Adaptive SGD learns optimal batch size for strong convex functions.
problem Finding optimal batch size for SGD in practice.
method Adaptive SGD method that learns optimal batch size.
result Adaptive SGD exhibits nearly optimal performance in experiments.
Standard optimizers perform as well as LARS and LAMB at large batch sizes.
problem Comparing optimizers for neural network training at large batch sizes.
method Used standard optimizers like Nesterov momentum and Adam to match or exceed LARS and LAMB results.
result Standard optimizers can match or exceed LARS and LAMB at large batch sizes.
SGD's performance improves with critical batch size, minimizing SFO complexity.
problem Optimizing SGD's performance with batch size and learning rate.
method Analysis of SGD using constant and decaying learning rates, focusing on batch size effects.
result SGD with critical batch size minimizes SFO complexity.
New algorithm improves stability of optimization algorithms by adapting step-size.
problem Optimization algorithms' effectiveness is sensitive to step-size hyperparameters.
method Adapts NGN step-size method with momentum to enhance stability.
result Achieves convergence rate of O(1/√K) without restrictive assumptions.
A new scaling law predicts optimal batch size for training models.
problem Finding the optimal batch size for training models efficiently.
method Proposed a three-term scaling law that considers model size, training data, training steps, and batch size.
result The three-term law accurately recovers the optimal batch size and can be robustly fit with fewer training runs.
Optimal microlending group size is 5 people.
problem Determining the best group size for microlending to minimize default risk.
method Mathematical modeling with interacting forces and precise hypotheses.
result The optimal microlending group size is 5 people.
Improved variance reduction for Riemannian non-convex optimization with adaptive batch size.
problem Optimizing non-convex functions on Riemannian manifolds.
method Batch size adaptation in R-SVRG, R-SRG, and R-SPIDER.
result Achieves lower total complexities for various non-convex functions.
We make policy optimization algorithms batch size-invariant by decoupling proximal and behavior policies.
problem Some policy optimization algorithms do not have batch size-invariance, leading to inefficiencies.
method We decouple the proximal policy from the behavior policy to achieve batch size-invariance.
result Our approach makes policy optimization algorithms more efficient and allows them to use stale data more effectively.
Ensembles of random-feature models can't outperform a single large model.
problem Finding the optimal balance between model size and ensemble size.
method Deterministic equivalent risk estimates and scaling laws analysis.
result Ensembles of random-feature models achieve near-optimal performance only under specific conditions.
We propose an adaptive optimization method for deep learning that dynamically adjusts batch size.
problem Optimizing deep learning models with varying sensitivity to batch size selection.
method Adaptive regularization with dynamically determined stochastic batch size based on gradient norms.
result Our method outperforms state-of-the-art optimization algorithms in generalization and robustness.
Increasing the batch size is a popular way to speed up neural network training, but beyond some critical batch size, larger batch sizes yield diminishing returns. In this work, we study how the critical batch size changes based on properties of the optimization algorithm, including acceleration and preconditioning, thr…
We present the Integrated Size and Price Optimization Problem (ISPO) for a fashion discounter with many branches. Based on a two-stage stochastic programming model with recourse, we develop an exact algorithm and a production-compliant heuristic that produces small optimality gaps. In a field study we show that a distr…
Adaptive step-size improves optimization in complex geometries.
problem Optimizing functions with non-Euclidean geometries.
method Adaptive step-size strategy for optimization algorithms.
result Guaranteed convergence for Adaptive Conditional Gradient Descent.
A simple block configures optimal kernel sizes for time series classification.
problem Choosing the right kernel size for time series classification.
method Proposes Omni-Scale block (OS-block) with kernel sizes determined by prime numbers.
result Models with OS-block achieve state-of-the-art performance on time series benchmarks.
New adaptive step-size method for convex optimization without tuning.
problem Optimizing convex functions efficiently with stochastic gradients.
method Adapted Adaptive Gradient Descent Without Descent to stochastic setting.
result Stochastic gradient descent converges under various assumptions.
Study finds optimal vocabulary size for neural machine translation.
problem Imbalanced class distribution in language data affects NMT performance.
method Casts NMT as a classification task, analyzes vocabulary sizes, and tests multiple languages.
result Certain vocabulary sizes outperform others, explaining NMT performance.
Seesaw optimizes training by balancing learning rate and batch size, accelerating model pretraining.
problem Optimizing training efficiency for large language models with adaptive optimizers.
method Develops a principled framework for batch-size scheduling, introducing Seesaw which multiplies learning rate by 1/√2 and doubles batch size.
result Empirically, Seesaw reduces wall-clock time by approximately 36% compared to cosine decay, matching theoretical limits.
