Deviation inequalities for stochastic approximation methods.
problem Establishing bounds on the deviation of stochastic approximation methods.
method Martingale approximation method for separately Lipschitz functions.
result Established various deviation inequalities for stochastic approximation by averaging and minimization.
Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e.g., sparsity) efficiently. In this paper, we propose a novel accelerated dual-averaging primal-dual algorithm for minimizing a composite convex function. We also derive a stoch…
We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging method with variance reduction. Our methods generate a sparser solution than the…
We present explicit formulas - that are also computer code - for 101 real-life quantitative trading alphas. Their average holding period approximately ranges 0.6-6.4 days. The average pair-wise correlation of these alphas is low, 15.9%. The returns are strongly correlated with volatility, but have no significant depend…
FP-BMA improves generalization by encouraging flat posteriors in Bayesian Model Averaging.
problem Lack of flat posterior in approximate Bayesian inference methods hinders effective Bayesian Model Averaging.
method Proposes Flat Posterior-aware Bayesian Model Averaging (FP-BMA) and Flat Posterior-aware Bayesian Transfer Learning schemes.
result FP-BMA successfully captures flat posteriors, improving generalization performance.
Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.
problem Proving sharper concentration bounds for MCERA.
method Deriving new bounds through self-bounding functions and concentration of measure.
result Novel bounds depend on data-dependent quantities, improving over standard methods.
We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sa…
KL regularization helps RL algorithms by implicitly averaging q-values.
problem Understanding why KL regularization improves RL performance.
method An approximate value iteration scheme, studying KL and entropy regularization.
result Strong performance bound combining linear horizon dependency and averaging effect of estimation errors.
New TD method stabilizes average-reward learning.
problem Stability issues in average-reward TD learning.
method Implicit fixed point update for average-reward TD(λ). result Improved numerical stability and broader step-size range.
Theory and methods to mitigate omitted variable bias in causal machine learning.
problem Mitigating omitted variable bias in causal machine learning models.
method Developed a general theory and flexible statistical inference methods for bounding and testing the magnitude of omitted variable bias.
result Simple plausibility judgments can bound the magnitude of omitted variable bias in complex, nonlinear models.
We propose a practical approach based on federated learning to solve out-of-domain issues with continuously running embedded speech-based models such as wake word detectors. We conduct an extensive empirical study of the federated averaging algorithm for the "Hey Snips" wake word based on a crowdsourced dataset that mi…
We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an unbiased gradient estimator of the empirical average loss. In contrast, we develop a co…
Deep ensembles mimic Bayesian averaging with learned priors.
problem Quantifying uncertainty in neural networks.
method Showed deep ensembles perform exact Bayesian averaging with an implicitly learned data-dependent prior.
result Deep ensembles are Bayesian and provide an explanation for their strong empirical performance.
Ensemble learning is a method of combining multiple trained models to improve model accuracy. We propose the usage of such methods, specifically ensemble average, inside Convolutional Neural Network (CNN) architectures by replacing the single convolutional layers with Inner Average Ensembles (IEA) of multiple convoluti…
New method SF-AdamW trains large models without decay phases or memory overhead.
problem Inadequate fixed compute budgets for large-scale training.
method Schedule-Free (SF) method revisited and refined.
result SF-AdamW effectively navigates loss landscape without decay phases or memory overhead.
On-line portfolio selection has attracted increasing interests in machine learning and AI communities recently. Empirical evidences show that stock's high and low prices are temporary and stock price relatives are likely to follow the mean reversion phenomenon. While the existing mean reversion strategies are shown to …
A new method for averaging model predictions using minimum divergence.
problem Improving model averaging methods, especially in small samples.
method Minimum divergence framework for model weight calculation.
result Empirically outperforms standard model averaging methods.
Paper introduces stability in model averaging and proposes a L2-penalty method.
problem Theoretical properties of model averaging from stability perspective.
method Introduces stability, defines asymptotic empirical risk minimizer, and proposes L2-penalty model averaging method.
result Proposed L2-penalty method ensures stability and consistency under reasonable conditions.
