Paper explores weighted averaging schemes for SGD, achieving asymptotic normality and optimality.
problem Improving convergence of SGD in various settings.
method Develops a general weighted averaging scheme for SGD and establishes asymptotic normality.
result Establishes asymptotic normality and optimality of weighted averaged SGD solutions.
A new averaging scheme improves stochastic gradient methods.
problem Improving the performance of stochastic gradient descent.
method Proposes a weighted averaging scheme with decaying weights.
result The method has a regularizing effect equivalent to ridge regression.
Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness assumptions, which do not apply to many modern applications of SGD with non-smooth object…
Increasing iterate averaging improves convergence rates for saddle-point problems.
problem Solving saddle-point problems efficiently.
method Increasing iterate averaging schemes applied to various first-order methods.
result Increasing iterate averaging preserves the O(1/T) convergence rate with no additional assumptions or overhead. This paper analyzes SGD with increasingly weighted averaging for optimization and generalization.
problem Improving optimization and generalization for non-strongly convex objectives.
method Comprehensive analysis of increasingly weighted averaging schemes for convex, strongly convex, and non-convex objectives.
result The weight α affects both optimization and generalization errors, revealing a trade-off. In this paper, a standard PDE for the pricing of arithmetic average strike Asian call option is presented. A Crank-Nicolson Implicit Method and a Higher Order Compact finite difference scheme for this pricing problem is derived. Both these schemes were implemented for various values of risk free rate and volatility. Th…
We introduce a new wavelet transform suitable for analyzing functions on point clouds and graphs. Our construction is based on a generalization of the average interpolating refinement scheme of Donoho. The most important ingredient of the original scheme that needs to be altered is the choice of the interpolant. Here, …
New averaging technique speeds up Newton method convergence.
problem Superlinear convergence of stochastic Newton methods with noisy Hessians.
method Hessian averaging to reduce noise and maintain superlinear convergence.
result Hessian averaging achieves superlinear convergence with a non-asymptotic rate.
Q-learning for average cost MDPs gets a concentration bound.
problem Finding bounds for Q-learning in average cost MDPs.
method Derives a concentration bound using shortest path problem equivalence.
result Numerical comparison with relative value iteration shows the bound's effectiveness.
New aggregation methods improve robustness and efficiency in distributed learning.
problem Outliers and malicious agents compromise traditional averaging in distributed learning.
method Developed statistically efficient and robust aggregation schemes based on median and trimmed mean variations.
result Achieved higher sample efficiency compared to traditional robust aggregation schemes.
New SVRG and SARAH schemes reduce tuning effort for variance reduction.
problem Optimal performance of SVRG and SARAH requires tuning of parameters.
method Introduces Barzilai-Borwein step sizes, averaging, and adaptive inner loop length.
result Improves SVRG, SARAH, and BB variants' convergence rates and performance.
Study classifies stock price data into stationary and non-stationary periods for mechanical trading.
problem Classifying stock price fluctuations into stationary and non-stationary periods for trading.
method Stationarity analysis using KM2O-Langevin theory and trend-based indicators for stationary periods, oscillator-based indicators for non-stationary periods. result Back testing confirms the strategy is a safe trading strategy with small maximum drawdown.
The definition of the covariant space-time averaging scheme for the objects (tensors, geometric objects, etc.) on differentiable metric manifolds with a volume n-form, which has been proposed for the formulation of macroscopic gravity, is analyzed. An overview of the space-time averaging procedure in Minkowski spacetim…
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.
This work analyzes mini-batching and averaging in SGD for least squares regression.
problem Improving parallelization and reducing variance in SGD for least squares regression.
method Characterizes mini-batching and tail-averaging for least squares regression, providing non-asymptotic excess risk bounds.
result Proves near-linear parallelization speedups and minimax risk for SGD with nearly the same number of updates as batch gradient descent.
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.
New method approximates CVaR with less data for heavy-tailed risks.
problem Lack of data for accurate CVaR approximation in heavy-tailed distributions.
method Importance sampling based extrapolation for heavy-tailed distributions.
result Statistically consistent approximations with reduced data requirements.
