Learning representations for solutions of constrained optimization problems (COPs) with unknown cost functions is challenging, as models like (Variational) Autoencoders struggle to enforce constraints when decoding structured outputs. We propose an Inverse Optimization Latent Variable Model (IO-LVM) that learns a latent space of COP cost functions from observed solutions and reconstructs feasible outputs by solving a COP with a solver in the loop. Our approach leverages estimated gradients of a Fenchel-Young loss through a non-differentiable deterministic solver to shape the latent space. Unlike standard Inverse Optimization or Inverse Reinforcement Learning methods, which typically recover a single or context-specific cost function, IO-LVM captures a distribution over cost functions, enabling the identification of diverse solution behaviors arising from different agents or conditions not available during the training process. We validate our method on real-world datasets of ship and taxi routes, as well as paths in synthetic graphs, demonstrating its ability to reconstruct paths and cycles, predict their distributions, and yield interpretable latent representations.

Abstract Machine learning predictive models rely on data to make predictions for new input data. However, accurate predictions are not always the end goal; practitioners often aim to make informed decisions through optimization problems (OPs) based on these predictions. While the idea that better predictions lead to better decisions was widely accepted, the latest literature highlights that even small inaccuracies in predictions can lead to poor decisions depending on the structure of the OP. Therefore, recent research has been focused on end-to-end learning approaches that directly improve decision quality without considering prediction accuracy when solving data-driven OPs. Some of these end-to-end learning approaches are mainly called “predict-and-optimize” (PaO), and they aim to learn a predictor based on the quality of the downstream task decisions by incorporating mathematical programming into the learning process. This literature review discusses the variations of and approaches to PaO problems by proposing a unified notation and a taxonomy for them. Throughout the paper, we aim to provide a valuable roadmap for researchers and practitioners in the field, guiding them to choose data-driven methods to solve their decision problems effectively.

Estimating treatment effects from observational data is paramount in healthcare, education, and economics, but current deep disentanglement-based methods to address selection bias are insufficiently handling irrelevant variables. We demonstrate in experiments that this leads to prediction errors. We disentangle pre-treatment variables with a deep embedding method and explicitly identify and represent irrelevant variables, additionally to instrumental, confounding and adjustment latent factors. To this end, we introduce a reconstruction objective and create an embedding space for irrelevant variables using an attached autoencoder. Instead of relying on serendipitous suppression of irrelevant variables as in previous deep disentanglement approaches, we explicitly force irrelevant variables into this embedding space and employ orthogonalization to prevent irrelevant information from leaking into the latent space representations of the other factors. Our experiments with synthetic and real-world benchmark datasets show that we can better identify irrelevant variables and more precisely predict treatment effects than previous methods, while prediction quality degrades less when additional irrelevant variables are introduced.

Reinforcement learning (RL) for complex tasks remains a challenge, primarily due to the difficulties of engineering scalar reward functions and the inherent inefficiency of training models from scratch. Instead, it would be better to specify complex tasks in terms of elementary subtasks and to reuse subtask solutions whenever possible. In this work, we address continuous space lexicographic multi-objective RL problems, consisting of prioritized subtasks, which are notoriously difficult to solve. We show that these can be scalarized with a subtask transformation and then solved incrementally using value decomposition. Exploiting this insight, we propose prioritized soft Q-decomposition (PSQD), a novel algorithm for learning and adapting subtask solutions under lexicographic priorities in continuous state-action spaces. PSQD offers the ability to reuse previously learned subtask solutions in a zero-shot composition, followed by an adaptation step. Its ability to use retained subtask training data for offline learning eliminates the need for new environment interaction during adaptation. We demonstrate the efficacy of our approach by presenting successful learning, reuse, and adaptation results for both low- and high-dimensional simulated robot control tasks, as well as offline learning results. In contrast to baseline approaches, PSQD does not trade off between conflicting subtasks or priority constraints and satisfies subtask priorities during learning. PSQD provides an intuitive framework for tackling complex RL problems, offering insights into the inner workings of the subtask composition.

