New scaling laws optimize model size, training, and inference for better performance.
problem Trade-off between model size and inference cost in modern LLMs.
method Train-to-Test (T2) scaling laws that jointly optimize model size, training tokens, and inference samples. result Optimal pretraining decisions shift into overtraining regime, leading to stronger performance.
Optimizer choice affects neural scaling laws, changing the exponent α.
problem The exponent α in neural scaling laws L(N)∝N−α varies with the optimizer used. method Controlled random-feature regression experiments with five optimizer variants and six spectral conditions.
result Preconditioned optimizers yield steeper scaling (larger α), with the α-shift increasing across most of the tested spectral range. 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. Classical scaling is shown to be optimal under various noisy conditions.
problem Consistency of classical scaling under general noise conditions.
method Established using finite fourth moments of noise, derived convergence rates, and matching minimax lower bounds.
result Classical scaling achieves minimax optimality in recovering true configuration from noisy dissimilarities.
Efficiently solves large-scale robust portfolio optimization problems.
problem High computational demands in large-scale robust portfolio optimization.
method Extended supporting hyperplane approximation for distributionally robust portfolio problems.
result Significantly reduces computational time from several thousand seconds to just a few.
Bayesian optimization speeds up bioprocess development across scales.
problem Costly and complex bioprocess development across scales and biocatalyst selection.
method Multi-fidelity batch Bayesian optimization framework integrating Gaussian Processes and mixed-variable optimization.
result Reduction in experimental costs and increased yield in bioprocess optimization.
BanditLP optimizes personalized recommendations for large-scale systems.
problem Optimizing personalized recommendations for large-scale systems with constraints.
method Unified neural Thompson Sampling for learning and large-scale linear programming for action selection.
result Consistent gains over strong baselines in experiments and business win in LinkedIn's email marketing system.
In this paper we combine two important extensions of ordinary least squares regression: regularization and optimal scaling. Optimal scaling (sometimes also called optimal scoring) has originally been developed for categorical data, and the process finds quantifications for the categories that are optimal for the regres…
We derive scaling laws for optimizing neural networks in hardware.
problem Optimizing the large parameter space of neural networks in hardware.
method Analytical derivation of scaling laws for Coordinate Descent optimization.
result Convergence is exponential and scales linearly with the number of neurons.
Study scaling of optimal solutions for reliability constraints in resource provisioning.
problem Achieving high reliability in resource provisioning under stringent requirements.
method Chance-constrained optimization, distributionally robust optimization, f-divergence balls, line search.
result Correct scaling properties of optimal decisions are preserved by using appropriate f-divergence balls, leading to conservative yet near-optimal solutions.
New phases identified in neural scaling laws with compute limits.
problem Understanding neural scaling laws under compute constraints.
method Solved neural scaling model with stochastic gradient descent, derived loss curves, analyzed model-parameter-count phases.
result Identified 4 phases (+3 subphases) in data-complexity/target-complexity phase-plane, derived exponents.
Unintended effects from scaling neural network outputs with adaptive learning rates.
problem Adaptive learning rate optimization's behavior is altered by output scaling, leading to misinterpretation.
method Presented a modified optimization algorithm to mitigate unintended effects.
result Adaptive learning rate's effectiveness is significantly impacted by output scaling, especially for small scaling factors.
This study reveals the critical role of scale vectors in large language models, improving optimization and expressivity.
problem Understanding and optimizing the scale vectors in large language models.
method Systematic study of scale vectors from expressivity, optimization, and architectural perspectives; theoretical and empirical analysis of weight decay; proposing and evaluating improvements.
result Scale vectors improve optimization through a self-amplifying preconditioning effect and are beneficial for expressivity in certain architectures.
We introduce a few variants on Frank-Wolfe style algorithms suitable for large scale optimization. We show how to modify the standard Frank-Wolfe algorithm using stochastic gradients, approximate subproblem solutions, and sketched decision variables in order to scale to enormous problems while preserving (up to constan…
New algorithm reduces robust optimization scale for better constraint satisfaction.
problem Finding robust solutions to optimization problems with unknown constraints.
method Empirical domain reduction to determine robustness scale.
result Our algorithm's scale is less affected by parameter dimensionality.
