Asymptotic and Non-Asymptotic Convergence Analysis of AdaGrad for Non-Convex Optimization via Novel Stopping Time-based Analysis

Adaptive optimizers have emerged as powerful tools in deep learning, dynamically adjusting the learning rate based on iterative gradients. These adaptive methods have significantly succeeded in various deep learning tasks, outperforming stochastic gradient descent (SGD). However, although AdaGrad is a cornerstone adaptive optimizer, its theoretical analysis is inadequate in addressing asymptotic convergence and non-asymptotic convergence rates on non-convex optimization. This study aims to provide a comprehensive analysis and complete picture of AdaGrad. We first introduce a novel stopping time technique from probabilistic theory to establish stability for the norm version of AdaGrad under milder conditions. We further derive two forms of asymptotic convergence: almost sure and mean-square. Furthermore, we demonstrate the near-optimal non-asymptotic convergence rate measured by the average-squared gradients in expectation, which is rarely explored and stronger than the existing high-probability results, under the mild assumptions. The techniques developed in this work are potentially independent of interest for future research on other adaptive stochastic algorithms.

Generalized Multi-hop Traffic Pressure for Heterogeneous Traffic Perimeter Control

Perimeter control prevents loss of traffic network capacity due to congestion in urban areas. Homogeneous perimeter control allows all access points to a protected region to have the same maximal permitted inflow. However, homogeneous perimeter control performs poorly when the congestion in the protected region is heterogeneous (e.g., imbalanced demand) since the homogeneous perimeter control does not consider location-specific traffic conditions around the perimeter. When the protected region has spatially heterogeneous congestion, it can often make sense to modulate the perimeter inflow rate to be higher near low-density regions and vice versa for high-density regions. To assist with this modulation, we can leverage the concept of 1-hop traffic pressure to measure intersection-level traffic congestion. However, as we show, 1-hop pressure turns out to be too spatially myopic for perimeter control and hence we formulate multi-hop generalizations of pressure that look ``deeper'' inside the perimeter beyond the entry intersection. In addition, we formulate a simple heterogeneous perimeter control methodology that can leverage this novel multi-hop pressure to redistribute the total permitted inflow provided by the homogeneous perimeter controller. Experimental results show that our heterogeneous perimeter control policies leveraging multi-hop pressure significantly outperform homogeneous perimeter control in scenarios where the origin-destination flows are highly imbalanced with high spatial heterogeneity.

Decentralized Federated Learning with Model Caching on Mobile Agents

Federated Learning (FL) aims to train a shared model using data and computation power on distributed agents coordinated by a central server. Decentralized FL (DFL) utilizes local model exchange and aggregation between agents to reduce the communication and computation overheads on the central server. However, when agents are mobile, the communication opportunity between agents can be sporadic, largely hindering the convergence and accuracy of DFL. In this paper, we study delay-tolerant model spreading and aggregation enabled by model caching on mobile agents. Each agent stores not only its own model, but also models of agents encountered in the recent past. When two agents meet, they exchange their own models as well as the cached models. Local model aggregation works on all models in the cache. We theoretically analyze the convergence of DFL with cached models, explicitly taking into account the model staleness introduced by caching. We design and compare different model caching algorithms for different DFL and mobility scenarios. We conduct detailed case studies in a vehicular network to systematically investigate the interplay between agent mobility, cache staleness, and model convergence. In our experiments, cached DFL converges quickly, and significantly outperforms DFL without caching.

