相关论文: Signatures Meet Dynamic Programming: Generalizing …
We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is…
We provide an introduction to the topic of path signatures as means of feature extraction for machine learning from data streams. The article stresses the mathematical theory underlying the signature methodology, highlighting the conceptual…
Robotic locomotion often relies on sequenced gaits to efficiently convert control input into desired motion. Despite extensive studies on gait optimization, achieving smooth and efficient gait transitions remains challenging. In this paper,…
The physical coupling between robots has the potential to improve the capabilities of multi-robot systems in challenging manufacturing processes. However, the path tracking accuracy of physically coupled robots is not studied adequately,…
We present a unified framework for path-parametric planning and control. This formulation is universal as it standardizes the entire spectrum of path-parametric techniques -- from traditional path following to more recent contouring or…
Stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm) are increasingly used to model systems with rough dynamics and long-range dependence, such as those arising in quantitative finance and reliability…
Model predictive control has emerged as an effective approach for real-time optimal control of connected and automated vehicles. However, nonlinear dynamics of vehicle and traffic systems make accurate modeling and real-time optimization…
An adaptive controller is proposed and analyzed for the class of infinite-horizon optimal control problems in positive linear systems presented in (Ohlin et al., 2024b). This controller is derived from the solution of a "data-driven…
Rough path theory is focused on capturing and making precise the interactions between highly oscillatory and non-linear systems. It draws on the analysis of LC Young and the geometric algebra of KT Chen. The concepts and the uniform…
High-frequency quantitative trading strategies have long been of significant interest in futures market. While advanced statistical arbitrage and deep learning enhance high-frequency data processing, they diminish opportunities for…
Paths of persistence diagrams provide a summary of the dynamic topological structure of a one-parameter family of metric spaces. These summaries can be used to study and characterize the dynamic shape of data such as swarming behavior in…
Despite their ability to aid developers in detecting potential defects early in the software development life cycle, static analysis tools often suffer from precision issues (i.e., high false positive rates of reported alarms). To improve…
The contributions of this short technical note are two-fold. Firstly, we introduce a modified version of a generalized Bellman-Ford algorithm calculating the value function of optimal control problems defined on hyper-graphs. Those…
The solutions to many sequential decision-making problems are characterized by dynamic programming and Bellman's principle of optimality. However, due to the inherent complexity of solving Bellman's equation exactly, there has been…
We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in…
Modeling continuous-time dynamics constitutes a foundational challenge, and uncovering inter-component correlations within complex systems holds promise for enhancing the efficacy of dynamic modeling. The prevailing approach of integrating…
We consider challenging dynamic programming models where the associated Bellman equation, and the value and policy iteration algorithms commonly exhibit complex and even pathological behavior. Our analysis is based on the new notion of…
In complex engineered systems, completing an objective is sometimes not enough. The system must be able to reach a set performance characteristic, such as an unmanned aerial vehicle flying from point A to point B, \textit{under 10 seconds}.…
The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is here examined through the lens of algebraic geometry.…
Real-world reinforcement learning is often \emph{nonstationary}: rewards and dynamics drift, accelerate, oscillate, and trigger abrupt switches in the optimal action. Existing theory often represents nonstationarity with coarse-scale models…