The paper tackles learning to control systems with unknown parameters using Brownian noise.
problem Learning to control systems with unknown parameters.
method Proposes algorithms based on moving empirical averages and integrates statistical methods with stochastic control theory.
result Achieves a logarithmic expected regret rate.
New algorithm uses Whittle index to improve Q-learning for restless bandits.
problem Optimizing decision-making in multiarmed restless bandits with average reward.
method Introduces a novel reinforcement learning algorithm combining Q-learning and Whittle index policy.
result Demonstrates significant computational gains and excellent empirical performance.
The variance reduction class of algorithms including the representative ones, SVRG and SARAH, have well documented merits for empirical risk minimization problems. However, they require grid search to tune parameters (step size and the number of iterations per inner loop) for optimal performance. This work introduces `…
This paper presents a methodology for selecting the mini-batch size that minimizes Stochastic Gradient Descent (SGD) learning time for single and multiple learner problems. By decoupling algorithmic analysis issues from hardware and software implementation details, we reveal a robust empirical inverse law between mini-…
Improved generalization with iterate averaging and adaptive algorithms.
problem Enhancing model generalization performance in high-dimensional settings.
method Gaussian process perturbation model, combine IA with large learning rates and regularisation, less frequent averaging, adaptive gradient methods.
result Iterate averaging with adaptive algorithms significantly outperforms SGD on various datasets.
Adversarial robustness has become an important research topic given empirical demonstrations on the lack of robustness of deep neural networks. Unfortunately, recent theoretical results suggest that adversarial training induces a strict tradeoff between classification accuracy and adversarial robustness. In this paper,…
This work analyzes benefits and limitations of data augmentation and feature averaging in deep learning models.
problem Theoretical understanding of incorporating invariance into deep learning models is lacking.
method Data augmentation and feature averaging are analyzed in the context of invariance in deep learning.
result Training with data augmentation leads to better estimates of risk and gradients, and feature averaging reduces generalization error with convex losses.
In many high-dimensional estimation problems the main task consists in minimizing a cost function, which is often strongly non-convex when scanned in the space of parameters to be estimated. A standard solution to flatten the corresponding rough landscape consists in summing the losses associated to different data poin…
The paper examines the consistency of item embeddings in recommendation systems.
problem The relevance of averaging item embeddings for user or concept representation.
method Proposes an expected precision score to measure consistency and analyzes it theoretically and empirically.
result Real-world averages are less consistent for recommendation compared to theoretical assumptions.
Previous studies of the stock price response to individual trades focused on single stocks. We empirically investigate the price response of one stock to the trades of other stocks. How large is the impact of one stock on others and vice versa? -- This impact of trades on the price change across stocks appears to be tr…
Averaged SGD optimizes a smoothed objective, leading to better generalization.
problem Improving generalization performance in machine learning models.
method Analyzed the smoothed objective function of SGD and proved that averaged SGD can optimize this smoothed function efficiently.
result Averaged SGD can efficiently optimize a smoothed objective, leading to better generalization.
We present a method to obtain the average and the typical value of the number of critical points of the empirical risk landscape for generalized linear estimation problems and variants. This represents a substantial extension of previous applications of the Kac-Rice method since it allows to analyze the critical points…
PACE optimizes training for averaged language models, improving performance.
problem How to optimize training for averaged language model iterates.
method Formulated as an optimal-control problem, solved for minimizing error of the average with a penalty on intervention size.
result PACE improves the limiting squared error of the iterate-average estimator by an arbitrarily large factor on some instances.
In structural credit risk models, default events and the ensuing losses are both derived from the asset values at maturity. Hence it is of utmost importance to choose a distribution for these asset values which is in accordance with empirical data. At the same time, it is desirable to still preserve some analytical tra…
In this note, we present a new averaging technique for the projected stochastic subgradient method. By using a weighted average with a weight of t+1 for each iterate w_t at iteration t, we obtain the convergence rate of O(1/t) with both an easy proof and an easy implementation. The new scheme is compared empirically to…
Improving optimization for iterate-averaged language models
problem How to optimize the averaged model returned by Language Model pipelines
method Formulating optimizer design as an optimal-control problem
result Proven convergence rate and strict improvement in squared error
The paper improves Monte Carlo methods for optimization problems.
problem Efficiently solving optimization problems with biased Monte Carlo estimators.
method Introduces Multilevel Monte Carlo (MLMC) within Sample Average Approximation (SAA).
result Establishes uniform convergence and sample complexity for MLMC in SAA.
