Simpler, parameter-free AdaGrad and Adam variants with convergence guarantees.
problem Inefficiencies in ad-hoc learning rate tuning for optimization algorithms.
method Developed AdaGrad++ and Adam++ without predefined learning rates and proved their convergence.
result AdaGrad++ and Adam++ achieve comparable convergence rates to AdaGrad and Adam respectively.
Develops methods to measure and set function-space learning rates in neural networks.
problem Measuring and optimizing changes in neural network output functions.
method Efficient methods to measure and set function-space learning rates, requiring minimal computational overhead.
result Demonstrates FLeRM (Function-space Learning Rate Matching) for hyperparameter transfer across model scales.
Unsupervised pretraining and dropout have been well studied, especially with respect to regularization and output consistency. However, our understanding about the explicit convergence rates of the parameter estimates, and their dependence on the learning (like denoising and dropout rate) and structural (like depth and…
This paper demonstrates dynamic hyper-parameter setting, for deep neural network training, using Mutual Information (MI). The specific hyper-parameter studied in this paper is the learning rate. MI between the output layer and true outcomes is used to dynamically set the learning rate of the network through the trainin…
Paper studies MCCR models with scale parameters tending to zero, revealing optimal learning rate and comparing robustness.
problem Analyzing MCCR models with scale parameters approaching zero.
method Investigates MCCR models with scale parameters tending to zero, revealing optimal learning rate and comparing robustness.
result Optimal learning rate of MCCR models is O(n−1) in the asymptotic sense. Elo ratings learn model parameters quickly using Markov chains.
problem Ranking players in online settings.
method Bradley--Terry--Luce model and Markov chain theory.
result Elo learns model parameters at a competitive rate.
Learning Rate (LR) is an important hyper-parameter to tune for effective training of deep neural networks (DNNs). Even for the baseline of a constant learning rate, it is non-trivial to choose a good constant value for training a DNN. Dynamic learning rates involve multi-step tuning of LR values at various stages of th…
Single training run learns optimal VAE parameters for various β values.
problem Training VAEs with varying β values for optimal trade-off between distortion and rate.
method Introduced Multi-Rate VAE (MR-VAE) using hypernetworks to map β to optimal parameters.
result MR-VAEs can construct the full rate-distortion curve without additional training.
Study reveals convergence properties of SGD with random learning rate.
problem Analyzing convergence of SGD with random learning rate in non-convex optimization.
method Introduced Poisson SGD with random learning rate and used stationary distribution analysis.
result Poisson SGD converges to a stationary distribution and finds global minima in non-convex optimization.
Learning rate annealing improves robustness in stochastic optimization.
problem Tuning learning rates in large-scale models is costly and prone to errors.
method We analyze and demonstrate the benefits of learning rate annealing schemes.
result Stochastic gradient descent with annealed schedules converges more robustly to the optimal solution.
New research shows unlabeled data is equally valuable as labeled data in certain semi-supervised learning scenarios.
problem Improving learning performance with limited labeled data.
method Statistical models with continuous parameters, showing equal utility of unlabeled data under specific conditions.
result The learning rate of semi-supervised learning scales similarly to supervised learning when unlabeled data is abundant.
Proposes a learning rate method for shallow nets based on gradient Lipschitz constant.
problem Finding optimal learning rates for shallow neural networks.
method Associates learning rate with gradient Lipschitz constant and proposes a search algorithm.
result The proposed method significantly outperforms existing tuning methods.
Large learning rates cause parameter instability, leading to better generalization.
problem Understanding why deep neural networks perform well despite operating outside the traditional stability regime.
method Analyzing the effect of large learning rates on the orientation of Hessian eigenvectors and parameter exploration.
result Large learning rates induce parameter instability, leading to better generalization through exploration of flatter regions of the loss landscape.
We consider the problem of minimizing a convex risk with stochastic subgradients guaranteeing ε-locally differentially private (ε-LDP). While it has been shown that stochastic optimization is possible with ε-LDP via the standard SGD (Song et al., 2013), its convergence rate largely depends on the learning rate, w…
Study shows fast rates for inverse reinforcement learning with linear rewards.
problem Entropy-regularized min-max inverse reinforcement learning in finite-horizon MDPs.
method Structural and statistical analysis of Min-Max-IRL with pseudo-self-concordance.
result Both trajectory-level KL divergence and parameter error decay at O(n−1). New loss function connects learning rate and momentum.
problem Finding optimal learning rate and momentum empirically.
method Proposes a new information-theoretical loss function.
result Loss, learning rate, and momentum are closely connected.
