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When training the parameters of a linear dynamical model, the gradient descent algorithm is likely to fail to converge if the squared-error loss is used as the training loss function. Restricting the parameter space to a smaller subset and…
Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric…
Learning from Demonstration (LfD) techniques enable robots to learn and generalize tasks from user demonstrations, eliminating the need for coding expertise among end-users. One established technique to implement LfD in robots is to encode…
Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to…
Input to the Load Balanced Demand Distribution (LBDD) consists of the following: (a) a set of service centers; (b) a set of demand nodes and; (c) a cost matrix containing the cost of assignment for each (demand node, service center) pair.…
The control problem of the working tool movement along a predefined trajectory is considered. The integral of kinetic energy and weighted inertia forces for the whole period of motion is considered as a cost functional. The trajectory is…
Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…
We introduce a generalization of local density of states which is "windowed" with respect to position and energy, called the windowed local density of states (wLDOS). This definition generalizes the usual LDOS in the sense that the usual…
Recent work on approximate linear programming (ALP) techniques for first-order Markov Decision Processes (FOMDPs) represents the value function linearly w.r.t. a set of first-order basis functions and uses linear programming techniques to…
Orbital debris is a pressing problem which presents a danger to global space operations and a barrier to continued development of the space economy and space infrastructure. As research continues regarding orbital debris, there is a need…
Consider the generalized linear least squares (GLS) problem $\min\|Lx\|_2 \ \mathrm{s.t.} \ \|M(Ax-b)\|_2=\min$. The weighted pseudoinverse $A_{ML}^{\dag}$ is the matrix that maps $b$ to the minimum 2-norm solution of this GLS problem. By…
Autonomous Dynamic System (DS)-based algorithms hold a pivotal and foundational role in the field of Learning from Demonstration (LfD). Nevertheless, they confront the formidable challenge of striking a delicate balance between achieving…
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a matrix $M \in \mathbb{Q}^{d \times d}$, an initial vector…
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an…
We demonstrate when and how an entire left-infinite orbit of an underlying dynamical system or observations from such left-infinite orbits can be uniquely represented by a pair of elements in a different space, a phenomenon which we call…
Reinforcement learning algorithms typically consider discrete-time dynamics, even though the underlying systems are often continuous in time. In this paper, we introduce a model-based reinforcement learning algorithm that represents…
Following the development of weighted asymptotic approximation properties of matrices, we introduce the analogous uniform approximation properties (that is, study the improvability of Dirichlet's Theorem). An added feature is the use of…
We consider \emph{random linear programs} (rlps) as a subclass of \emph{random optimization problems} (rops) and study their typical behavior. Our particular focus is on appropriate linear objectives which connect the rlps to the mean…
The mixture of Dirichlet process (MDP) defines a flexible prior distribution on the space of probability measures. This study shows that ordinary least-squares (OLS) estimator, as a functional of the MDP posterior distribution, has…
This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree $\Delta$, and each node has up to $L$ units of load. The task is to distribute the load more evenly so that the loads of…