A lifted Bregman strategy for training unfolded proximal neural network Gaussian denoisers

Unfolded proximal neural networks (PNNs) form a family of methods that combines deep learning and proximal optimization approaches. They consist in designing a neural network for a specific task by unrolling a proximal algorithm for a fixed number of iterations, where linearities can be learned from prior training procedure. PNNs have shown to be more robust than traditional deep learning approaches while reaching at least as good performances, in particular in computational imaging. However, training PNNs still depends on the efficiency of available training algorithms. In this work, we propose a lifted training formulation based on Bregman distances for unfolded PNNs. Leveraging the deterministic mini-batch block-coordinate forward-backward method, we design a bespoke computational strategy beyond traditional back-propagation methods for solving the resulting learning problem efficiently. We assess the behaviour of the proposed training approach for PNNs through numerical simulations on image denoising, considering a denoising PNN whose structure is based on dual proximal-gradient iterations.

ScaleBiO: Scalable Bilevel Optimization for LLM Data Reweighting

Bilevel optimization has shown its utility across various machine learning settings, yet most algorithms in practice require second-order information, making it challenging to scale them up. Only recently, a paradigm of first-order algorithms emerged, capable of effectively addressing bilevel optimization problems. Nevertheless, the practical efficiency of this paradigm remains unverified, particularly in the context of large language models (LLMs). This paper introduces the first scalable instantiation of this paradigm called ScaleBiO, focusing on bilevel optimization for large-scale LLM data reweighting. By combining with a recently proposed memory-efficient training technique called LISA, our novel algorithm allows the paradigm to scale to 34-billion-parameter LLMs on eight A40 GPUs, marking the first successful application of bilevel optimization under practical scenarios for large-sized LLMs. Empirically, extensive experiments on data reweighting verify the effectiveness of ScaleBiO for different-scaled models, including GPT-2, LLaMA-3-8B, GPT-NeoX-20B, and Yi-34B, where bilevel optimization succeeds in filtering irrelevant data samples and selecting informative samples. Theoretically, ScaleBiO ensures the optimality of the learned data weights, along with a convergence guarantee matching the conventional first-order bilevel optimization paradigm on smooth and strongly convex objectives.

Joint Power Allocation and Beamforming Design for Active IRS-Aided Directional Modulation Secure Systems

Since the secrecy rate (SR) performance improvement obtained by secure directional modulation (DM) network is limited, an active intelligent reflective surface (IRS)-assisted DM network is considered to attain a high SR. To address the SR maximization problem, a novel method based on Lagrangian dual transform and closed-form fractional programming algorithm (LDT-CFFP) is proposed, where the solutions to base station (BS) beamforming vectors and IRS reflection coefficient matrix are achieved. However, the computational complexity of LDT-CFFP method is high . To reduce its complexity, a blocked IRS-assisted DM network is designed. To meet the requirements of the network performance, a power allocation (PA) strategy is proposed and adopted in the system. Specifically, the system power between BS and IRS, as well as the transmission power for confidential messages (CM) and artificial noise (AN) from the BS, are allocated separately. Then we put forward null-space projection (NSP) method, maximum-ratio-reflecting (MRR) algorithm and PA strategy (NSP-MRR-PA) to solve the SR maximization problem. The CF solutions to BS beamforming vectors and IRS reflection coefficient matrix are respectively attained via NSP and MRR algorithms. For the PA factors, we take advantage of exhaustive search (ES) algorithm, particle swarm optimization (PSO) and simulated annealing (SA) algorithm to search for the solutions. From simulation results, it is verified that the LDT-CFFP method derives a higher SR gain over NSP-MRR-PA method. For NSP-MRR-PA method, the number of IRS units in each block possesses a significant SR performance. In addition, the application PA strategies, namely ES, PSO, SA methods outperforms the other PA strategies with fixed PA factors.