The paper interprets learned step sizes in deep-unfolded gradient descent.
problem Intuitive interpretation of learned non-constant step sizes in deep-unfolded gradient descent.
method Theoretical analysis and optimization of spectral radius.
result Chebyshev steps achieve the lower bound of convergence rate for first-order methods.
Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting the hyper-parameters remains a black art that requires years of experience to ac…
D-Adaptation automatically sets optimal learning rates without manual tuning.
problem Optimizing learning rates for efficient convergence in machine learning.
method D-Adaptation, which asymptotically achieves optimal learning rates without back-tracking or additional evaluations.
result D-Adaptation automatically matches hand-tuned learning rates across diverse problems.
Cyclical learning rates improve DRL performance without manual tuning.
problem Manual hyperparameter tuning in DRL is time-consuming and error-prone.
method Proposes cyclical learning rates for DRL problems.
result Cyclical learning achieves similar or better results than fixed learning rates.
APO optimizes neural network parameters by amortizing proximal point methods.
problem Optimizing neural network parameters online and adaptively.
method APO framework that meta-learns proximal point parameters.
result APO can recover and outperform existing optimizers and schedules.
Stochastic Gradient TreeBoost is often found in many winning solutions in public data science challenges. Unfortunately, the best performance requires extensive parameter tuning and can be prone to overfitting. We propose PaloBoost, a Stochastic Gradient TreeBoost model that uses novel regularization techniques to guar…
We present the first adaptive strategy for active learning in the setting of classification with smooth decision boundary. The problem of adaptivity (to unknown distributional parameters) has remained opened since the seminal work of Castro and Nowak (2007), which first established (active learning) rates for this sett…
Analyzes convergence rates for Gaussian-gated MoE model.
problem Theoretical understanding of Gaussian-gated MoE model is incomplete.
method Maximum likelihood estimation with novel Voronoi loss functions.
result MLE has distinct behaviors under different settings of Gaussian gating function parameters.
The paper studies estimation rates for MoE models with a new prompt.
problem Estimating parameters in a softmax-contaminated MoE model.
method Analytic notion of distinguishability, minimax optimal estimation rates.
result Estimation rates are minimax optimal under distinguishability, but slower otherwise.
AutoSGD automatically adjusts learning rates for SGD.
problem Inefficient manual learning rate selection for SGD.
method AutoSGD automatically adjusts learning rates based on iteration.
result Empirical results show strong performance across various optimization tasks.
One of the main obstacles to broad application of reinforcement learning methods is the parameter sensitivity of our core learning algorithms. In many large-scale applications, online computation and function approximation represent key strategies in scaling up reinforcement learning algorithms. In this setting, we hav…
It is common practice to decay the learning rate. Here we show one can usually obtain the same learning curve on both training and test sets by instead increasing the batch size during training. This procedure is successful for stochastic gradient descent (SGD), SGD with momentum, Nesterov momentum, and Adam. It reache…
TempBalance improves neural network training by balancing learning rates across layers.
problem Improving neural network training performance.
method Layer-wise learning rate scheduling based on HT-SR Theory.
result TempBalance significantly outperforms ordinary SGD and state-of-the-art optimizers.
Develops a parameter-free SGD algorithm with optimal convergence rate.
problem Optimizing parameters in stochastic convex optimization.
method A novel parameter-free algorithm for SGD with high-probability guarantees and adaptive properties.
result Achieves optimal convergence rate with only a double-logarithmic factor increase compared to known-parameter settings.
Adjusting the learning rate schedule in stochastic gradient methods is an important unresolved problem which requires tuning in practice. If certain parameters of the loss function such as smoothness or strong convexity constants are known, theoretical learning rate schedules can be applied. However, in practice, such …
New algorithm closes empirical gap in PFSGD performance.
problem Empirical performance gap between tuned SGD and PFSGD.
method Parameter-free algorithm based on Coin-Betting ODE updates.
result New algorithm outperforms tuned baselines and matches optimal performance.