Deep-FExt uses machine learning to improve vessel segmentation and centerline detection in medical images.
problem Improving vessel segmentation and centerline detection in medical images.
method Inception models for feature extraction, multi-scale and multi-layer convolutional operators, fully convolutional networks.
result Deep-FExt outperforms existing schemes with high Dice scores on DRIVE and STARE datasets.
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…
Enhances trading signals using image analysis and weighted moving averages.
problem Improving price trend trading strategies in financial markets.
method Image-induced importance weights applied to weighted moving averages of trading signals.
result Significant enhancement of price trend trading signals with improved portfolio selection.
A novel fully asynchronous scheme for distributed reinforcement learning over networks.
problem Policy evaluation in distributed reinforcement learning over networks.
method Design of a stochastic average gradient (SAG) based distributed algorithm and push-pull augmented graph approach.
result The proposed algorithm converges at a linear rate of \(\mathcal{O}(c^k)\) with \(c\in(0,1)\) and \(k\) increasing by one per node update.
In this work we develop a new algorithm for regularized empirical risk minimization. Our method extends recent techniques of Shalev-Shwartz [02/2015], which enable a dual-free analysis of SDCA, to arbitrary mini-batching schemes. Moreover, our method is able to better utilize the information in the data defining the ER…
The paper studies risk-sensitive learning schemes and provides learning bounds for empirical OCE minimizers.
problem Risk-sensitive learning aims to minimize risk-averse measures of loss.
method Proposes learning bounds for empirical OCE minimizers based on Rademacher average and variance.
result Provides two learning bounds on the performance of empirical OCE minimizers.
PEAK tests means of multiple data streams with sequential betting.
problem Testing means of multiple data streams with nonparametric methods.
method Sequential, nonparametric testing using a betting scheme.
result PEAK provides up to 85% reduction in samples for stopping.
Paper analyzes how EMA improves SGD in linear regression.
problem Understanding the effectiveness of EMA in training deep learning models.
method Established risk bound for online SGD with EMA in linear regression.
result SGD with EMA has smaller variance error and exponentially decaying bias error.
SQR Averaging improves probabilistic electricity price forecasting.
problem Accurate short-term price forecasting in electricity markets.
method Smoothing Quantile Regression Averaging.
result SQR Averaging leads to profit increases of up to 3.5% in day-ahead power trading.
Paper proposes efficient communication scheme for statistical learning.
problem Efficiently conveying a statistical hypothesis from a client to a server.
method Joint training and source coding scheme with KL divergence constraints.
result Guarantees small average empirical risk, generalization error, and communication cost.
LASSO-PCA combines LASSO and PCA for automated forecast averaging.
problem Automating the selection of forecast averaging methods and tuning parameters.
method LASSO estimation combined with PCA, using information criteria for parameter selection.
result LASSO-PCA outperforms other methods in forecast error reduction.
Low-rank structure have been profoundly studied in data mining and machine learning. In this paper, we show a dense matrix X's low-rank approximation can be rapidly built from its left and right random projections Y1=XA1 and Y2=XTA2, or bilateral random projection (BRP). We then show power scheme can further…
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.
The paper uses potential functions to help reinforcement learning agents learn optimal policies.
problem Learning optimal stochastic policies in reinforcement learning.
method Augmenting the reward with potential functions and applying these to policy gradient algorithms.
result Potential-based reward shaping preserves optimality of stochastic policies and speeds up learning.
Strategy evaluation schemes are a crucial factor in any agent-based market model, as they determine the agents' strategy preferences and consequently their behavioral pattern. This study investigates how the strategy evaluation schemes adopted by agents affect their performance in conjunction with the market circumstan…
Study optimal reward schemes for inducing desired player performance in risky contests.
problem Designing optimal rewards to encourage desired performance levels in risky contests.
method Analyzed the optimal reward schemes for inducing average and specific rank performance.
result Optimal reward schemes can have surprising shapes, not just related to inequality.
Hybrid approach improves probabilistic forecasts for electricity trading.
problem Improving probabilistic forecasts for electricity trading markets.
method Combines QRA and factor-based averaging for probabilistic forecasting.
result The hybrid approach outperforms benchmarks in statistical measures and economic value.