Preconditioned Neural Posterior Estimation for Likelihood-free Inference

Simulation based inference (SBI) methods enable the estimation of posterior distributions when the likelihood function is intractable, but where model simulation is feasible. Popular neural approaches to SBI are the neural posterior estimator (NPE) and its sequential version (SNPE). These methods can outperform statistical SBI approaches such as approximate Bayesian computation (ABC), particularly for relatively small numbers of model simulations. However, we show in this paper that the NPE methods are not guaranteed to be highly accurate, even on problems with low dimension. In such settings the posterior cannot be accurately trained over the prior predictive space, and even the sequential extension remains sub-optimal. To overcome this, we propose preconditioned NPE (PNPE) and its sequential version (PSNPE), which uses a short run of ABC to effectively eliminate regions of parameter space that produce large discrepancy between simulations and data and allow the posterior emulator to be more accurately trained. We present comprehensive empirical evidence that this melding of neural and statistical SBI methods improves performance over a range of examples, including a motivating example involving a complex agent-based model applied to real tumour growth data.

SynFog: A Photo-realistic Synthetic Fog Dataset based on End-to-end Imaging Simulation for Advancing Real-World Defogging in Autonomous Driving

To advance research in learning-based defogging algorithms, various synthetic fog datasets have been developed. However, existing datasets created using the Atmospheric Scattering Model (ASM) or real-time rendering engines often struggle to produce photo-realistic foggy images that accurately mimic the actual imaging process. This limitation hinders the effective generalization of models from synthetic to real data. In this paper, we introduce an end-to-end simulation pipeline designed to generate photo-realistic foggy images. This pipeline comprehensively considers the entire physically-based foggy scene imaging process, closely aligning with real-world image capture methods. Based on this pipeline, we present a new synthetic fog dataset named SynFog, which features both sky light and active lighting conditions, as well as three levels of fog density. Experimental results demonstrate that models trained on SynFog exhibit superior performance in visual perception and detection accuracy compared to others when applied to real-world foggy images.

Accelerated Convergence of Stochastic Heavy Ball Method under Anisotropic Gradient Noise

Heavy-ball momentum with decaying learning rates is widely used with SGD for optimizing deep learning models. In contrast to its empirical popularity, the understanding of its theoretical property is still quite limited, especially under the standard anisotropic gradient noise condition for quadratic regression problems. Although it is widely conjectured that heavy-ball momentum method can provide accelerated convergence and should work well in large batch settings, there is no rigorous theoretical analysis. In this paper, we fill this theoretical gap by establishing a non-asymptotic convergence bound for stochastic heavy-ball methods with step decay scheduler on quadratic objectives, under the anisotropic gradient noise condition. As a direct implication, we show that heavy-ball momentum can provide $\tilde{\mathcal{O}}(\sqrt{\kappa})$ accelerated convergence of the bias term of SGD while still achieving near-optimal convergence rate with respect to the stochastic variance term. The combined effect implies an overall convergence rate within log factors from the statistical minimax rate. This means SGD with heavy-ball momentum is useful in the large-batch settings such as distributed machine learning or federated learning, where a smaller number of iterations can significantly reduce the number of communication rounds, leading to acceleration in practice.

Learning county from pixels: Corn yield prediction with attention-weighted multiple instance learning

Remote sensing technology has become a promising tool in yield prediction. Most prior work employs satellite imagery for county-level corn yield prediction by spatially aggregating all pixels within a county into a single value, potentially overlooking the detailed information and valuable insights offered by more granular data. To this end, this research examines each county at the pixel level and applies multiple instance learning to leverage detailed information within a county. In addition, our method addresses the "mixed pixel" issue caused by the inconsistent resolution between feature datasets and crop mask, which may introduce noise into the model and therefore hinder accurate yield prediction. Specifically, the attention mechanism is employed to automatically assign weights to different pixels, which can mitigate the influence of mixed pixels. The experimental results show that the developed model outperforms four other machine learning models over the past five years in the U.S. corn belt and demonstrates its best performance in 2022, achieving a coefficient of determination (R2) value of 0.84 and a root mean square error (RMSE) of 0.83. This paper demonstrates the advantages of our approach from both spatial and temporal perspectives. Furthermore, through an in-depth study of the relationship between mixed pixels and attention, it is verified that our approach can capture critical feature information while filtering out noise from mixed pixels.