Achieving highly accurate dynamic or simulator models that are close to the real robot can facilitate model-based controls (e.g., model predictive control or linear-quadradic regulators), model-based trajectory planning (e.g., trajectory optimization), and decrease the amount of learning time necessary for reinforcement learning methods. Thus, the objective of this work is to learn the residual errors between a dynamic and/or simulator model and the real robot. This is achieved using a neural network, where the parameters of a neural network are updated through an Unscented Kalman Filter (UKF) formulation. Using this method, we model these residual errors with only small amounts of data -- a necessity as we improve the simulator/dynamic model by learning directly from real-world operation. We demonstrate our method on robotic hardware (e.g., manipulator arm, and a wheeled robot), and show that with the learned residual errors, we can further close the reality gap between dynamic models, simulations, and actual hardware.

This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach is the requirement for manual hyperparameter tuning, making it impractical in the absence of validation data or prior knowledge of the solution. Our investigations of the loss landscapes and backpropagated gradients in the presence of physics reveal that existing methods produce non-convex loss landscapes that are hard to navigate. Our findings demonstrate that high-order PDEs contaminate backpropagated gradients and hinder convergence. To address these challenges, we introduce a novel method that bypasses the calculation of high-order derivative operators and mitigates the contamination of backpropagated gradients. Consequently, we reduce the dimension of the search space and make learning PDEs with non-smooth solutions feasible. Our method also provides a mechanism to focus on complex regions of the domain. Besides, we present a dual unconstrained formulation based on Lagrange multiplier method to enforce equality constraints on the model's prediction, with adaptive and independent learning rates inspired by adaptive subgradient methods. We apply our approach to solve various linear and non-linear PDEs.

Allocation and planning with a collection of tasks and a group of agents is an important problem in multiagent systems. One commonly faced bottleneck is scalability, as in general the multiagent model increases exponentially in size with the number of agents. We consider the combination of random task assignment and multiagent planning under multiple-objective constraints, and show that this problem can be decentralised to individual agent-task models. We present an algorithm of point-oriented Pareto computation, which checks whether a point corresponding to given cost and probability thresholds for our formal problem is feasible or not. If the given point is infeasible, our algorithm finds a Pareto-optimal point which is closest to the given point. We provide the first multi-objective model checking framework that simultaneously uses GPU and multi-core acceleration. Our framework manages CPU and GPU devices as a load balancing problem for parallel computation. Our experiments demonstrate that parallelisation achieves significant run time speed-up over sequential computation.

System designers frequently use the idea of providing incentives to stakeholders as a powerful means of steering the stakeholders for their own benefit. Operations management includes many such examples, such as offering performance-based bonuses to ride-hailing drivers, providing monetary incentives to patients for medical adherence, quality-contingent bonus payments for workers in crowdsourcing platforms, and vertical collaboration between shippers and carriers in transportation planning. In many real-world settings, the problem of designing efficient incentives can be posed as a repeated principal-agent problem where a principal (i.e., system designer) designs sequential incentive policies to motivate an agent (i.e., stakeholder) to convey certain behaviors that eventually serve the goal of maximizing the principal's cumulative net reward. Typically, there is an element of information asymmetry in these systems which arises between the principal and the agent in the form of either adverse selection (i.e., hidden information) or moral hazard (i.e., hidden actions) (Bolton and Dewatripont 2004). For instance, in the context of employment incentives designed by an employer, the hidden information in an adverse selection setting could be the level of productivity of an employee whereas a hidden action in the moral hazard setting could be the total effort level of the employee. More generally, the hidden information in the adverse selection setting can be seen as an unknown "type" or "preferences" of the agent that directly affects the action chosen by the agent, which in turn determines both the agent's utility and the principal's reward. These situations require specification of the agent's private information and the distributional-knowledge that the principal has concerning that information. Existing literature on repeated principal-agent models mostly studies the moral hazard setting, with a more recent focus on the problem of estimating agent's unknown model parameters under hidden actions (e.g., Ho et al. 2016, Kaynar and Siddiq 2022). On the other hand, the adverse selection setting is mostly studied either for single-period static games (Navabi and Nayyar 2018, Chade and Swinkels 2019, Gottlieb and Moreira 2022) or else for the repeated dynamic games where restrictive assumptions are made on, for example, dimension of the agent's action space, utility Dogan et.

An abstraction can be used to relate two structural causal models representing the same system at different levels of resolution. Learning abstractions which guarantee consistency with respect to interventional distributions would allow one to jointly reason about evidence across multiple levels of granularity while respecting the underlying cause-effect relationships. In this paper, we introduce a first framework for causal abstraction learning between SCMs based on the formalization of abstraction recently proposed by Rischel (2020). Based on that, we propose a differentiable programming solution that jointly solves a number of combinatorial sub-problems, and we study its performance and benefits against independent and sequential approaches on synthetic settings and on a challenging real-world problem related to electric vehicle battery manufacturing.

