Information-Theoretic Approach for Model Reduction Over Finite Time Horizon
This paper presents an information-theoretic approach for model reduction for finite time simulation. Although system models are typically used for simulation over a finite time, most of the metrics (and pseudo-metrics) used for model accuracy assessment consider asymptotic behavior e.g., Hankel singular values and Kullback-Leibler(KL) rate metric. These metrics could further be used for model order reduction. Hence, in this paper, we propose a generalization of KL divergence-based metric called n-step KL rate metric, which could be used to compare models over a finite time horizon. We then demonstrate that the asymptotic metrics for comparing dynamical systems may not accurately assess the model prediction uncertainties over a finite time horizon. Motivated by this finite time analysis, we propose a new pragmatic approach to compute the influence of a subset of states on a combination of states called information transfer (IT). Model reduction typically involves the removal or truncation of states. IT combines the concepts from the n-step KL rate metric and model reduction. Finally, we demonstrate the application of information transfer for model reduction. Although the analysis and definitions presented in this paper assume linear systems, they can be extended for nonlinear systems.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A Thermodynamic Theory of Learning I: Irreversible Ensemble Transport and Epistemic Costs
Learning systems acquire structured internal representations from data, yet classical information-theoretic results state that deterministic transformations do not increase information. This raises a fundamental question…
Near-Optimal Offline Reinforcement Learning via Double Variance Reduction
We consider the problem of offline reinforcement learning (RL) -- a well-motivated setting of RL that aims at policy optimization using only historical data. Despite its wide applicability, theoretical understandings of …
Offline RLreinforcement-learningReinforcement LearningReinforcement Learning (RL)Finite-Time Information-Theoretic Bounds in Queueing Control
We establish the first finite-time information-theoretic lower bounds-and derive new policies that achieve them-for the total queue length in scheduling problems over stochastic processing networks with both adversarial …
SchedulingGreedy-GQ with Variance Reduction: Finite-time Analysis and Improved Complexity
Greedy-GQ is a value-based reinforcement learning (RL) algorithm for optimal control. Recently, the finite-time analysis of Greedy-GQ has been developed under linear function approximation and Markovian sampling, and the…
Reinforcement Learning (RL)Logical reduction of metarules
Many forms of inductive logic programming (ILP) use \emph{metarules}, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given le…
Inductive logic programming