Generative flow networks (GFlowNets) are amortized variational inference algorithms that treat sampling from a distribution over compositional objects as a sequential decision-making problem with a learnable action policy. Unlike other algorithms for hierarchical sampling that optimize a variational bound, GFlowNet algorithms can stably run off-policy, which can be advantageous for discovering modes of the target distribution. Despite this flexibility in the choice of behaviour policy, the optimal way of efficiently selecting trajectories for training has not yet been systematically explored. In this paper, we view the choice of trajectories for training as an active learning problem and approach it using Bayesian techniques inspired by methods for multi-armed bandits. The proposed algorithm, Thompson sampling GFlowNets (TS-GFN), maintains an approximate posterior distribution over policies and samples trajectories from this posterior for training. We show in two domains that TS-GFN yields improved exploration and thus faster convergence to the target distribution than the off-policy exploration strategies used in past work.

To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing these systems often exhibit nonlinearity so that render the resolution of the parameter inverse problem from the observed spatiotemporal data a challenging endeavor. Starting from the observed data obtained from such systems, we propose a novel framework that facilitates the investigation of parameter identification for multi-state systems governed by spatiotemporal varying parametric partial differential equations. Our framework consists of two integral components: a constrained self-adaptive physics-informed neural network, encompassing a sub-network, as our methodology for parameter identification, and a finite mixture model approach to detect regions of probable parameter variations. Through our scheme, we can precisely ascertain the unknown varying parameters of the complex multi-state system, thereby accomplishing the inversion of the varying parameters. Furthermore, we have showcased the efficacy of our framework on two numerical cases: the 1D Burgers' equation with time-varying parameters and the 2D wave equation with a space-varying parameter.

Regardless of the domain, forecasting the future behaviour of a running process instance is a question of interest for decision makers, especially when multiple instances interact. Fostered by the recent advances in machine learning research, several methods have been proposed to predict the next activity, outcome or remaining time of a process automatically. Still, building a model with high predictive power requires both - intrinsic knowledge of how to extract meaningful features from the event log data and a model that captures complex patterns in data. This work builds upon the recent progress in inter-case Predictive Process Monitoring (PPM) and comprehensively benchmarks the impact of inter-case features on prediction accuracy. Moreover, it includes quantum machine learning models, which are expected to provide an advantage over classical models with a scaling amount of feature dimensions. The evaluation on real-world training data from the BPI challenge shows that the inter-case features provide a significant boost by more than four percent in accuracy and quantum algorithms are indeed competitive in a handful of feature configurations. Yet, as quantum hardware is still in its early stages of development, this paper critically discusses these findings in the light of runtime, noise and the risk to overfit on the training data. Finally, the implementation of an open-source plugin demonstrates the technical feasibility to connect a state-of-the-art workflow engine such as Camunda to an IBM quantum computing cloud service.

The automation of key processes in metal cutting would substantially benefit many industries such as manufacturing and metal recycling. We present a vision-based control scheme for automated metal cutting with oxy-fuel torches, an established cutting medium in industry. The system consists of a robot equipped with a cutting torch and an eye-in-hand camera observing the scene behind a tinted visor. We develop a vision-based control algorithm to servo the torch's motion by visually observing its effects on the metal surface. As such, the vision system processes the metal surface's heat pool and computes its associated features, specifically pool convexity and intensity, which are then used for control. The operating conditions of the control problem are defined within which the stability is proven. In addition, metal cutting experiments are performed using a physical 1-DOF robot and oxy-fuel cutting equipment. Our results demonstrate the successful cutting of metal plates across three different plate thicknesses, relying purely on visual information without a priori knowledge of the thicknesses.

Abstract--Convex optimization is crucial in controlling legged robots, where stability and optimal control are vital. Many control problems can be formulated as convex optimization problems, with a convex cost function and constraints capturing system dynamics. Our review focuses on active balancing problems and presents a general framework for formulating them as second-order cone programming (SOCP) for robustness and efficiency with existing interior point algorithms. We then discuss some prior work around the Zero Moment Point stability criterion, Linear Quadratic Regulator Control, and then the feedback model predictive control (MPC) approach to improve prediction accuracy and reduce computational costs. Finally, these techniques are applied to stabilize the robot for jumping and landing tasks. Further research in convex optimization of legged robots can have a significant societal impact. These advancements have the potential to revolutionize industries and help humans in daily life. Control problems can be formulated as optimization problems We start with some literature and initial works on convex by defining an objective function that quantifies the optimization applications in legged robots, which lay the desired behavior of the system, and a set of constraints that foundation to the most widely used optimization methods, capture the physical limitations of the system and any other Model Predictive Control.