Investor skill levels affect optimal portfolio size, study shows.
problem Optimal portfolio size for different skill levels of investors.
method Mathematical methods to study annual and continuous portfolio diversification, regression analysis.
result Strong investors should hold concentrated portfolios, poor investors should hold diversified portfolios.
Muon optimizes training efficiency by improving data retention at large batch sizes.
problem Improving training efficiency and data retention at large batch sizes.
method Introducing Muon, a second-order optimizer, and combining it with muP for efficient hyperparameter transfer.
result Muon outperforms AdamW in retaining data efficiency at large batch sizes, enabling more economical training.
Mini-batch stochastic gradient descent and variants thereof have become standard for large-scale empirical risk minimization like the training of neural networks. These methods are usually used with a constant batch size chosen by simple empirical inspection. The batch size significantly influences the behavior of the …
As neural networks become widely deployed in different applications and on different hardware, it has become increasingly important to optimize inference time and model size along with model accuracy. Most current techniques optimize model size, model accuracy and inference time in different stages, resulting in subopt…
Adaptive batch sizes improve active learning efficiency and flexibility.
problem Fixed batch sizes in active learning are inefficient due to dynamic cost-speed trade-offs.
method Probabilistic Numerics framework that adaptively changes batch sizes based on integration error and precision objectives.
result Significant enhancement in learning efficiency and flexibility across various applications.
A new algorithm improves efficiency and robustness of heuristic optimization in simulation-based problems.
problem Optimizing input parameters for stochastic simulation-based optimization.
method Reactive sample size algorithm based on parametric tests and indifference-zone selection.
result The reactive method improves efficiency and robustness of heuristic optimization techniques.
AdAdaGrad optimizes batch sizes for deep learning models, reducing the generalization gap.
problem The generalization gap between large-batch and small-batch training in deep learning.
method AdAdaGrad introduces adaptive batch size strategies derived from adaptive sampling methods.
result AdAdaGradNorm converges to a first-order stationary point with a rate of O(1/K) in K iterations.
New analysis reveals batch size effects on stochastic conditional gradient methods.
problem Understanding the role of batch size in stochastic conditional gradient methods.
method Deriving a new analysis focusing on momentum-based stochastic conditional gradient algorithms (e.g., Scion).
result Increasing batch size initially improves optimization accuracy but can degrade performance beyond a critical threshold.
The paper analyzes the risk of bagging regularized M-estimators under proportional asymptotics.
problem Characterizing the risk of ensemble estimators trained with subsamples and regularizers.
method Developed a consistent estimator for the risk of ensemble estimators under proportional asymptotics.
result Optimal subsample size k⋆ tends to be in the overparameterized regime for the full-ensemble estimator. Study ridge ensembles in proportional feature-to-sample size regime, proving risk equivalence and GCV consistency.
problem Characterizing and optimizing ridge ensembles in proportional feature-to-sample size regimes.
method Proportional asymptotics analysis, GCV for tuning, proving risk equivalence.
result Risk of optimal full ridgeless ensemble matches optimal ridge predictor's risk.
Proposes a neural network for learning step-size policies for L-BFGS optimization.
problem Optimizing step sizes for L-BFGS in large-scale problems.
method Neural network architecture using local iterate information, trained via stochastic optimization.
result Outperforms existing step size selection methods in training classifiers.
New SPS variant improves non-smooth optimization without small gradients.
problem Improving non-smooth optimization without small gradients.
method Safeguarded Stochastic Polyak Step Size (SPSsafe) for non-smooth optimization. result Rigorous convergence guarantees for non-smooth convex optimization without strong assumptions.
Develops a generalized version of Chung's Lemma for stochastic optimization methods.
problem Establishing asymptotic convergence rates for stochastic optimization methods under various step size rules.
method Generalized version of Chung's Lemma for a broader family of step size rules.
result Demonstrates tight non-asymptotic convergence rates for various stochastic methods.
Variance-reduced algorithms, although achieve great theoretical performance, can run slowly in practice due to the periodic gradient estimation with a large batch of data. Batch-size adaptation thus arises as a promising approach to accelerate such algorithms. However, existing schemes either apply prescribed batch-siz…
This paper explores the limits of large batch sizes in deep learning.
problem Understanding the optimal batch size for deep learning models.
method Detailed numerical optimization and experimental analysis of large batch sizes.
result Improvement of 18% top-1 test accuracy with an optimized batch size recipe.
