We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for learning alternate paths to mean-field games. Based on these connections we pose a flexible family of optimization problems for identifying tilted paths of measures for DMT and advocate for the use of objective terms which encourage smoothness of the corresponding velocities. We present a numerical algorithm for solving these problems based on recent Gaussian process methods for solution of partial differential equations and demonstrate the ability of our method to recover more efficient and smooth transport models compared to those which use an untilted reference path.

A central part of geometric statistics is to compute the Fréchet mean. This is a well-known intrinsic mean on a Riemannian manifold that minimizes the sum of squared Riemannian distances from the mean point to all other data points. The Fréchet mean is simple to define and generalizes the Euclidean mean, but for most manifolds even minimizing the Riemannian distance involves solving an optimization problem. Therefore, numerical computations of the Fréchet mean require solving an embedded optimization problem in each iteration. We introduce the GEORCE-FM algorithm to simultaneously compute the Fréchet mean and Riemannian distances in each iteration in a local chart, making it faster than previous methods. We extend the algorithm to Finsler manifolds and introduce an adaptive extension such that GEORCE-FM scales to a large number of data points. Theoretically, we show that GEORCE-FM has global convergence and local quadratic convergence and prove that the adaptive extension converges in expectation to the Fréchet mean. We further empirically demonstrate that GEORCE-FM outperforms existing baseline methods to estimate the Fréchet mean in terms of both accuracy and runtime.

Hardware accelerators, especially those designed for tensor processing, have become ubiquitous in today's computing landscape. However, even with significant efforts in building compilers, programming these tensor accelerators remains challenging, leaving much of their potential underutilized. Recently, large language models (LLMs), trained on large amounts of code, have shown significant promise in code generation and optimization tasks, but generating low-resource languages, such as specialized tensor accelerator code still poses a significant challenge. We tackle this challenge with Autocomp, an approach that empowers accelerator programmers to leverage domain knowledge and hardware feedback to optimize code via an automated LLM-driven search. We accomplish this by: 1) formulating each optimization pass as a structured two-phase prompt, divided into planning and code generation phases, 2) inserting domain knowledge during planning via a concise and adaptable optimization menu, and 3) integrating correctness and performance metrics from hardware as feedback at each search iteration. Across three distinct hardware platforms, we demonstrate that Autocomp-optimized code runs 5.6x faster than the vendor-provided library (Gemmini), outperforms expert-level hand-tuned code by 1.9x (AWS Trainium), and achieves 3.8x higher performance than a machine learning-based cost model for GPUs (NVIDIA L40S). Additionally, we demonstrate that optimization schedules generated from Autocomp can be reused across similar tensor operations, improving speedups by up to 24% under a fixed sample budget.

Parameter-efficient training, based on low-rank optimization, has become a highly successful tool for fine-tuning large deep-learning models. However, these methods fail at low-rank pre-training tasks where maintaining the low-rank structure and the objective remains a challenging task. We propose the Quadratic Reweighted Rank Regularizer dubbed Q3R, which leads to a novel low-rank inducing training strategy inspired by the iteratively reweighted least squares (IRLS) framework. Q3R is based on a quadratic regularizer term which majorizes a smoothed log determinant serving as rank surrogate objective. Unlike other low-rank training techniques, Q3R is able to train weight matrices with prescribed, low target ranks of models that achieve comparable predictive performance as dense models, with small computational overhead, while remaining fully compatible with existing architectures. For example, we demonstrated one experiment where we are able to truncate $60\%$ and $80\%$ of the parameters of a ViT-Tiny model with $~1.3\%$ and $~4\%$ accuracy drop in CIFAR-10 performance respectively. The efficacy of Q3R is confirmed on Transformers across both image and language tasks, including for low-rank fine-tuning.

Heavy-tailed noise has attracted growing attention in nonconvex stochastic optimization, as numerous empirical studies suggest it offers a more realistic assumption than standard bounded variance assumption. In this work, we investigate nonconvex-PL minimax optimization under heavy-tailed gradient noise in federated learning. We propose two novel algorithms: Fed-NSGDA-M, which integrates normalized gradients, and FedMuon-DA, which leverages the Muon optimizer for local updates. Both algorithms are designed to effectively address heavy-tailed noise in federated minimax optimization, under a milder condition. We theoretically establish that both algorithms achieve a convergence rate of $O({1}/{(TNp)^{\frac{s-1}{2s}}})$. To the best of our knowledge, these are the first federated minimax optimization algorithms with rigorous theoretical guarantees under heavy-tailed noise. Extensive experiments further validate their effectiveness.

