NAPP-ERM improves ERM with differential privacy guarantees by iteratively achieving target regularization and delivering strong convexity.
problem Over-regularization in privacy-preserving ERM approaches.
method Noise-Augmented Privacy-Preserving Empirical Risk Minimization (NAPP-ERM) with a dual-purpose l2 regularizer and privacy budget retrieval strategy.
result Mitigates over-regularization and achieves strong convexity through a single regularizer.
Entropy asymmetry affects regularization in ERM, leading to biased solutions.
problem Analyzing the impact of relative entropy asymmetry in ERM regularization.
method Examined Type-I and Type-II ERM-RER, comparing their solutions and properties.
result Type-II ERM-RER regularization introduces a strong bias against training data.
Simple DP algorithms find approximate solutions for nonconvex ERM.
problem Finding approximate solutions to nonconvex ERM problems with privacy.
method Differential privacy, descent directions, line search, mini-batching, two-phase strategy.
result Effective algorithms for nonconvex ERM with privacy guarantees.
Study on Privileged ERM showing limitations and providing capacity analysis.
problem Improving classification accuracy with privileged information.
method Theoretical analysis of Privileged ERM using VC dimension and generalization bounds.
result Worst-case guarantees for Privileged ERM cannot improve over standard ERM unless privileged information capacity is similar or smaller.
New dual formulation reduces generalization error for ERM-fDR.
problem Generalization error in constrained optimization problems.
method Introduces a dual formulation of ERM-fDR using Legendre-Fenchel transform and implicit function theorem.
result Explicit characterizations of generalization error for algorithms under mild conditions.
Paper shows ERM's suboptimality due to bias, not variance.
problem Understanding why ERM fails to achieve optimal rates.
method Probabilistic and admissibility proofs for ERM in various settings.
result ERM's suboptimality is due to bias, not variance.
While many solutions for privacy-preserving convex empirical risk minimization (ERM) have been developed, privacy-preserving nonconvex ERM remains a challenge. We study nonconvex ERM, which takes the form of minimizing a finite-sum of nonconvex loss functions over a training set. We propose a new differentially private…
Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM is still not understood. We address this issue for multiple popular ERM problems…
Paper proposes a new method for SP with covariates using PADR and ERM.
problem Stochastic programming with covariate information.
method Empirical risk minimization (ERM) with nonconvex piecewise affine decision rules (PADR).
result The method provides theoretical consistency and computational tractability for nonconvex SP problems.
Study on tradeoffs between mistakes and ERM oracle calls in online and transductive learning.
problem Analyzing online and transductive learning with limited ERM and weak consistency oracle access.
method Proves lower bounds and upper bounds on mistakes and oracle calls, considering realizable and agnostic cases.
result Achieves optimal mistake bounds with weak consistency queries for certain concept classes.
This paper studies universal rates of ERM for binary classification under agnostic learning.
problem The challenge of achieving universal rates of ERM for binary classification under agnostic learning.
method The paper explores the agnostic universal rates of ERM for binary classification, revealing three possible rates: e − n e^{-n} e − n , o ( n − 1 / 2 ) o(n^{-1/2}) o ( n − 1/2 ) , or arbitrarily slow. result The paper provides a complete characterization of which concept classes fall into each of the three categories of agnostic universal rates.
Default-ERM shortcut learning persists even without additional information.
problem Default-ERM shortcut learning in perception tasks despite stable feature sufficiency.
method Studied linear perception task; developed margin control (MARG-CTRL) loss functions.
result Margin control mitigates shortcut learning on various tasks.
Dual optimization connects ERM-fDR to normalization function.
problem Empirical risk minimization with f-divergence regularization.
method Dual formulation, Legendre-Fenchel transform, implicit function theorem, nonlinear ODE.
result Computational method to calculate normalization function efficiently.
Paper presents ERM with f f f -divergence regularization and its properties.
problem Minimizing empirical risk with f f f -divergence constraints. method Introduces normalization function and solves ERM- f f f DR via ODE. result Characterizes difference between empirical risks and provides numerical algorithm.
Develops a new learning framework for dynamic data.
problem Poor performance of existing strategies in dynamic data and goals.
method Prospective Learning framework and Prospective ERM algorithm.
result Prospective ERM converges to Bayes risk under certain assumptions.
ERM struggles with synthetic data, but some algorithms can still learn correctly.
problem Learning from a mix of natural and synthetic data.
method Modeling the scenario as a sequence of learning tasks with oblivious algorithms, studying ERM and its limitations.
result ERM converges to the true mean but is outperformed by weighted algorithms. ERM does not always converge in the PAC setting, but there are algorithms capable of learning the correct hypothesis.