Long-term human motion prediction (LHMP) is essential for safely operating autonomous robots and vehicles in populated environments. It is fundamental for various applications, including motion planning, tracking, human-robot interaction and safety monitoring. However, accurate prediction of human trajectories is challenging due to complex factors, including, for example, social norms and environmental conditions. The influence of such factors can be captured through Maps of Dynamics (MoDs), which encode spatial motion patterns learned from (possibly scattered and partial) past observations of motion in the environment and which can be used for data-efficient, interpretable motion prediction (MoD-LHMP). To address the limitations of prior work, especially regarding accuracy and sensitivity to anomalies in long-term prediction, we propose the Laminar Component Enhanced LHMP approach (LaCE-LHMP). Our approach is inspired by data-driven airflow modelling, which estimates laminar and turbulent flow components and uses predominantly the laminar components to make flow predictions. Based on the hypothesis that human trajectory patterns also manifest laminar flow (that represents predictable motion) and turbulent flow components (that reflect more unpredictable and arbitrary motion), LaCE-LHMP extracts the laminar patterns in human dynamics and uses them for human motion prediction. We demonstrate the superior prediction performance of LaCE-LHMP through benchmark comparisons with state-of-the-art LHMP methods, offering an unconventional perspective and a more intuitive understanding of human movement patterns.

Learning latent costs of transitions on graphs from trajectories demonstrations under various contextual features is challenging but useful for path planning. Yet, existing methods either oversimplify cost assumptions or scale poorly with the number of observed trajectories. This paper introduces DataSP, a differentiable all-to-all shortest path algorithm to facilitate learning latent costs from trajectories. It allows to learn from a large number of trajectories in each learning step without additional computation. Complex latent cost functions from contextual features can be represented in the algorithm through a neural network approximation. We further propose a method to sample paths from DataSP in order to reconstruct/mimic observed paths’ distributions. We prove that the inferred distribution follows the maximum entropy principle. We show that DataSP outperforms state-of-the-art differentiable combinatorial solver and classical machine learning approaches in predicting paths on graphs.

There is an increasing need to derive semantics from real-world observations to facilitate natural information sharing between machine and human. Conceptual spaces theory is a possible approach and has been proposed as mid-level representation between symbolic and sub-symbolic representations, whereby concepts are represented in a geometrical space that is characterised by a number of quality dimensions. Currently, much of the work has demonstrated how conceptual spaces are created in a knowledge-driven manner, relying on prior knowledge to form concepts and identify quality dimensions. This paper presents a method to create semantic representations using data-driven conceptual spaces which are then used to derive linguistic descriptions of numerical data. Our contribution is a principled approach to automatically construct a conceptual space from a set of known observations wherein the quality dimensions and domains are not known a priori. This novelty of the approach is the ability to select and group semantic features to discriminate between concepts in a data-driven manner while preserving the semantic interpretation that is needed to infer linguistic descriptions for interaction with humans. Two data sets representing leaf images and time series signals are used to evaluate the method. An empirical evaluation for each case study assesses how well linguistic descriptions generated from the conceptual spaces identify unknown observations. Furthermore, comparisons are made with descriptions derived on alternative approaches for generating semantic models.

Sensor networks have limited capabilities to model complex phenomena occuring between sensing nodes. Mobile robots can be used to close this gap and learn local interpolation models. In this paper, we utilize Echo State Networks in order to learn the calibration and interpolation model between sensor nodes using measurements collected by a mobile robot. The use of Echo State Networks allows to deal with temporal dependencies implicitly, while the spatial mapping with a Gaussian Process estimator exploits the fact that Echo State Networks learn linear combinations of complex temporal dynamics. The resulting Echo State Map elegantly combines spatial and temporal cues into a single representation. We showcase the method in the exposure modeling task of building dust distribution maps for foundries, a challenge which is of great interest to occupational health researchers. Results from simulated data and real world experiments highlight the potential of Echo State Maps. While we focus on particulate matter measurements, the method can be applied for any other environmental variables like temperature or gas concentration.

Creating an accurate model of gas emissions is an important task in monitoring and surveillance applications. A promising solution for a range of real-world applications are gas-sensitive mobile robots with spectroscopy-based remote sensors that are used to create a tomographic reconstruction of the gas distribution. The quality of these reconstructions depends crucially on the chosen sensing geometry. In this paper we address the problem of sensor planning by investigating sensing geometries that minimize reconstruction errors, and then formulate an optimization algorithm that chooses sensing configurations accordingly. The algorithm decouples sensor planning for single high concentration regions (hotspots) and subsequently fuses the individual solutions to a global solution consisting of sensing poses and the shortest path between them. The proposed algorithm compares favorably to a template matching technique in a simple simulation and in a real-world experiment. In the latter, we also compare the proposed sensor planning strategy to the sensing strategy of a human expert and find indications that the quality of the reconstructed map is higher with the proposed algorithm.