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.
New framework explains fast transfer of hyperparameters across model scales.
problem Understanding and optimizing hyperparameters for large-scale models.
method Developed a conceptual framework for HP transfer across scale, showing fast transfer is equivalent to useful transfer for compute-optimal grid search.
result Fast transfer of hyperparameters is equivalent to useful transfer for compute-optimal grid search, offering asymptotic computational advantage.
New algorithm reduces regret bounds for Bayesian optimization with unknown hyperparameters.
problem Optimizing black-box functions with unknown hyperparameters, especially length scale.
method Length Scale Balancing (LB) - aggregating multiple surrogate models with varying length scales.
result LB achieves a regret bound only logaritically away from the oracle algorithm.
Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization problem in a Markovian setting under each single scale, the slow one in [Fouque and…
This paper improves traditional Markowitz optimization by considering variance at multiple time scales.
problem Traditional Markowitz optimization limits to a single time scale, ignoring variance across different frequencies.
method Introduces multifrequency optimization allowing specification of target Hurst exponents across multiple time scales.
result Effective risk management strategy that aligns with investor preferences at various time scales.
New analysis of stochastic approximation with non-expansive mappings.
problem Finite-time analysis of two-time-scale stochastic approximation with non-expansive mappings.
method Studied two-time-scale stochastic approximation algorithms with non-expansive mappings and projection steps.
result Last-iterate mean square residual error decays at a rate O(1/k1/4−ε). 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.
We are motivated by large scale submodular optimization problems, where standard algorithms that treat the submodular functions in the \emph{value oracle model} do not scale. In this paper, we present a model called the \emph{precomputational complexity model}, along with a unifying memoization based framework, which l…
Two approaches scale up DNN optimization for diverse edge devices.
problem Optimizing DNNs for edge devices with varying performance requirements.
method Reuse performance predictors on proxy devices and build scalable predictors.
result Optimized DNN designs for many different edge devices without lengthy optimization.
AdamP optimizes momentum-based optimizers for scale-invariant weights, improving model performance.
problem Premature decay of effective step sizes in momentum-based optimizers for scale-invariant weights.
method Proposes SGDP and AdamP to eliminate the radial component at each optimizer step, preserving convergence properties.
result Uniform gains across multiple benchmarks, improving model performance.
The optimal dividend problem by De Finetti (1957) has been recently generalized to the spectrally negative Lévy model where the implementation of optimal strategies draws upon the computation of scale functions and their derivatives. This paper proposes a phase-type fitting approximation of the optimal strategy. We con…
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. Improved bounds for non-linear SA with fast convergence.
problem Stochastic approximation with non-linear mappings and multiple time scales.
method Mean squared error bounds with O(1/k) rate for contractive mappings. result First O(1/k) rate for non-linear two-time-scale SA without additional smoothness assumptions. Meta-SAGE improves deep RL scalability for CO tasks by adapting pre-trained models to larger-scale problems.
problem Improving scalability of deep reinforcement learning models for combinatorial optimization tasks.
method Meta-SAGE combines a scale meta-learner and scheduled adaptation with guided exploration to adjust model parameters for larger-scale problems.
result Meta-SAGE outperforms previous methods and significantly improves scalability in CO tasks.
New algorithms optimize risk for large datasets, improving efficiency.
problem Optimizing risk for large datasets with robust methods.
method Proposed algorithms for distributionally robust optimization with CVaR and χ² divergence uncertainty sets.
result Algorithms require independent gradient evaluations of training set size and parameters, suitable for large-scale applications.
Model predicts neural network performance scaling laws across various factors.
problem Understanding the performance of neural networks across different training factors.
method Random feature model trained with gradient descent, analyzing compute-optimal scaling laws.
result Predicts asymmetric compute-optimal scaling rule and behavior of training and test loss gap.
Proposes MamBO for efficient high-dimensional large-scale optimization.
problem High-dimensional and large-scale optimization problems in machine learning and simulation.
method Combines subsampling and subspace embeddings with model aggregation to address uncertainty in surrogate models.
result Improves robustness of Bayesian optimization algorithm and achieves superior performance.