The design of machine learning systems often requires trading off different objectives, for example, prediction error and energy consumption for deep neural networks (DNNs). Typically, no single design performs well in all objectives; therefore, finding Pareto-optimal designs is of interest. The search for Pareto-optimal designs involves evaluating designs in an iterative process, and the measurements are used to evaluate an acquisition function that guides the search process. However, measuring different objectives incurs different costs. For example, the cost of measuring the prediction error of DNNs is orders of magnitude higher than that of measuring the energy consumption of a pre-trained DNN as it requires re-training the DNN. Current state-of-the-art methods do not consider this difference in objective evaluation cost, potentially incurring expensive evaluations of objective functions in the optimization process. In this paper, we develop a novel decoupled and cost-aware multi-objective optimization algorithm, which we call Flexible Multi-Objective Bayesian Optimization (FlexiBO) to address this issue. For evaluating each design, FlexiBO selects the objective with higher relative gain by weighting the improvement of the hypervolume of the Pareto region with the measurement cost of each objective. This strategy, therefore, balances the expense of collecting new information with the knowledge gained through objective evaluations, preventing FlexiBO from performing expensive measurements for little to no gain. We evaluate FlexiBO on seven state-of-the-art DNNs for image recognition, natural language processing (NLP), and speech-to-text translation. Our results indicate that, given the same total experimental budget, FlexiBO discovers designs with 4.8% to 12.4% lower hypervolume error than the best method in state-of-the-art multi-objective optimization.

Practical density functional theory (DFT) owes its success to the groundbreaking work of Kohn and Sham that introduced the exact calculation of the non-interacting kinetic energy of the electrons using an auxiliary mean-field system. However, the full power of DFT will not be unleashed until the exact relationship between the electron density and the non-interacting kinetic energy is found. Various attempts have been made to approximate this functional, similar to the exchange--correlation functional, with much less success due to the larger contribution of kinetic energy and its more non-local nature. In this work we propose a new and efficient regularization method to train density functionals based on deep neural networks, with particular interest in the kinetic-energy functional. The method is tested on (effectively) one-dimensional systems, including the hydrogen chain, non-interacting electrons, and atoms of the first two periods, with excellent results. For the atomic systems, the generalizability of the regularization method is demonstrated by training also an exchange--correlation functional, and the contrasting nature of the two functionals is discussed from a machine-learning perspective.

Despite its importance in both industrial and service robotics, mobile manipulation remains a significant challenge as it requires a seamless integration of end-effector trajectory generation with navigation skills as well as reasoning over long-horizons. Existing methods struggle to control the large configuration space, and to navigate dynamic and unknown environments. In previous work, we proposed to decompose mobile manipulation tasks into a simplified motion generator for the end-effector in task space and a trained reinforcement learning agent for the mobile base to account for kinematic feasibility of the motion. In this work, we introduce Neural Navigation for Mobile Manipulation (N$^2$M$^2$) which extends this decomposition to complex obstacle environments and enables it to tackle a broad range of tasks in real world settings. The resulting approach can perform unseen, long-horizon tasks in unexplored environments while instantly reacting to dynamic obstacles and environmental changes. At the same time, it provides a simple way to define new mobile manipulation tasks. We demonstrate the capabilities of our proposed approach in extensive simulation and real-world experiments on multiple kinematically diverse mobile manipulators. Code and videos are publicly available at http://mobile-rl.cs.uni-freiburg.de.

Dynamics models learned from visual observations have shown to be effective in various robotic manipulation tasks. One of the key questions for learning such dynamics models is what scene representation to use. Prior works typically assume representation at a fixed dimension or resolution, which may be inefficient for simple tasks and ineffective for more complicated tasks. In this work, we investigate how to learn dynamic and adaptive representations at different levels of abstraction to achieve the optimal trade-off between efficiency and effectiveness. Specifically, we construct dynamic-resolution particle representations of the environment and learn a unified dynamics model using graph neural networks (GNNs) that allows continuous selection of the abstraction level. During test time, the agent can adaptively determine the optimal resolution at each model-predictive control (MPC) step. We evaluate our method in object pile manipulation, a task we commonly encounter in cooking, agriculture, manufacturing, and pharmaceutical applications. Through comprehensive evaluations both in the simulation and the real world, we show that our method achieves significantly better performance than state-of-the-art fixed-resolution baselines at the gathering, sorting, and redistribution of granular object piles made with various instances like coffee beans, almonds, corn, etc.

Recently, Ye et al. (Mathematical Programming 2023) designed an algorithm for solving a specific class of bilevel programs with an emphasis on applications related to hyperparameter selection, utilizing the difference of convex algorithm based on the value function approach reformulation. The proposed algorithm is particularly powerful when the lower level problem is fully convex , such as a support vector machine model or a least absolute shrinkage and selection operator model. In this paper, to suit more applications related to machine learning and statistics, we substantially weaken the underlying assumption from lower level full convexity to weak convexity. Accordingly, we propose a new reformulation using Moreau envelope of the lower level problem and demonstrate that this reformulation is a difference of weakly convex program. Subsequently, we develop a sequentially convergent algorithm for solving this difference of weakly convex program. To evaluate the effectiveness of our approach, we conduct numerical experiments on the bilevel hyperparameter selection problem from elastic net, sparse group lasso, and RBF kernel support vector machine models.