Bayesian scheme optimally learns worker quality in crowdsourced regression.
problem Learning the quality of workers in crowdsourced regression tasks.
method Iterative Bayesian learning approach.
result Proves optimal mean squared error performance.
We apply stochastic average gradient (SAG) algorithms for training conditional random fields (CRFs). We describe a practical implementation that uses structure in the CRF gradient to reduce the memory requirement of this linearly-convergent stochastic gradient method, propose a non-uniform sampling scheme that substant…
Federated learning technique improves convergence speed with communication delays.
problem Communication delays between edge nodes and aggregator in federated learning.
method Developed FedDelAvg, a technique that generalizes federated averaging to incorporate a weighting between current local model and delayed global model.
result FedDelAvg achieves a significant improvement in convergence speed, especially when optimizing the weighting scheme to account for delays.
This paper analyzes the convergence of Federated Average under relaxed assumptions.
problem Lack of theoretical analysis for Federated Average under assumptions beyond smoothness.
method Relaxing assumptions of strong smoothness to semi-smoothness and semi-Lipschitz properties, and introducing a bound on the gradient.
result Provides a theoretical convergence study on Federated Learning under new assumptions.
Extends algorithms to solve minimization problems faster.
problem Solving minimization problems with sparsity-inducing regularizers.
method Extends semismooth Newton algorithms to take advantage of sparsity.
result The resulting algorithms are a specific case of the Krasnosel'skiĭ--Mann scheme.
Revises Bayesian model averaging for foundation models.
problem Ensemble pre-trained and lightly-finetuned foundation models for improved classification performance.
method Introduces trainable linear classifiers and computationally cheaper model averaging scheme (OMA).
result Ensembled models can better predict on various datasets.
Study shows different initialization schemes for LoRA finetuning impact performance.
problem The impact of initialization schemes on LoRA finetuning performance.
method Compared two initialization schemes: B=0, A=random vs. A=0, B=random.
result First initialization scheme yields better performance on average.
Proposes a non-convex optimization method for a parsimonious weighted naive Bayes classifier.
problem Improving naïve Bayes classifier performance with a large number of input variables.
method Sparse regularization of model log-likelihood for direct estimation of variable weights.
result Optimization-based weighted naïve Bayes classifiers achieve equivalent performance to averaging-based classifiers.
New CNN initialization scheme derived from modern architectures.
problem Stability of CNN model parameters initialization.
method Derived new initialization scheme from modern CNN architectures.
result New initialization method outperforms de facto standard schemes.
The paper develops and tests operator splitting schemes for American options in a complex model.
problem Efficient numerical solution of American options under a two-asset Merton jump-diffusion model.
method Adaptation of IMEX and ADI operator splitting schemes to solve the two-dimensional PIDCP.
result Investigates and compares the convergence and performance of eight operator splitting methods.
Paper analyzes complexity of solving nonconvex-strongly-concave problems.
problem Finding approximate stationary points of nonconvex-strongly-concave minimax problems.
method Introduces a generic acceleration scheme to solve crafted subproblems.
result Algorithm nearly matches lower complexity bounds in general setting.
SQWA improves low-precision DNNs with model averaging and quantization.
problem Designing good generalization DNNs with quantized weights.
method Floating-point model training, direct quantization, multiple low-precision models, weight averaging, re-quantization, fine-tuning, loss visualization.
result State-of-the-art results for 2-bit QDNNs on CIFAR-100 and ImageNet datasets.
A new algorithm speeds up multi-agent reinforcement learning.
problem Complex interactions between agents in multi-agent reinforcement learning.
method Double averaging scheme for decentralized convex-concave saddle-point problems.
result The algorithm converges to the optimal solution at a global geometric rate.
The paper provides bounds for regression schemes using nonstationary training samples.
problem Developing confidence intervals for nonparametric regression with nonstationary data.
method The approach involves Rademacher and Vapnik-Chervonenkis theories to analyze the cost and optimality of regression schemes.
result The paper establishes nonasymptotic bounds for regression schemes and optimality in L2-distance.