We present an efficient algorithm for regularized optimal transport.

The complexity of the traditional LP solver is still at least quadratic in the problem dimension, i.e., the

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We present an efficient algorithm for regularized optimal transport.

L 1) for any maximal monotone F, and are contractive (i.e. We will mainly use two well-known properties of these operators. First assume W is of this form. J. (B8) Thus, we can always solve the above equation with the v term of the form W Jv =( I + D) Jv = v. (B9) This gives us a (linear) operator splitting problem with the F and G operators given in (14). C.1 Inversion via the discrete Fourier transform However, the original form (C2) is more convenient mathematically and we use that here.

This work has been published in the IEEE Access with DOI: 10.1109/ACCESS.2025.3586594. Abstract --Millimeter-wave (mmWave) communication enables high data rates for cellular-connected Uncrewed Aerial V ehicles (UA Vs). However, a robust beam management remains challenging due to significant path loss and the dynamic mobility of UA Vs, which can destabilize the UA V-base station (BS) link. This research presents a GPS-aided deep learning (DL) model that simultaneously predicts current and future optimal beams for UA V mmWave communications, maintaining a T op-1 prediction accuracy exceeding 70% and an average power loss below 0.6 dB across all prediction steps. These outcomes stem from a proposed data set splitting method ensuring balanced label distribution, paired with a GPS preprocessing technique that extracts key positional features, and a DL architecture that maps sequential position data to beam index predictions. The model reduces overhead by approximately 93% (requiring the training of 2 3 beams instead of 32 beams) with 95% beam prediction accuracy guarantees, and ensures 94% to 96% of predictions exhibit mean power loss not exceeding 1 dB. Uncrewed Aerial V ehicles (UA V) are expected to serve two roles in wireless networks both as user equipment (UE) that accesses cellular network (cellular-connected UA V) and as UA V -assisted communication platforms providing aerial base stations (BS) and relays for terrestrial users [1] As the high path loss characteristic of mmWave, deploying large antenna arrays on the BS side helps mitigate it by generating narrow beams with strong beamforming gains [4]. As a result, mmWave communications rely heavily on efficient beam management--including beam training and tracking--to quickly select the appropriate beams during intra-and inter-cell mobility, minimizing the risk of beam misalignment [5].

This paper presents an improved forward-backward splitting algorithm with two inertial parameters. It aims to find a point in the real Hilbert space at which the sum of a co-coercive operator and a maximal monotone operator vanishes. Under standard assumptions, our proposed algorithm demonstrates weak convergence. We present numerous experimental results to demonstrate the behavior of the developed algorithm by comparing it with existing algorithms in the literature for regression and data classification problems. Furthermore, these implementations suggest our proposed algorithm yields superior outcomes when benchmarked against other relevant algorithms in existing literature.

We explore an explicit link between stochastic gradient descent using common batching strategies and splitting methods for ordinary differential equations. From this perspective, we introduce a new minibatching strategy (called Symmetric Minibatching Strategy) for stochastic gradient optimisation which shows greatly reduced stochastic gradient bias (from $\mathcal{O}(h^2)$ to $\mathcal{O}(h^4)$ in the optimiser stepsize $h$), when combined with momentum-based optimisers. We justify why momentum is needed to obtain the improved performance using the theory of backward analysis for splitting integrators and provide a detailed analytic computation of the stochastic gradient bias on a simple example. Further, we provide improved convergence guarantees for this new minibatching strategy using Lyapunov techniques that show reduced stochastic gradient bias for a fixed stepsize (or learning rate) over the class of strongly-convex and smooth objective functions. Via the same techniques we also improve the known results for the Random Reshuffling strategy for stochastic gradient descent methods with momentum. We argue that this also leads to a faster convergence rate when considering a decreasing stepsize schedule. Both the reduced bias and efficacy of decreasing stepsizes are demonstrated numerically on several motivating examples.

We present an efficient algorithm for regularized optimal transport. In contrast toprevious methods, we use the Douglas-Rachford splitting technique to developan efficient solver that can handle a broad class of regularizers. We illustrate its competitiveness in several applications, includingdomain adaptation and learning of generative models.

Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations offer distinct advantages over sampling based methods in their computational cost and continuous representation. State-of-the-art Gaussian mixture approaches are adaptive in that individual Gaussian mixands are selectively split into mixtures to yield better approximations of the true propagated distribution. Despite the importance of the splitting process to accuracy and computational efficiency, relatively little work has been devoted to mixand selection and splitting direction optimization. The first part of this work presents splitting methods that preserve the mean and covariance of the original distribution. Then, we present and compare a number of novel heuristics for selecting the splitting direction. The choice of splitting direction is informed by the initial uncertainty distribution, properties of the nonlinear function through which the original distribution is propagated, and a whitening based natural scaling method to avoid dependence of the splitting direction on the scaling of coordinates. We compare these novel heuristics to existing techniques in three distinct examples involving Cartesian to polar coordinate transformation, Keplerian orbital element propagation, and uncertainty propagation in the circular restricted three-body problem.