New algorithms optimize spectral risk measures, improving interpolation between average and worst-case performance.
problem Optimizing spectral risk measures for learning systems.
method Developed stochastic algorithms to optimize spectral risk measures by characterizing their subdifferential and addressing challenges like biasedness of subgradient estimates and non-smoothness.
result Our approach outperforms out-of-the-box stochastic subgradient and dual averaging methods in optimizing spectral risk measures.
Proposes a method to estimate causal effects of continuous treatments using instrumental variables.
problem Estimating causal effects of continuous treatments in the presence of unmeasured confounders.
method Introduces a novel framework using instrumental variables and a uniform regular weighting function to identify and estimate average dose-response functions.
result Establishes the asymptotic properties of the proposed methods for estimating average dose-response functions.
New algorithm for federated learning with non-smooth regularizers.
problem Federated Learning with non-smooth composite optimization problems.
method Proposed Federated Dual Averaging (FedDualAvg) algorithm to overcome convergence issues.
result FedDualAvg outperforms other algorithms in federated composite optimization.
This work proposes a model averaging method for SVM that avoids redundant covariates and achieves asymptotic optimality.
problem Redundant covariates impair SVM performance in high-dimensional settings.
method Frequentist model averaging procedure for SVM using cross-validation to select optimal weights.
result The proposed method achieves asymptotic optimality in SVM model averaging.
We study the problem of learning Bayesian network structures from data. We develop an algorithm for finding the k-best Bayesian network structures. We propose to compute the posterior probabilities of hypotheses of interest by Bayesian model averaging over the k-best Bayesian networks. We present empirical results on s…
This paper strengthens the computational separation between multimodal and unimodal learning, showing unimodal learning is hard on typical instances.
problem Theoretical justification for empirical success of multimodal machine learning.
method Introduced a stronger average-case computational separation between unimodal and multimodal learning.
result For typical instances, unimodal learning is computationally hard, while multimodal learning is easy.
Proposes a new framework for balancing average- and worst-case performance in machine learning.
problem Robustness issues in machine learning, especially in safety-critical domains.
method Probabilistic robustness framework that balances average- and worst-case performance.
result Effective algorithm balances average- and worst-case performance with lower computational cost.
The study examines how averaging data improves model performance.
problem Understanding the generalization gap in machine learning models.
method Data averaging, covariance analysis, and stochastic gradient descent (SGD) noise modeling.
result A modified generalization gap is always non-negative for a large class of model parameter distributions.
Paper assesses error estimates of Random Forests classification.
problem Quantitative assessment of Random Forests error estimates.
method Theoretical and empirical investigation of various error estimation methods.
result Random Forests' error estimates are closer to true error rate than average prediction error.
Proposes a new method for deep ensembles that improves accuracy and calibration.
problem Improving accuracy and calibration of deep ensembles.
method Estimates confusion matrices of ensemble members and weighs them according to their inferred performance.
result Empirically shows superiority of soft Dawid Skene over ensemble averaging.
GPA improves LLM training speed by 8.71% for Llama-160M models.
problem Training Large Language Models (LLMs) with high memory overhead and slow convergence.
method Generalized Primal Averaging (GPA) extends Nesterov's method to eliminate memory-intensive two-loop structure.
result GPA achieves up to 10.13% speedup over AdamW in training Llama-1B model.
New generalization concept considers distribution of errors, not just average error.
problem Classical generalization fails to capture distributional differences in classifier outputs.
method Formal conjectures about distributional generalization based on model architecture, training procedure, and data distribution.
result Distributional generalization can be expected in specific conditions, as evidenced by empirical results.
Backward exploration reduces sample complexity in policy evaluation.
problem Empirical policy evaluation in reinforcement learning.
method Backward exploration algorithms from high-cost states.
result Reduced average-case sample complexity to O(logS).