of Michigan（密歇根大学电子工程与计算机科学系）；Department of Statistics, Rutgers University（罗格斯大学统计学系）
SPLASH! Sample-efficient Preference-based inverse reinforcement learning for Long-horizon Adversarial tasks from Suboptimal Hierarchical demonstrations
Boston University（波士顿大学）；MIT Lincoln Laboratory（麻省理工学院林肯实验室）；MIT Pavlab（麻省理工学院 Pavlab 实验室）；Woods Hole Oceanographic Institution（伍兹霍尔海洋研究所）；University of Maryland, College Park（马里兰大学学院公园分校）
Mila, Quebec AI Institute（米拉-魁北克人工智能研究所）；McGill University（麦吉尔大学）
Multi-agent adversarial inverse reinforcement learning (MA-AIRL) is a recent approach that applies single-agent AIRL to multi-agent problems where we seek to recover both policies for our agents and reward functions that promote expert-like behavior. While MA-AIRL has promising results on cooperative and competitive tasks, it is sample-inefficient and has only been validated empirically for small numbers of agents -- its ability to scale to many agents remains an open question. We propose a multi-agent inverse RL algorithm that is more sample-efficient and scalable than previous works. Specifi…
Henan University（河南大学）；University of Florida（佛罗里达大学）
Sparse representation based classification (SRC) methods have achieved remarkable results. SRC, however, still suffer from requiring enough training samples, insufficient use of test samples and instability of representation. In this paper, a stable inverse projection representation based classification (IPRC) is presented to tackle these problems by effectively using test samples. An IPR is firstly proposed and its feasibility and stability are analyzed. A classification criterion named category contribution rate is constructed to match the IPR and complete classification. Moreover, a statist…