Simpler majority vote of three classifiers achieves optimal error bounds.
problem Developing an optimal PAC learning algorithm in the realizable setting.
method Returning the majority vote of three ERM classifiers.
result Achieves optimal in-expectation bound on error.
Paper explores universal rates of ERM in machine learning.
problem Understanding universal learning rates for ERM.
method Analyzes realizable concept classes and ERM principles.
result Four possible universal learning rates by ERM.
Algorithm solves online binary classification and infinite games using ERM oracle.
problem Online learning and solving infinite games with computationally inefficient oracles.
method Proposes an algorithm relying solely on ERM oracle calls for online binary classification and nonparametric games.
result Achieves finite and sublinearly growing regret in various settings.
Upper bounds and lower bounds show ERM outperforms DG methods in various settings.
problem Limitations of domain generalisation methods in various settings.
method Upper bounds and lower bounds on excess risk of ERM, and analysis of DG settings.
result It is not possible to significantly outperform ERM in DG settings.
Study risk bounds for distributed ERM with general loss functions and hypothesis spaces.
problem Limited theoretical analysis for distributed ERM with general loss functions and hypothesis spaces.
method Derive tight risk bounds under assumptions on hypothesis space and loss function.
result Developed more general risk bound for distributed ERM without strong convexity restriction.
ERM with square loss achieves sublinear error for learnable function classes with smoothed data.
problem Statistical and computational hardness in sequential decision-making.
method Empirical Risk Minimization (ERM) with square loss, focusing on unknown base measure and smooth data.
result ERM achieves error scaling as i l d e O ( c o m p ( F ) ⋅ T ) ilde O( \sqrt{\mathrm{comp}(\mathcal F)\cdot T} ) i l d e O ( comp ( F ) ⋅ T ) for learnable function classes. Sharp bounds on ERM's minimal error in regression.
problem Understanding ERM's performance in regression tasks.
method Sharp lower bounds for ERM in random and fixed design settings.
result ERM's performance depends on the global or local complexity of the model.
FeAT improves OOD generalization by learning richer features.
problem Improving feature learning for out-of-distribution (OOD) generalization.
method Feature Augmented Training (FeAT) iteratively augments and retains features from different subsets of training data.
result FeAT effectively learns richer features, boosting OOD performance.
Online TERM improves robustness and fairness in streaming data.
problem Streaming data's lack of worst-case fairness and robustness in ERM.
method Proposes an online TERM formulation to balance average-case accuracy with worst-case fairness and robustness.
result Negative tilting effectively suppresses outlier influence, positive tilting improves recall with minimal precision loss.
New algorithm reduces ERM problem size while maintaining accuracy.
problem Empirical risk minimization problem size reduction.
method Adaptive Deterministic Uniform-Weight Trimming (ADUWT) algorithm.
result Uniform ( 1 ± ε ) (1\pm\varepsilon) ( 1 ± ε ) relative-error approximation for ERM objective. Distributed machine learning is an approach allowing different parties to learn a model over all data sets without disclosing their own data. In this paper, we propose a weighted distributed differential privacy (WD-DP) empirical risk minimization (ERM) method to train a model in distributed setting, considering differ…
Study identifies and analyzes spurious correlations in data-driven models.
problem Spurious correlations in data-driven models are unreliable and hard to detect.
method Collect and analyze synthetic datasets generated from causal graphs to investigate spurious correlations.
result Patterns connecting spurious correlation hypotheses and model design choices were observed.
A new DP algorithm for weighted ERM protects sensitive data in predictive models.
problem Protecting sensitive personal information in predictive models trained via ERM.
method Proposes the first differentially private algorithm for weighted ERM with formal privacy guarantees.
result Demonstrates strong DP guarantees while maintaining robust performance in real-world data.
Recent work shows GRW approaches do not improve over ERM in distributional shift.
problem Improving robustness to distributional shift in machine learning models.
method Generalized Reweighting (GRW) algorithms, which iteratively update model parameters based on reweighting of training samples.
result GRW approaches do not significantly improve over ERM in real applications with distribution shift.
This guide simplifies high-probability regret bounds in empirical risk minimization.
problem High-probability regret bounds in empirical risk minimization.
method Modular presentation, three-step recipe, localized Rademacher complexity, local maximal inequalities, metric-entropy integrals.
result Recover familiar rates for various function classes and derive regret bounds for nuisance components.
