In many practical control applications, the performance level of a closed-loop system degrades over time due to the change of plant characteristics. Thus, there is a strong need for redesigning a controller without going through the system modeling process, which is often difficult for closed-loop systems. Reinforcement learning (RL) is one of the promising approaches that enable model-free redesign of optimal controllers for nonlinear dynamical systems based only on the measurement of the closed-loop system. However, the learning process of RL usually requires a considerable number of trial-and-error experiments using the poorly controlled system that may accumulate wear on the plant. To overcome this limitation, we propose a model-free two-step design approach that improves the transient learning performance of RL in an optimal regulator redesign problem for unknown nonlinear systems. Specifically, we first design a linear control law that attains some degree of control performance in a model-free manner, and then, train the nonlinear optimal control law with online RL by using the designed linear control law in parallel. We introduce an offline RL algorithm for the design of the linear control law and theoretically guarantee its convergence to the LQR controller under mild assumptions. Numerical simulations show that the proposed approach improves the transient learning performance and efficiency in hyperparameter tuning of RL.
相關內容
Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some problems, this simulation is infeasible, leading to the discretization of state variable space and the need to train one neural network for each data point. This approach becomes computationally inefficient when dealing with large state variable spaces. In this paper, we consider a class of this type of stochastic optimal control problems and introduce an effective solution employing multitask neural networks. To train our multitask neural network, we introduce a novel scheme that dynamically balances the learning across tasks. Through numerical experiments on real-world derivatives pricing problems, we prove that our method outperforms state-of-the-art approaches.
In Koopman operator theory, a finite-dimensional nonlinear system is transformed into an infinite but linear system using a set of observable functions. However, manually selecting observable functions that span the invariant subspace of the Koopman operator based on prior knowledge is inefficient and challenging, particularly when little or no information is available about the underlying systems. Furthermore, current methodologies tend to disregard the importance of the invertibility of observable functions, which leads to inaccurate results. To address these challenges, we propose the so-called FlowDMD, aka Flow-based Dynamic Mode Decomposition, that utilizes the Coupling Flow Invertible Neural Network (CF-INN) framework. FlowDMD leverages the intrinsically invertible characteristics of the CF-INN to learn the invariant subspaces of the Koopman operator and accurately reconstruct state variables. Numerical experiments demonstrate the superior performance of our algorithm compared to state-of-the-art methodologies.
Recently, addressing spatial confounding has become a major topic in spatial statistics. However, the literature has provided conflicting definitions, and many proposed definitions do not address the issue of confounding as it is understood in causal inference. We define spatial confounding as the existence of an unmeasured causal confounder with a spatial structure. We present a causal inference framework for nonparametric identification of the causal effect of a continuous exposure on an outcome in the presence of spatial confounding. We propose double machine learning (DML), a procedure in which flexible models are used to regress both the exposure and outcome variables on confounders to arrive at a causal estimator with favorable robustness properties and convergence rates, and we prove that this approach is consistent and asymptotically normal under spatial dependence. As far as we are aware, this is the first approach to spatial confounding that does not rely on restrictive parametric assumptions (such as linearity, effect homogeneity, or Gaussianity) for both identification and estimation. We demonstrate the advantages of the DML approach analytically and in simulations. We apply our methods and reasoning to a study of the effect of fine particulate matter exposure during pregnancy on birthweight in California.
On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes
For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than its expectation can be covered by a set of half-spaces whose sum of measures is small. We prove a conjecture of Talagrand that is the analog of this result in the Bernoulli-$p$ setting, and answer a question of Talagrand on the analogous result for general positive empirical processes.
Optimization under uncertainty is important in many applications, particularly to inform policy and decision making in areas such as public health. A key source of uncertainty arises from the incorporation of environmental variables as inputs into computational models or simulators. Such variables represent uncontrollable features of the optimization problem and reliable decision making must account for the uncertainty they propagate to the simulator outputs. Often, multiple, competing objectives are defined from these outputs such that the final optimal decision is a compromise between different goals. Here, we present emulation-based optimization methodology for such problems that extends expected quantile improvement (EQI) to address multi-objective optimization. Focusing on the practically important case of two objectives, we use a sequential design strategy to identify the Pareto front of optimal solutions. Uncertainty from the environmental variables is integrated out using Monte Carlo samples from the simulator. Interrogation of the expected output from the simulator is facilitated by use of (Gaussian process) emulators. The methodology is demonstrated on an optimization problem from public health involving the dispersion of anthrax spores across a spatial terrain. Environmental variables include meteorological features that impact the dispersion, and the methodology identifies the Pareto front even when there is considerable input uncertainty.