Graph Representation Learning (GRL) methods opened new avenues for addressing complex, real-world problems represented by graphs. However, many graphs used in these applications comprise millions of nodes and billions of edges and are beyond the capabilities of current methods and software implementations. We present GRAPE, a software resource for graph processing and embedding that can scale with big graphs by using specialized and smart data structures, algorithms, and a fast parallel implementation of random walk-based methods. Compared with state-of-the-art software resources, GRAPE shows an improvement of orders of magnitude in empirical space and time complexity, as well as a competitive edge and node label prediction performance. GRAPE comprises about 1.7 million well-documented lines of Python and Rust code and provides 69 node embedding methods, 25 inference models, a collection of efficient graph processing utilities and over 80,000 graphs from the literature and other sources. Standardized interfaces allow seamless integration of third-party libraries, while ready-to-use and modular pipelines permit an easy-to-use evaluation of GRL methods, therefore also positioning GRAPE as a software resource to perform a fair comparison between methods and libraries for graph processing and embedding.

Integrating renewable energy sources into the power grid is becoming increasingly important as the world moves towards a more sustainable energy future in line with SDG 7. However, the intermittent nature of renewable energy sources can make it challenging to manage the power grid and ensure a stable supply of electricity, which is crucial for achieving SDG 9. In this paper, we propose a deep learning-based approach for predicting energy demand in a smart power grid, which can improve the integration of renewable energy sources by providing accurate predictions of energy demand. Our approach aligns with SDG 13 on climate action, enabling more efficient management of renewable energy resources. We use long short-term memory networks, well-suited for time series data, to capture complex patterns and dependencies in energy demand data. The proposed approach is evaluated using four historical short-term energy demand data datasets from different energy distribution companies, including American Electric Power, Commonwealth Edison, Dayton Power and Light, and Pennsylvania-New Jersey-Maryland Interconnection. The proposed model is also compared with three other state-of-the-art forecasting algorithms: Facebook Prophet, Support Vector Regression, and Random Forest Regression. The experimental results show that the proposed REDf model can accurately predict energy demand with a mean absolute error of 1.4%, indicating its potential to enhance the stability and efficiency of the power grid and contribute to achieving SDGs 7, 9, and 13. The proposed model also has the potential to manage the integration of renewable energy sources in an effective manner.

The safety-critical control of robotic systems often must account for multiple, potentially conflicting, safety constraints. This paper proposes novel relaxation techniques to address safety-critical control problems in the presence of conflicting safety conditions. In particular, Control Barrier Function (CBFs) provide a means to encode safety as constraints in a Quadratic Program (QP), wherein multiple safety conditions yield multiple constraints. However, the QP problem becomes infeasible when the safety conditions cannot be simultaneously satisfied. To resolve this potential infeasibility, we introduce a hierarchy between the safety conditions and employ an additional variable to relax the less important safety conditions (Relaxed-CBF-QP), and formulate a cascaded structure to achieve smaller violations of lower-priority safety conditions (Hierarchical-CBF-QP). The proposed approach, therefore, ensures the existence of at least one solution to the QP problem with the CBFs while dynamically balancing enforcement of additional safety constraints. Importantly, this paper evaluates the impact of different weighting factors in the Hierarchical-CBF-QP and, due to the sensitivity of these weightings in the observed behavior, proposes a method to determine the weighting factors via a sampling-based technique. The validity of the proposed approach is demonstrated through simulations and experiments on a quadrupedal robot navigating to a goal through regions with different levels of danger.

The imputation of missing values represents a significant obstacle for many real-world data analysis pipelines. Here, we focus on time series data and put forward SSSD, an imputation model that relies on two emerging technologies, (conditional) diffusion models as state-of-the-art generative models and structured state space models as internal model architecture, which are particularly suited to capture long-term dependencies in time series data. We demonstrate that SSSD matches or even exceeds state-of-the-art probabilistic imputation and forecasting performance on a broad range of data sets and different missingness scenarios, including the challenging blackout-missing scenarios, where prior approaches failed to provide meaningful results.

Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented success in learning solution operators of partial differential equations. Due to their close proximity to fully connected architectures, these models mainly suffer from high memory usage and are generally limited to shallow deep learning models. In this paper, we propose U-shaped Neural Operator (U-NO), a U-shaped memory enhanced architecture that allows for deeper neural operators. U-NOs exploit the problem structures in function predictions and demonstrate fast training, data efficiency, and robustness with respect to hyperparameters choices. We study the performance of U-NO on PDE benchmarks, namely, Darcy's flow law and the Navier-Stokes equations. We show that U-NO results in an average of 26% and 44% prediction improvement on Darcy's flow and turbulent Navier-Stokes equations, respectively, over the state of art. On Navier-Stokes 3D spatiotemporal operator learning task, we show U-NO provides 37% improvement over the state of the art methods.