Analyzes symmetries in neural networks to predict learning dynamics.
problem Understanding the dynamics of neural network parameters during training.
method Unified theoretical framework based on symmetries and conservation laws.
result Symmetries impose geometric constraints on gradients and Hessians, leading to conservation laws.
Learning from small amounts of labeled data is a challenge in the area of deep learning. This is currently addressed by Transfer Learning where one learns the small data set as a transfer task from a larger source dataset. Transfer Learning can deliver higher accuracy if the hyperparameters and source dataset are chose…
The learning rate is one of the most important hyper-parameters for model training and generalization. However, current hand-designed parametric learning rate schedules offer limited flexibility and the predefined schedule may not match the training dynamics of high dimensional and non-convex optimization problems. In …
Improves risk control in predictions using semi-supervised calibration.
problem Noisy hyper-parameter tuning from limited labeled data.
method Semi-supervised calibration using unlabeled data to tune hyper-parameters rigorously.
result Improves prediction accuracy without sacrificing statistical validity.
Paper analyzes neural network distances and stability, leading to a new learning rule.
problem Stability and efficiency in training deep neural networks.
method Relational trust distance and descent lemma for neural networks.
result New learning rule requires minimal learning rate tuning.
Study on the limits of learning HMM parameters under various conditions.
problem Understanding the conditions under which hidden Markov model parameters can be learned.
method Nonasymptotic minimax upper and lower bounds, thresholds analysis.
result Nonasymptotic minimax bounds match up to constants, showing learnable thresholds.
A method learns common bias for multiple low-variance tasks without hyper-parameter tuning.
problem Learning common bias for multiple low-variance tasks without manual tuning.
method Two variants of online learning methods (aggressive and lazy) that update bias after each datapoint or at the end of each task.
result Across-tasks regret bound derived for the method, showing faster rates for aggressive variant and standard rates for lazy variant.
This paper analyzes the robust growth rate of leveraged ETFs under uncertain parameters.
problem Analyzing the robust long-term growth rate of leveraged ETFs with uncertain parameters.
method Derive worst-case parameters using comparison principle and martingale extraction method.
result Explicitly obtain robust long-term growth rates under various models.
Stochastic version of proximal distance algorithm analyzed and validated.
problem Optimization of constrained estimation problems.
method Stochastic proximal distance algorithm, with convergence guarantees and finite error bounds.
result Convergence guarantees and finite error bounds for the first time.
Recommender systems can be formulated as a matrix completion problem, predicting ratings from user and item parameter vectors. Optimizing these parameters by subsampling data becomes difficult as the number of users and items grows. We develop a novel approach to generate all latent variables on demand from the ratings…
GradaGrad adapts learning rate non-monotonically, overcoming AdaGrad's step size decrease.
problem Fixed learning rate in AdaGrad leads to step size decrease over time.
method Introduces GradaGrad, which grows or shrinks the learning rate based on a different accumulation in the denominator.
result GradaGrad achieves similar convergence rates as AdaGrad and demonstrates non-monotone adaptation.
A new dynamic learning-rate scheme for optimization.
problem Manual tuning of learning rates in optimization is time-consuming and error-prone.
method Locally optimal stepsize estimation for dynamic learning-rate scheduling.
result Our method achieves comparable performance with minimal tuning.
Optimizing deep neural networks is largely thought to be an empirical process, requiring manual tuning of several hyper-parameters, such as learning rate, weight decay, and dropout rate. Arguably, the learning rate is the most important of these to tune, and this has gained more attention in recent works. In this paper…
Deep networks learn sparse hierarchical features without CoD.
problem Overparameterized deep networks struggle with the curse of dimensionality.
method Norm-constrained neural networks for sparse compositional functions.
result Deep networks can learn sparse hierarchical features efficiently.
Proposes a new method to learn meta-priors from data.
problem Improving learning systems with domain knowledge and controlling parameter learning rates.
method Hierarchical Empirical Bayes approach to decouple learning rates of features.
result Meta-prior learning improves performance and convergence time in various applications.
We investigate how the final parameters found by stochastic gradient descent are influenced by over-parameterization. We generate families of models by increasing the number of channels in a base network, and then perform a large hyper-parameter search to study how the test error depends on learning rate, batch size, a…