Nonlinear receding horizon model predictive control is a powerful approach to controlling nonlinear dynamical systems. However, typical approaches that use the Jacobian, adjoint, and forward-backward passes may lose fidelity and efficacy for highly nonlinear problems. Here, we develop an Ensemble Model Predictive Control (EMPC) approach wherein the forward model remains fully nonlinear, and an ensemble-represented Gaussian process performs the backward calculations to determine optimal gains for the initial time. EMPC admits black box, possible non-differentiable models, simulations are executable in parallel over long horizons, and control is uncertainty quantifying and applicable to stochastic settings. We construct the EMPC for terminal control and regulation problems and apply it to the control of a quadrotor in a simulated, identical-twin study. Results suggest that the easily implemented approach is promising and amenable to controlling autonomous robotic systems with added state/parameter estimation and parallel computing.
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Objective: Finding events of interest is a common task in biomedical signal processing. The detection of epileptic seizures and signal artefacts are two key examples. Epoch-based classification is the typical machine learning framework to detect such signal events because of the straightforward application of classical machine learning techniques. Usually, post-processing is required to achieve good performance and enforce temporal dependencies. Designing the right post-processing scheme to convert these classification outputs into events is a tedious, and labor-intensive element of this framework. Methods: We propose an event-based modeling framework that directly works with events as learning targets, stepping away from ad-hoc post-processing schemes to turn model outputs into events. We illustrate the practical power of this framework on simulated data and real-world data, comparing it to epoch-based modeling approaches. Results: We show that event-based modeling (without post-processing) performs on par with or better than epoch-based modeling with extensive post-processing. Conclusion: These results show the power of treating events as direct learning targets, instead of using ad-hoc post-processing to obtain them, severely reducing design effort. Significance: The event-based modeling framework can easily be applied to other event detection problems in signal processing, removing the need for intensive task-specific post-processing.
Quantiles of a natural phenomena can provide scientists with an important understanding of different spreads of concentrations. When there are several available robots, it may be advantageous to pool resources in a collaborative way to improve performance. A multirobot team can be difficult to practically bring together and coordinate. To this end, we present a study across several axes of the impact of using multiple robots to estimate quantiles of a distribution of interest using an informative path planning formulation. We measure quantile estimation accuracy with increasing team size to understand what benefits result from a multirobot approach in a drone exploration task of analyzing the algae concentration in lakes. We additionally perform an analysis on several parameters, including the spread of robot initial positions, the planning budget, and inter-robot communication, and find that while using more robots generally results in lower estimation error, this benefit is achieved under certain conditions. We present our findings in the context of real field robotic applications and discuss the implications of the results and interesting directions for future work.
We are motivated by quantile estimation of algae concentration in lakes and how decentralized multirobot teams can effectively tackle this problem. We find that multirobot teams improve performance in this task over single robots, and communication-enabled teams further over communication-deprived teams; however, real robots are resource-constrained, and communication networks cannot support arbitrary message loads, making naive, constant information-sharing but also complex modeling and decision-making infeasible. With this in mind, we propose online, locally computable metrics for determining the utility of transmitting a given message to the other team members and a decision-theoretic approach that chooses to transmit only the most useful messages, using a decentralized and independent framework for maintaining beliefs of other teammates. We validate our approach in simulation on a real-world aquatic dataset, and we show that restricting communication via a utility estimation method based on the expected impact of a message on future teammate behavior results in a 42% decrease in network load while simultaneously decreasing quantile estimation error by 1.84%.
Multiobjective simulation optimization (MOSO) problems are optimization problems with multiple conflicting objectives, where evaluation of at least one of the objectives depends on a black-box numerical code or real-world experiment, which we refer to as a simulation. This paper describes the design goals driving the development of the parallel MOSO library ParMOO. We derive these goals from the research trends and real-world requirements that arise when designing and deploying solvers for generic MOSO problems. Our specific design goals were to provide a customizable MOSO framework that allows for exploitation of simulation-based problem structures, ease of deployment in scientific workflows, maintainability, and flexibility in our support for many problem types. We explain how we have achieved these goals in the ParMOO library and provide two examples demonstrating how customized ParMOO solvers can be quickly built and deployed in real-world MOSO problems.
The demand of computational resources for the modeling process increases as the scale of the datasets does, since traditional approaches for regression involve inverting huge data matrices. The main problem relies on the large data size, and so a standard approach is subsampling that aims at obtaining the most informative portion of the big data. In the current paper, we explore an existing approach based on leverage scores, proposed for subdata selection in linear model discrimination. Our objective is to propose the aforementioned approach for selecting the most informative data points to estimate unknown parameters in both the first-order linear model and a model with interactions. We conclude that the approach based on leverage scores improves existing approaches, providing simulation experiments as well as a real data application.
The goal of this work is to study waves interacting with partially immersed objects allowed to move freely in the vertical direction, and in a regime in which the propagation of the waves is described by the one dimensional Boussinesq-Abbott system. The problem can be reduced to a transmission problem for this Boussinesq system, in which the transmission conditions between the components of the domain at the left and at the right of the object are determined through the resolution of coupled forced ODEs in time satisfied by the vertical displacement of the object and the average discharge in the portion of the fluid located under the object. We propose a new extended formulation in which these ODEs are complemented by two other forced ODEs satisfied by the trace of the surface elevation at the contact points. The interest of this new extended formulation is that the forcing terms are easy to compute numerically and that the surface elevation at the contact points is furnished for free. Based on this formulation, we propose a second order scheme that involves a generalization of the MacCormack scheme with nonlocal flux and a source term, which is coupled to a second order Heun scheme for the ODEs. In order to validate this scheme, several explicit solutions for this wave-structure interaction problem are derived and can serve as benchmark for future codes. As a byproduct, our method provides a second order scheme for the generation of waves at the entrance of the numerical domain for the Boussinesq-Abbott system.
Model evolution and constant availability of data are two common phenomena in large-scale real-world machine learning applications, e.g. ads and recommendation systems. To adapt, the real-world system typically retrain with all available data and online learn with recently available data to update the models periodically with the goal of better serving performance. In this paper, we propose a novel framework, named Confidence Ranking, which designs the optimization objective as a ranking function with two different models. Our confidence ranking loss allows direct optimization of the logits output for different convex surrogate functions of metrics, e.g. AUC and Accuracy depending on the target task and dataset. Armed with our proposed methods, our experiments show that the introduction of confidence ranking loss can outperform all baselines on the CTR prediction tasks of public and industrial datasets. This framework has been deployed in the advertisement system of JD.com to serve the main traffic in the fine-rank stage.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.
We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.
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