Wide deep neural networks are easy to optimize without constraints.
problem Optimizing wide deep neural networks.
method Analysis of optimization landscapes and empirical-risk minimization.
result Wide neural networks have no confined points, making optimization easier.
Optimizes wireless power control using graph neural networks and counterfactual optimization.
problem Mitigating interference in wireless networks with multiple transmitter-receiver pairs.
method Graph neural network architecture combined with unsupervised primal-dual counterfactual optimization.
result Guarantees a minimum rate constraint that adapts to network size, balancing user rates.
New algorithm optimizes neural network architecture efficiently.
problem Optimizing neural network architecture with minimal layers and cost.
method Greedy Search for Neural Network Architecture.
result Our method outperforms state-of-the-art algorithms in terms of performance and time.
We solve the optimization of two-layer ReLU networks using convex math.
problem Optimizing two-layer ReLU neural networks.
method Exact characterization of optimal solutions via convex optimization.
result We prove that all globally optimal solutions can be found via convex optimization.
Optimizes control interventions in real-world networks using deep-learning and network science.
problem Optimizing control over socioeconomic networks subject to constraints.
method Integrates optimization tools from deep-learning with network science.
result Characterizes vulnerability of corporate networks to takeovers.
Introduces Deep Genetic Network for optimizing neural network hyperparameters.
problem Optimizing neural network hyperparameters is a tedious and time-consuming task.
method Uses genetic algorithms within a deep neural network architecture to optimize hyperparameters during training.
result Deep Genetic Network successfully optimizes hyperparameters in various types of neural network layers.
GT-DDP optimizer trains residual networks using game theory.
problem Applying DDP to residual networks.
method Game-theoretic DDP optimizer for residual networks.
result Improved training convergence and variance reduction.
Optimizes function networks by selectively evaluating parts of the network, reducing costs.
problem Optimizing expensive function networks where full evaluations are costly.
method Knowledge gradient acquisition function for cost-aware partial evaluations.
result Outperforms existing BOFN methods and benchmarks across various problems.
LiPopt uses polynomial optimization to estimate neural network Lipschitz constants efficiently.
problem Estimating the Lipschitz constant of neural networks efficiently.
method Sparse polynomial optimization, leveraging network connectivity to reduce complexity.
result Superior estimates of the ℓ∞-Lipschitz constant compared to existing methods. Optimal function approximation with Relu neural networks achieves minimal error.
problem Finding the minimal error in approximating convex functions with Relu networks.
method Established necessary and sufficient conditions for optimal approximations, presented neural network architectures, and proposed an algorithm for convergence.
result Proved the convergence of the proposed algorithm and validated it with experimental results.
Paper tackles optimal network compression for financial systems.
problem Optimal network compression for financial systems under shocks.
method Formulated as an NP-hard problem, studied systemic risk measures, and analyzed specific networks.
result Systemic fragility results no longer hold generally under shocks and heterogeneous networks.
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network wi…
HyperAdam learns to optimize neural networks by combining Adam's updates with varying decay rates.
problem Limitation of learned black-box optimizers in generalization ability.
method HyperAdam combines learned and traditional Adam optimizer, adaptively learning weights and decay rates.
result HyperAdam outperforms traditional optimizers in various network training tasks.
Self-Tuning Networks optimize hyperparameters using bilevel optimization and gated best-response functions.
problem Optimizing hyperparameters for neural networks.
method Bilevel optimization with gated best-response functions to adapt regularization hyperparameters online.
result Self-Tuning Networks outperform fixed hyperparameter values on large-scale deep learning problems.
Optimal rates for shallow ReLU networks in nonparametric regression.
problem Approximating smooth and non-smooth functions with shallow ReLU networks.
method Analysis of shallow ReLUk neural networks, using variation norms and deep learning theory. result Optimal approximation rates for shallow ReLU networks in nonparametric regression.
Frank-Wolfe optimization applied to a small deep network shows slower convergence compared to gradient descent.
problem Training deep neural networks is challenging due to many parameters and optimization difficulties.
method Frank-Wolfe optimization method applied to a deep network.
result Frank-Wolfe optimization converges slowly and is unstable in a stochastic setting.
Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the appropriate network structure for a target problem is a challenging task. In this paper, w…
Joslim optimizes both width and weight configurations for slimmable neural networks, improving model efficiency.
problem Optimizing both width and weight configurations for slimmable neural networks to improve efficiency.
method Proposes a general framework for joint optimization of width configurations and weights, and introduces Joslim algorithm.
result Improves model efficiency by up to 1.7% in top-1 accuracy on the ImageNet dataset.
Novel approach learns optimal transport using convex neural networks.
problem Learning optimal transport between distributions from samples.
method Solving a minimax optimization to learn two convex functions, representing the optimal transport map.
result The approach finds optimal transport mappings that are independent of initialization and can handle discontinuous distributions.
Researchers improve transformer networks' optimization and understanding.
problem Improving the understanding and optimization of transformer networks.
method Introducing a convex alternative to the self-attention mechanism and reformulating the training problem as a convex optimization problem.
result Revealed an implicit regularization mechanism that promotes sparsity across tokens.
Optimizes graph neural networks using natural gradient descent.
problem Improving efficiency and performance of graph neural networks.
method Employing natural gradient descent to optimize graph neural networks.
result Natural gradient optimization leads to superior performance compared to existing methods.
SVD improves neural network optimization.
problem Optimizing neural networks.
method Using SVD as an initial guess for neural network parameters.
result Better optimization results.
Survey of network analysis limits and optimal methods.
problem Graphon estimation, community detection, and hypothesis testing.
method Review of minimax optimal rates and procedures.
result Optimal algorithms for network analysis.
Optimization algorithms help overparameterized neural networks achieve high performance.
problem Understanding the convergence of optimization algorithms on overparameterized neural networks.
method Analyzing a broad class of optimization algorithms using dynamical systems and finite over-parameterized neural networks with ReLU activation.
result The Heavy Ball method converges to global minimum at a linear rate, while NAG converges sublinearly.
GAIL with neural networks converges to global optima and has a known rate.
problem Uncertainty about GAIL with neural networks achieving global optimality.
method Gradient-based alternating updates algorithm.
result Established sublinear convergence to globally optimal solution.
A novel neural network approach for optimization problems.
problem Constrained optimization problems.
method Neural Optimization Machine (NOM) using a specially designed NN architecture and training procedure.
result Solves optimization problems efficiently, especially in high-dimensional spaces.
The robustness and integrity of IP networks require efficient tools for traffic monitoring and analysis, which scale well with traffic volume and network size. We address the problem of optimal large-scale flow monitoring of computer networks under resource constraints. We propose a stochastic optimization framework wh…
A new distributed method for convex optimization over networks with fast convergence.
problem Large-scale convex optimization over networks with limited communication.
method Distributed cubic-regularized Newton method.
result Convergence rate of O(k−3) for convex functions with Lipschitz gradient and Hessian. Gradient descent methods for deep ReLU networks achieve optimal generalization rates.
problem Generalization of gradient descent methods for deep neural networks
method Establishing minimax-optimal rates for GD and SGD with deep ReLU networks
result Gradient descent methods for deep ReLU networks achieve optimal generalization rates
Neural networks improve structural optimization solutions.
problem Quality of structural optimization solutions depends on parameterization.
method Optimizing neural network parameters to output densities for optimization.
result Our approach produces the best design 50% more often than baselines.
Paper links network Lasso to network flow optimization.
problem Joint clustering and optimization of networked data.
method Exploration of duality between network Lasso and network flow optimization.
result nLasso is equivalent to a minimum-cost flow problem on the data network structure.
Ensembles of neural networks learn better by sharing information.
problem Improving performance of neural networks through collective learning.
method Modeling neural networks as socially interacting agents aiming to maximize their own performance and functional relations to others.
result Optimal collective performance emerges from local interactions between networks, leading to specialization and higher confidence.
Paper optimizes clustering for multi-layer networks and discrete mixtures.
problem Optimizing clustering in multi-layer networks and discrete mixtures.
method Two-stage method: tensor-based initialization and likelihood-based refinement.
result Achieves minimax optimal error rate for multi-layer networks and discrete mixtures.