In industrial environments, such as metallurgic facilities, human operators are exposed to harsh conditions where ambient air is often polluted with quartz, dust, lead debris and toxic fumes. Constant exposure to respirable particles can cause irreversible health damages and thus it is of high interest for occupational health experts to monitor the air quality on a regular basis. However, current monitoring procedures are carried out sparsely, with data collected in single day campaigns limited to few measurement locations. In this paper we explore the use and present first experimental results of a novel heterogeneous approach that uses a mobile robot and a network of low cost sensing nodes. The proposed system aims to address the spatial and temporal limitations of current monitoring techniques. The mobile robot, along with standard localization and mapping algorithms, allows to produce short term, spatially dense representations of the environment where dust, gas, ambient temperature and airflow information can be modelled. The sensing nodes on the other hand, can collect temporally dense (and usually spatially sparse) information during long periods of time, allowing in this way to register for example, daily variations in the pollution levels. Using data collected with the proposed system in an steel foundry, we show that a heterogeneous approach provides dense spatio-temporal information that can be used to improve the working conditions in industrial facilities.

The problem of gas detection is relevant to many real-world applications, such as leak detection in industrial settings and surveillance. In this paper we address the problem of gas detection in large areas with a mobile robotic platform equipped with a remote gas sensor. We propose a novel method based on convex relaxation for quickly finding an exploration plan that guarantees a complete coverage of the environment. Our method proves to be highly efficient in terms of computational requirements and to provide nearly-optimal solutions. We validate our approach both in simulation and in real environments, thus demonstrating its applicability to real-world problems.

In this paper we present an inspection robot to produce gas distribution maps and localize gas sources in large outdoor environments. The robot is equipped with a 3D laser range finder and a remote gas sensor that returns integral concentration measurements. We apply principles of tomography to create a spatial gas distribution model from integral gas concentration measurements. The gas distribution algorithm is framed as a convex optimization problem and it models the mean distribution and the fluctuations of gases. This is important since gas dispersion is not an static phenomenon and furthermore, areas of high fluctuation can be correlated with the location of an emitting source. We use a compact surface representation created from the measurements of the 3D laser range finder with a state of the art mapping algorithm to get a very accurate localization and estimation of the path of the laser beams. In addition, a conic model for the beam of the remote gas sensor is introduced. We observe a substantial improvement in the gas source localization capabilities over previous state-of-the-art in our evaluation carried out in an open field environment.

In this paper, we propose an approach for robotic manipulation systems to autonomously reason about their environments under incomplete information. The target application is to automate the task of unloading the content of shipping containers. Our goal is to capture possible support relations between objects in partially known static configurations. We employ support vector machines (SVM) to estimate the probability of a support relation between pairs of detected objects using features extracted from their geometrical properties and 3D sampled points of the scene. The set of probabilistic support relations is then used for reasoning about optimally selecting an object to be unloaded first. The proposed approach has been extensively tested and verified on data sets generated in simulation and from real world configurations.

Correctly identifying people who are interested in an interaction with a mobile robot is an essential task for a smart Human-Robot Interaction. In this paper an approach is presented for selecting suitable trajectory features in a task specific manner from a huge amount of different forms of possible representations. Different sub-sampling techniques are proposed to generate trajectory sequences from which features are extracted. The trajectory data was generated in real world experiments that include extensive user interviews to acquire information about user behaviors and intentions. Using those feature vectors in a classification method enables the robot to estimate the user's interaction interest. For generating low-dimensional feature vectors, a common method, the Principle Component Analysis, is applied. The selection and combination of useful features out of a set of possible features is carried out by an information theoretic approach based on the Mutual Information and Joint Mutual Information with respect to the user's interaction interest. The introduced procedure is evaluated with neural classifiers, which are trained with the extracted features of the trajectories and the user behavior gained by observation as well as user interviewing. The results achieved indicate that an estimation of the user's interaction interest using trajectory information is feasible.