We consider the problem of fitting a reinforcement learning (RL) model to some given behavioral data under a multi-armed bandit environment. These models have received much attention in recent years for characterizing human and animal decision making behavior. We provide a generic mathematical optimization problem formulation for the fitting problem of a wide range of RL models that appear frequently in scientific research applications, followed by a detailed theoretical analysis of its convexity properties. Based on the theoretical results, we introduce a novel solution method for the fitting problem of RL models based on convex relaxation and optimization. Our method is then evaluated in several simulated bandit environments to compare with some benchmark methods that appear in the literature. Numerical results indicate that our method achieves comparable performance to the state-of-the-art, while significantly reducing computation time. We also provide an open-source Python package for our proposed method to empower researchers to apply it in the analysis of their datasets directly, without prior knowledge of convex optimization.

This is the accepted version of the paper published in Journal of Theoretical & Applied Information Technology Vol 4 No 8 (2008) . ABSTRACT This paper presents a reinforced genetic approach to a defined d - resource system optimization problem . The classical evolution schema was ineffective due to a very strict feasibility function in the studied problem. Hence, the presented strategy has introduced several modifications and adaptations to standard genetic routines, e.g.: a migration operator which is an analogy to the biological random genetic drift. INTRODUCTION A funda mental goal in computer science is to provide an algorithm which would determine an optimal solution in acceptable time. Computational Complexity Theory is the field which studies the efficiency of computation; its major goals are to find efficient algorit hms for natural problems or to show that no efficient solutions exist. NP - hard (Nondeterministic Polynomial - time hard), represents a class of problems which are'at least as difficult as problems in NP' [7] [19] . NP - complete problems can be solve d by means of exhaustive search.

Safe reinforcement learning (safe RL) aims to respect safety requirements while optimizing long-term performance. In many practical applications, however, the problem involves an infinite number of constraints, known as semi-infinite safe RL (SI-safe RL). Such constraints typically appear when safety conditions must be enforced across an entire continuous parameter space, such as ensuring adequate resource distribution at every spatial location. In this paper, we propose exchange policy optimization (EPO), an algorithmic framework that achieves optimal policy performance and deterministic bounded safety. EPO works by iteratively solving safe RL subproblems with finite constraint sets and adaptively adjusting the active set through constraint expansion and deletion. At each iteration, constraints with violations exceeding the predefined tolerance are added to refine the policy, while those with zero Lagrange multipliers are removed after the policy update. This exchange rule prevents uncontrolled growth of the working set and supports effective policy training. Our theoretical analysis demonstrates that, under mild assumptions, strategies trained via EPO achieve performance comparable to optimal solutions with global constraint violations strictly remaining within a prescribed bound.

Quantization plays a crucial role in accelerating the inference of large-scale models, and rotational matrices have been shown to effectively improve quantization performance by smoothing outliers. However, end-to-end fine-tuning of rotational optimization algorithms incurs high computational costs and is prone to overfitting. To address this challenge, we propose an efficient distribution-aware rotational calibration method, DartQuant, which reduces the complexity of rotational optimization by constraining the distribution of the activations after rotation. This approach also effectively reduces reliance on task-specific losses, thereby mitigating the risk of overfitting. Additionally, we introduce the QR-Orth optimization scheme, which replaces expensive alternating optimization with a more efficient solution. In a variety of model quantization experiments, DartQuant demonstrates superior performance. Compared to existing methods, it achieves 47$\times$ acceleration and 10$\times$ memory savings for rotational optimization on a 70B model. Furthermore, it is the first to successfully complete rotational calibration for a 70B model on a single 3090 GPU, making quantization of large language models feasible in resource-constrained environments. Code is available at https://github.com/CAS-CLab/DartQuant.git.

Future planetary exploration missions demand high-performance, fault-tolerant computing to enable autonomous Guidance, Navigation, and Control (GNC) and Lander Vision System (LVS) operations during Entry, Descent, and Landing (EDL). This paper evaluates the deployment of GNC and LVS algorithms on next-generation multi-core processors--HPSC, Snapdragon VOXL2, and AMD Xilinx Versal--demonstrating up to 15x speedup for LVS image processing and over 250x speedup for Guidance for Fuel-Optimal Large Divert (GFOLD) trajectory optimization compared to legacy spaceflight hardware. To ensure computational reliability, we present ARBITER (Asynchronous Redundant Behavior Inspection for Trusted Execution and Recovery), a Multi-Core Voting (MV) mechanism that performs real-time fault detection and correction across redundant cores. ARBITER is validated in both static optimization tasks (GFOLD) and dynamic closed-loop control (Attitude Control System). A fault injection study further identifies the gradient computation stage in GFOLD as the most sensitive to bit-level errors, motivating selective protection strategies and vector-based output arbitration. This work establishes a scalable and energy-efficient architecture for future missions, including Mars Sample Return, Enceladus Orbilander, and Ceres Sample Return, where onboard autonomy, low latency, and fault resilience are critical.