ERM uses energy-based selection to improve recursive reasoning.
problem Lack of principled inference mechanism in recursive models.
method Energy-guided Recursive Model (ERM) introduces Hopfield energies for trajectory selection.
result ERM achieves optimal solutions on various puzzles.
Reweighting improves risk bounds in certain data regions.
problem Improving risk bounds in classification and heteroscedastic regression.
method Weighted empirical risk minimization with a data-dependent weight function.
result A weighted ERM estimator can achieve superior performance in specific sub-regions.
Study shows minimizing the norm of the ERM solution stabilizes kernel ridge-less regression.
problem Stability of kernel ridge-less regression.
method Minimizing the norm of the ERM solution to minimize CV stability.
result Interpolating solution with minimum norm minimizes CV stability.
New method approximates CV efficiently for large-scale problems.
problem High computational cost of standard CV in large-scale problems.
method Iterative first-order algorithm to approximate CV solution.
result Extends CV approximation guarantees to non-converged solutions.
New DP-CD method outperforms DP-SGD in solving composite DP-ERM problems.
problem Privacy-preserving machine learning with differential privacy.
method Differentially Private proximal Coordinate Descent (DP-CD) for composite Empirical Risk Minimization (ERM).
result DP-CD outperforms DP-SGD due to larger step sizes and better gradient exploitation.
Study shows how bias in optimization affects robustness in adversarial settings.
problem Understanding and mitigating implicit bias in adversarially robust models.
method Analyzes the implicit bias in robust empirical risk minimization and its impact on generalization.
result Implicit bias in optimization can significantly affect robust generalization.
New framework shows ERM is optimal for both interpolation and extrapolation in domain generalization.
problem Formalizing and solving the challenges of domain generalization.
method Reformulated domain generalization as an online game between a risk-minimizing player and an adversary.
result ERM is minimax-optimal for both interpolation and extrapolation in domain generalization.
We present efficient algorithms for the problem of contextual bandits with i.i.d. covariates, an arbitrary sequence of rewards, and an arbitrary class of policies. Our algorithm BISTRO requires d calls to the empirical risk minimization (ERM) oracle per round, where d is the number of actions. The method uses unlabeled…
JTT improves model worst-group accuracy without group annotations.
problem Low worst-group accuracy in standard ERM models with spurious correlations.
method Two-stage approach: first ERM, then upweight misclassified examples.
result JTT closes 75% of the gap in worst-group accuracy compared to group DRO.
Extends ERM with exponential tilting for improved machine learning performance.
problem Improving machine learning models by adjusting loss weights for fairness and robustness.
method Tilted Empirical Risk Minimization (TERM) using exponential tilting.
result TERM can outperform traditional ERM and deliver competitive performance with state-of-the-art methods.
We analyze Gibbs-based transfer learning algorithms using information theory.
problem Understanding the generalization error of transfer learning.
method Information-theoretic analysis focusing on α α α -weighted-ERM and two-stage-ERM. result Exact characterization of generalization behavior using conditional symmetrized KL information.
Unified view connects CoCoA and ADMM for distributed ERM.
problem Connection between CoCoA and ADMM for distributed ERM.
method Unified primal-dual perspective reformulation.
result Unified ADMM variants perform at least as good as CoCoA in ridge-regularized ERM.
New algorithm learns efficiently with a simple 'yes/no' oracle.
problem Can efficient learning be achieved with a simpler oracle than ERM?
method Developed an oracle that returns 'yes' or 'no' for realizable datasets.
result Learnability is possible with a polynomial price in VC dimension.
New regularization method reduces support of empirical risk minimization solutions.
problem Regularization in empirical risk minimization with relative entropy.
method Introduces Type-II regularization, characterizes solutions, analyzes properties of relative entropy.
result Type-II regularization collapses solution support into reference measure's support.
We consider large scale empirical risk minimization (ERM) problems, where both the problem dimension and variable size is large. In these cases, most second order methods are infeasible due to the high cost in both computing the Hessian over all samples and computing its inverse in high dimensions. In this paper, we pr…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable to both the primal and the dual ERM problem. Current second-order and quasi-New…
The study provides theoretical guarantees for the statistical performance of optimal decision trees.
problem Theoretical limits on the statistical performance of globally optimal decision trees.
method Sharp oracle inequalities and uniform concentration framework based on Rademacher complexity.
result Derivation of minimax optimal rates for piecewise sparse heterogeneous anisotropic Besov space.