We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting. Decentralized optimization techniques rely on a consensus step that is well understood in Euclidean spaces because of their linearity. However, in positively curved Riemannian spaces, a main technical challenge is that geodesic distances may not induce a globally convex structure. In this work, we first analyze a curvature-aware Riemannian consensus step that enables a linear convergence beyond Hadamard manifolds. Building on this step, we establish a $O(\sqrt{T})$ regret bound for the decentralized online Riemannian gradient descent algorithm. Then, we investigate the two-point bandit feedback setup, where we employ computationally efficient gradient estimators using smoothing techniques, and we demonstrate the same $O(\sqrt{T})$ regret bound through the subconvexity analysis of smoothed objectives.

Abstract--The complexity of large-scale 6G-and-beyond networks demands innovative approaches for multi-objective optimization over vast search spaces, a task often intractable. Quantum computing (QC) emerges as a promising technology for efficient large-scale optimization. We present our vision of leveraging QC to tackle key classes of problems in future mobile networks. By analyzing and identifying common features, particularly their graph-centric representation, we propose a unified strategy involving QC algorithms. Specifically, we outline a methodology for optimization using quantum annealing as well as quantum reinforcement learning. Additionally, we discuss the main challenges that QC algorithms and hardware must overcome to effectively optimize future networks. Quantum computing (QC) has rapidly emerged as a promising field, with its unparalleled potential to tackle problems typically intractable for classical computers. Quantum bits (qubits) leverage the principles of superposition, interference and entanglement to accelerate computations and open the door to previously unimaginable algorithms. This fundamental characteristic allows quantum computers to perform complex calculations at speeds exponentially faster than their classical counterparts in certain domains, enabling breakthroughs in fields such as cryptography, materials science, and artificial intelligence (AI). Developments in QC pave the way for novel solutions to intractable optimization problems and are expected to play a disruptive role in multiple industries.

IQM Germany Abstract--Quantum policy evaluation (QPE) is a reinforcement learning (RL) algorithm which is quadratically more efficient than an analogous classical Monte Carlo estimation. It makes use of a direct quantum mechanical realization of a finite Markov decision process, in which the agent and the environment are modeled by unitary operators and exchange states, actions, and rewards in superposition. Previously, the quantum environment has been implemented and parametrized manually for an illustrative benchmark using a quantum simulator . In this paper, we demonstrate how these environment parameters can be learned from a batch of classical observational data through quantum machine learning (QML) on quantum hardware. The learned quantum environment is then applied in QPE to also compute policy evaluations on quantum hardware. Our experiments reveal that, despite challenges such as noise and short coherence times, the integration of QML and QPE shows promising potential for achieving quantum advantage in RL.

Modern transportation systems face significant challenges in ensuring road safety, given serious injuries caused by road accidents. The rapid growth of autonomous vehicles (AVs) has prompted new traffic designs that aim to optimize interactions among AVs. However, effective interactions between AVs remains challenging due to the absence of centralized control. Besides, there is a need for balancing multiple factors, including passenger demands and overall traffic efficiency. Traditional rule-based, optimization-based, and game-theoretic approaches each have limitations in addressing these challenges. Rule-based methods struggle with adaptability and generalization in complex scenarios, while optimization-based methods often require high computational resources. Game-theoretic approaches, such as Stackelberg and Nash games, suffer from limited adaptability and potential inefficiencies in cooperative settings. This paper proposes an Evolutionary Game Theory (EGT)-based framework for AV interactions that overcomes these limitations by utilizing a decentralized and adaptive strategy evolution mechanism. A causal evaluation module (CEGT) is introduced to optimize the evolutionary rate, balancing mutation and evolution by learning from historical interactions. Simulation results demonstrate the proposed CEGT outperforms EGT and popular benchmark games in terms of lower collision rates, improved safety distances, higher speeds, and overall better performance compared to Nash and Stackelberg games across diverse scenarios and parameter settings.

Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow tail-convergence typical of first-order schemes, thus requiring many iterations to achieve high-accuracy solutions. Moreover, hyperparameter tuning significantly impacts on the solver performance but how to find an appropriate parameter configuration remains an elusive research question. To address these issues, we explore how data-driven approaches can accelerate the solution process. Aiming at high-accuracy solutions, we focus on a stabilized interior-point solver and carefully handle its two-loop flow and control parameters. We will show that reinforcement learning can make a significant contribution to facilitating the solver tuning and to speeding up the optimization process. Numerical experiments demonstrate that, after a lightweight training, the learned policy generalizes well to different problem classes with varying dimensions and to various solver configurations.

We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and port-Hamiltonian systems might share the same initial total energy of a closed system, it is challenging for a single Hamiltonian network model to capture the distinctive and varying motion dynamics and physics of a phase space, from sampled observational phase space trajectories. To address this complicated Hamiltonian manifold learning challenge, we extend sparse symplectic, random Fourier Gaussian processes learning with predictive successive numerical estimations of the Hamiltonian landscape, using a generalized form of state and conjugate momentum Hamiltonian dynamics, appropriate to different classes of conservative, dissipative and port-Hamiltonian physical systems. In addition to the kernelized evidence lower bound (ELBO) loss for data fidelity, we incorporate stability and conservation constraints as additional hyper-parameter balanced loss terms to regularize the model's multi-gradients, enforcing physics correctness for improved prediction accuracy with bounded uncertainty.