In this paper, we propose a novel approach to automatically determine the batch size in stochastic gradient descent methods. The choice of the batch size induces a trade-off between the accuracy of the gradient estimate and the cost in terms of samples of each update. We propose to determine the batch size by optimizin…
Random Function Descent improves optimization in high dimensions.
problem Lack of effective optimization methods in high-dimensional spaces.
method Introducing a 'random function' framework to optimize classical optimization problems.
result Random Function Descent (RFD) is a scalable optimization method that bridges Bayesian and classical optimization.
Adaptive batch size schedules improve language model training efficiency and generalization.
problem Dilemma of choosing batch sizes in large-scale model training.
method General-purpose adaptive batch size schedules compatible with data and model parallelism.
result Adaptive batch size schedules outperform constant batch sizes and heuristic warmup schedules.
Study optimizes step size for Metropolis algorithm in non-identifiable cases.
problem Optimizing step size for Metropolis algorithm in non-identifiable models.
method Analytical derivation of average acceptance rate for non-identifiable cases.
result Developed optimization principle for step size based on average acceptance rate.
A note on setting swap parameters for traders.
problem Determining optimal slippage parameters and trade size for wealth swapping.
method Theoretical solution and framework for optimal slippage parameters and trade size.
result Offers a method to solve optimal slippage parameters and trade size for wealth swapping.
New method improves model accuracy in Byzantine-robust distributed learning by optimizing batch size.
problem Reduces model accuracy drop due to large variance of stochastic gradients in Byzantine-robust distributed learning.
method Proposes ByzSGDnm, a novel BRDL method that uses normalized momentum to mitigate accuracy drop in large batch sizes.
result The optimal batch size increases with the fraction of Byzantine workers, leading to better model accuracy under Byzantine attacks.
Downsampling can improve generalization in ridgeless linear regression, especially with optimal sketching size.
problem Improving generalization in ridgeless linear regression with limited data.
method Investigating the effects of downsampling on the sketched ridgeless least square estimator in the proportional regime.
result Optimal sketching size minimizes out-of-sample prediction risks and stabilizes risk curves.
Optimal regularization can prevent the double descent phenomenon in learning models.
problem The double descent phenomenon in learning models, where test performance is non-monotonic in sample size and model size.
method Theoretical and empirical study of optimal ℓ2 regularization for linear regression models and neural networks. result Optimally-tuned ℓ2 regularization achieves monotonic test performance for certain models and mitigates the double descent phenomenon for more general models. In this paper we study a family of variance reduction methods with randomized batch size---at each step, the algorithm first randomly chooses the batch size and then selects a batch of samples to conduct a variance-reduced stochastic update. We give the linear convergence rate for this framework for composite functions…
We analyze the learning properties of the stochastic gradient method when multiple passes over the data and mini-batches are allowed. We study how regularization properties are controlled by the step-size, the number of passes and the mini-batch size. In particular, we consider the square loss and show that for a unive…
In this work, we provide a framework linking microstructural properties of an asset to the tick value of the exchange. In particular, we bring to light a quantity, referred to as implicit spread, playing the role of spread for large tick assets, for which the effective spread is almost always equal to one tick. The rel…
Proposes an exponentially increasing step-size for faster parameter estimation in statistical models.
problem Slow convergence of gradient descent in locally convex loss functions.
method Exponentially increasing step-size in gradient descent algorithm.
result Converges linearly to optimal solution under homogeneous assumptions.
This work provides a scaling rule for model EMA optimization across batch sizes.
problem Training dynamics and performance differences across batch sizes when using model EMA.
method Developed a scaling rule for model EMA optimization, demonstrating its validity across various architectures and data modalities.
result Enabled SSL methods like BYOL to train at larger batch sizes without performance degradation.
Optimal portfolios are formed by combining momentum, size, and volatility characteristics, enhancing utility for all investors.
problem Estimation error in forming optimal portfolios from characteristics.
method Maximizing an in-sample loss function that is more concave than the utility function, linking weights to characteristics.
result Optimal portfolios with significantly higher certainty equivalents than benchmarks for all investors.
Optimal scaling found to depend on operator norm across large models and datasets.
problem Lack of unifying principle for optimal hyperparameter scaling across models and datasets.
method Discovered that optimal scaling is conditioned on the operator norm of the output layer.
result The optimal learning rate/batch size pair (η∗,B∗) consistently has the same operator norm value. New convergence results for NGVI with various step sizes and sample sizes.
problem Understanding convergence of stochastic NGVI for various schedules.
method Projected stochastic NGVI for exponential family variational distributions.
result Geometric convergence and $\mathcal{O}\left(\frac{1}{T^ρ}
ight)$ rates for different schedules.