Novel framework finds globally optimal energy-efficient power control in wireless networks.
problem Energy-efficient power control in wireless networks.
method Branch-and-bound procedure with problem-specific bounds for faster convergence.
result Global solution for common energy-efficient power control problems with reduced complexity.
Improved hypernetwork for efficient neural network hyperparameter tuning.
problem Efficiently optimizing hyperparameters in neural networks.
method Proposed Δ-STN architecture focusing on accurate best-response Jacobian approximation. result Significantly improved hyperparameter tuning accuracy and stability.
EGO optimizes neural network architectures without manual tuning.
problem Designing optimal neural network architectures is difficult and time-consuming.
method Adapted EGO algorithm for efficient optimization of neural network architectures.
result Automatically optimized neural networks achieve competitive performance compared to hand-crafted ones.
This paper proposes a gossip-based algorithm for distributed bilevel optimization over networks.
problem Distributed bilevel optimization over networks with limited communication.
method Gossip-based distributed bilevel learning algorithm.
result Achieves optimal sample complexities for general and strongly convex objectives.
DEEP-BO optimizes hyperparameters of deep networks, outperforming existing methods.
problem Hyperparameter optimization of deep networks is challenging due to the complexity and sensitivity of DNN performance.
method Enhanced Bayesian Optimization (DEEP-BO) specifically designed for deep networks, incorporating diversification, early termination, and parallelism.
result DEEP-BO outperforms or matches other state-of-the-art methods on six DNN benchmarks.
Optimal stock price prediction model using recurrent neural networks with RMSprop optimizer.
problem Stock price prediction using neural networks.
method Comparison of fully connected, convolutional, and recurrent architectures; inclusion of three optimization techniques.
result Single layer recurrent neural network with RMSprop optimizer produces optimal results with validation and test MAE of 0.0150 and 0.0148 respectively.
DGBO optimizes attributed graphs efficiently.
problem Optimizing graphs with rich contextual features.
method Deep graph neural network surrogate for scalable Bayesian optimization.
result DGBO scales linearly with observations and outperforms state-of-the-art methods.
Neural networks help prove PPO and TRPO can find global policy.
problem Proving global convergence of PPO and TRPO with neural networks.
method Proved convergence of neural network-based PPO and TRPO to globally optimal policy.
result Proved sublinear convergence rate to globally optimal policy.
Study on the optimization of neural networks with ReLU activation and the degeneracy of their parametrizations.
problem Understanding the optimization landscape of neural networks with ReLU activation.
method Analyzing the optimization problem over the space of neural network realizations and establishing inverse stability of the realization map.
result Inverse stability of the realization map is not guaranteed in general but can be established for shallow networks, allowing optimization over restricted sets.
Neural-optimized objective functions simplify optimization tasks.
problem Designing effective objective functions for optimization problems is challenging.
method A neural network learns the objective function from training data through an inner and outer optimization process.
result The approach can learn objective functions from data and produce solutions for optimization tasks.
Deep neural networks can solve optimal stopping problems without dimensionality issues.
problem Optimal stopping problems in high-dimensional state spaces.
method Established a general framework for deep ReLU neural networks to approximate value functions and continuation values.
result Deep neural networks can approximate value functions and continuation values with error at most ε of size κd^q ε^(-r).
Wide networks avoid bad local minima, proving phase transition.
problem Understanding the optimization landscape of neural networks.
method Proving phase transitions in loss surfaces of wide and narrow networks.
result Phase transition from narrow to wide networks: no bad local minima.
The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multi-agent co-ordination, est…
Study on deep neural networks using concentration inequalities and optimal stopping.
problem Understanding the performance and structure of stochastic deep neural networks.
method Introduced concentration inequalities for SDNN outputs and an EC classifier. Determined the optimal number of layers via an optimal stopping procedure.
result Optimal number of layers for SDNNs determined via an optimal stopping procedure.
Unified framework reveals regularization mechanism in deep ReLU networks via convex optimization.
problem Understanding the success of deep neural networks.
method Developed a unified framework using convex optimization to reveal regularization mechanisms.
result ReLU networks can be globally optimized via convex programs, enforcing sparsity.