In multi-task learning (MTL), gradient conflict poses a significant challenge. Effective methods for addressing this problem, including PCGrad, CAGrad, and GradNorm, in their original implementations are computationally demanding, which significantly limits their application in modern large models and transformers. We propose Gradient Conductor (GCond), a method that builds upon PCGrad principles by combining them with gradient accumulation and an adaptive arbitration mechanism. We evaluated GCond on self-supervised learning tasks using MobileNetV3-Small and ConvNeXt architectures on the ImageNet 1K dataset and a combined head and neck CT scan dataset, comparing the proposed method against baseline linear combinations and state-of-the-art gradient conflict resolution methods. The stochastic mode of GCond achieved a two-fold computational speedup while maintaining optimization quality, and demonstrated superior performance across all evaluated metrics, achieving lower L1 and SSIM losses compared to other methods on both datasets. GCond exhibited high scalability, being successfully applied to both compact models (MobileNetV3-Small) and large architectures (ConvNeXt-tiny and ConvNeXt-Base). It also showed compatibility with modern optimizers such as AdamW and Lion/LARS. Therefore, GCond offers a scalable and efficient solution to the problem of gradient conflicts in multi-task learning.

This paper presents a practical investigation into fine-tuning model parameters for mathematical reasoning tasks through experimenting with various configurations including randomness control, reasoning depth, and sampling strategies, careful tuning demonstrates substantial improvements in efficiency as well as performance. A holistically optimized framework is introduced for five state-of-the-art models on mathematical reasoning tasks, exhibiting significant performance boosts while maintaining solution correctness. Through systematic parameter optimization across Qwen2.5-72B, Llama-3.1-70B, DeepSeek-V3, Mixtral-8x22B, and Yi-Lightning, consistent efficiency gains are demonstrated with 100% optimization success rate. The methodology achieves an average 29.4% reduction in computational cost and 23.9% improvement in inference speed across all tested models. This framework systematically searches parameter spaces including temperature (0.1-0.5), reasoning steps (4-12), planning periods (1-4), and nucleus sampling (0.85-0.98), determining optimal configurations through testing on mathematical reasoning benchmarks. Critical findings show that lower temperature regimes (0.1-0.4) and reduced reasoning steps (4-6) consistently enhance efficiency without compromising accuracy. DeepSeek-V3 achieves the highest accuracy at 98%, while Mixtral-8x22B delivers the most cost-effective performance at 361.5 tokens per accurate response. Key contributions include: (1) the first comprehensive optimization study for five diverse SOTA models in mathematical reasoning, (2) a standardized production-oriented parameter optimization framework, (3) discovery of universal optimization trends applicable across model architectures, and (4) production-ready configurations with extensive performance characterization.

Image segmentation is a critical task in microscopy, essential for accurately analyzing and interpreting complex visual data. This task can be performed using custom models trained on domain-specific datasets, transfer learning from pre-trained models, or foundational models that offer broad applicability. However, foundational models often present a considerable number of non-transparent tuning parameters that require extensive manual optimization, limiting their usability for real-time streaming data analysis. Here, we introduce a reward function-based optimization to fine-tune foundational models and illustrate this approach for SAM (Segment Anything Model) framework by Meta. The reward functions can be constructed to represent the physics of the imaged system, including particle size distributions, geometries, and other criteria. By integrating a reward-driven optimization framework, we enhance SAM's adaptability and performance, leading to an optimized variant, SAM$^{*}$, that better aligns with the requirements of diverse segmentation tasks and particularly allows for real-time streaming data segmentation. We demonstrate the effectiveness of this approach in microscopy imaging, where precise segmentation is crucial for analyzing cellular structures, material interfaces, and nanoscale features.

In reliability engineering, conventional surrogate models encounter the "curse of dimensionality" as the number of random variables increases. While the active learning Kriging surrogate approaches with high-dimensional model representation (HDMR) enable effective approximation of high-dimensional functions and are widely applied to optimization problems, there are rare studies specifically focused on reliability analysis, which prioritizes prediction accuracy in critical regions over uniform accuracy across the entire domain. This study develops an active learning surrogate model method based on the Kriging-HDMR modeling for reliability analysis. The proposed approach facilitates the approximation of high-dimensional limit state functions through a composite representation constructed from multiple low-dimensional sub-surrogate models. The architecture of the surrogate modeling framework comprises three distinct stages: developing single-variable sub-surrogate models for all random variables, identifying the requirements for coupling-variable sub-surrogate models, and constructing the coupling-variable sub-surrogate models. Optimization mathematical models for selection of design of experiment samples are formulated based on each stage's characteristics, with objectives incorporating uncertainty variance, predicted mean, sample location and inter-sample distances. A candidate sample pool-free approach is adopted to achieve the selection of informative samples. Numerical experiments demonstrate that the proposed method achieves high computational efficiency while maintaining strong predictive accuracy in solving high-dimensional reliability problems.