New adaptive first-order methods improve on quasi-Newton variants.
problem Designing efficient gradient methods for practical applications.
method Online scaled gradient methods (OSGM) with new adaptive methods OSGM-Best.
result OSGM-Best matches quasi-Newton variants but requires less memory and cheaper iterations.
It is well known that neural networks with rectified linear units (ReLU) activation functions are positively scale-invariant. Conventional algorithms like stochastic gradient descent optimize the neural networks in the vector space of weights, which is, however, not positively scale-invariant. This mismatch may lead to…
New method predicts and optimizes test-time scaling for LLMs.
problem Lack of principled guidance on scaling LLMs efficiently.
method Tail-guided search to predict and allocate compute.
result SLG Search achieves higher rewards with less compute.
Sharp theory of neural network scaling laws for hierarchical targets.
problem Learning hierarchical multi-index models in neural networks.
method Sharp information-theoretic scaling laws derived for two-layer neural networks.
result Optimal rates achieved by a simple spectral estimator.
SignSGD outperforms SGD in linear regression with optimal scaling laws under PLRF model.
problem Improving linear regression performance with signSGD under power-law random features.
method Analysis of signSGD risk under PLRF model, comparison with SGD, identification of unique effects.
result SignSGD can have a steeper compute-optimal slope than SGD in noisy regimes, especially with WSD schedule.
Optimal scaling for proximal MALA in high dimensions confirmed.
problem Optimizing sampling efficiency in high-dimensional target densities.
method Introduced and analyzed the proximal MALA algorithm, showing it maintains optimal scaling.
result Proximal MALA achieves optimal scaling in high dimensions with an average acceptance probability of 0.574.
Introduces new performance measures using scaled utility functions.
problem Performance measurement in financial contexts.
method Certainty equivalents defined via scaled utility functions, well-posed portfolio optimization problem under generic conditions.
result Link between portfolio dynamics, benchmark process, and utility function choice in the long-run setting.
Paper proposes a faster SPIDER-EM variant for large-scale nonconvex optimization.
problem High computational cost of EM algorithm in large-scale learning.
method Extension of SPIDER-EM for nonconvex finite-sum optimization problems.
result Achieves state-of-the-art complexity bounds and linear convergence under certain conditions.
The optimal capital structure model with endogenous bankruptcy was first studied by Leland (1994) and Leland and Toft (1996), and was later extended to the spectrally negative Levy model by Hilberink and Rogers (2002) and Kyprianou and Surya (2007). This paper incorporates the scale effects by allowing the values of ba…
Optimizing full likelihoods adapts loss scales and shapes for robust modeling.
problem Rigid loss functions limit model adaptability and robustness.
method Optimize full likelihoods with adjustable parameters.
result Adaptive tuning of loss scales and shapes improves model robustness.
TiAda adapts adaptive gradient methods for nonconvex minimax optimization.
problem Nonconvex minimax optimization challenges in achieving convergence.
method TiAda is a time-scale adaptive GDA algorithm for nonconvex minimax optimization.
result TiAda achieves near-optimal complexities in deterministic and stochastic settings.
New optimizers control network width scaling, improving stability and transfer across different model sizes.
problem Designing stable optimizers for networks of varying widths.
method Interpreting optimizers as steepest descent under mean-normalized operator norms, enabling layerwise composability and width-independent bounds.
result New optimizers like row normalization and column normalization provide stable learning-rate transfer across different model widths.
Sharp feature transitions revealed in extensive-width networks.
problem Learning hierarchical features from noisy queries in large networks.
method Information-theoretic analysis and heuristic decoupling argument.
result Sequential phase transitions in feature learnability and effective width.
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local quadratic approximation, and hence, allows incorporating curvature information to sp…
This paper improves linear system solving by optimizing matrix diagonal scaling.
problem Improving the condition number of a matrix for faster iterative methods.
method Left or right diagonal rescaling of the matrix A, with new bounds and algorithms.
result Jacobi preconditioning reduces A's condition number to within a quadratic factor of the best possible scaling.
QS-BO optimizes functions using only rank-based feedback.
problem Optimizing expensive functions with unreliable or unavailable metric values.
method Quantile-scaling pipeline to convert ranks into Gaussian targets.
result QS-BO consistently achieves lower objective values and is statistically significant.