Recently, a family of unconventional integrators for ODEs with polynomial vector fields was proposed, based on the polarization of vector fields. The simplest instance is the by now famous Kahan discretization for quadratic vector fields. All these integrators seem to possess remarkable conservation properties. In particular, it has been proved that, when the underlying ODE is Hamiltonian, its polarization discretization possesses an integral of motion and an invariant volume form. In this note, we propose a new algebraic approach to derivation of the integrals of motion for polarization discretizations.
Comparisons of frequency distributions often invoke the concept of shift to describe directional changes in properties such as the mean. In the present study, we sought to define shift as a property in and of itself. Specifically, we define distributional shift (DS) as the concentration of frequencies away from the discrete class having the greatest value (e.g., the right-most bin of a histogram). We derive a measure of DS using the normalized sum of exponentiated cumulative frequencies. We then define relative distributional shift (RDS) as the difference in DS between two distributions, revealing the magnitude and direction by which one distribution is concentrated to lesser or greater discrete classes relative to another. We find that RDS is highly related to popular measures that, while based on the comparison of frequency distributions, do not explicitly consider shift. While RDS provides a useful complement to other comparative measures, DS allows shift to be quantified as a property of individual distributions, similar in concept to a statistical moment.
Supervised transfer learning has received considerable attention due to its potential to boost the predictive power of machine learning in scenarios where data are scarce. Generally, a given set of source models and a dataset from a target domain are used to adapt the pre-trained models to a target domain by statistically learning domain shift and domain-specific factors. While such procedurally and intuitively plausible methods have achieved great success in a wide range of real-world applications, the lack of a theoretical basis hinders further methodological development. This paper presents a general class of transfer learning regression called affine model transfer, following the principle of expected-square loss minimization. It is shown that the affine model transfer broadly encompasses various existing methods, including the most common procedure based on neural feature extractors. Furthermore, the current paper clarifies theoretical properties of the affine model transfer such as generalization error and excess risk. Through several case studies, we demonstrate the practical benefits of modeling and estimating inter-domain commonality and domain-specific factors separately with the affine-type transfer models.
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial Differential Equations containing such operators and integrated in time with exponential integrators, it is then of paramount importance to efficiently approximate the actions of $\varphi$-functions of the arising matrices. In this work, we show how to produce directional split approximations of third order with respect to the time step size. They conveniently employ tensor-matrix products (the so-called $\mu$-mode product and related Tucker operator, realized in practice with high performance level 3 BLAS), and allow for the effective usage of exponential Runge--Kutta integrators up to order three. The technique can also be efficiently implemented on modern computer hardware such as Graphic Processing Units. The approach has been successfully tested against state-of-the-art techniques on two well-known physical models that lead to Turing patterns, namely the 2D Schnakenberg and the 3D FitzHugh--Nagumo systems, on different architectures.
Deterministic communication is required for applications of several industry verticals including manufacturing, automotive, financial, and health care, etc. These applications rely on reliable and time-synchronized delivery of information among the communicating devices. Therefore, large delay variations in packet delivery or inaccuracies in time synchronization cannot be tolerated. In particular, the industrial revolution on digitization, connectivity of digital and physical systems, and flexible production design require deterministic and time-synchronized communication. A network supporting deterministic communication guarantees data delivery in a specified time with high reliability. The IEEE 802.1 TSN task group is developing standards to provide deterministic communication through IEEE 802 networks. The IEEE 802.1AS standard defines time synchronization mechanism for accurate distribution of time among the communicating devices. The time synchronization accuracy depends on the accurate calculation of the residence time which is the time between the ingress and the egress ports of the bridge and includes the processing, queuing, transmission, and link latency of the timing information. This paper discusses time synchronization mechanisms supported in current wired and wireless integrated systems.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191