Examines optimal risk sharing with realistic risk attitudes, finding risk seeking in certain subdomains.
problem Optimal risk sharing with empirically realistic risk attitudes.
method Allows for risk-seeking agents, generalizes expected utility, and uses counter-monotonic improvement theorem.
result First empirical results on optimal risk sharing with realistic risk attitudes.
New approach avoids excess empirical risk in domain generalization.
problem Learning models that generalize to unseen distributions from diverse data sets.
method Minimizes penalty under constraint of optimal empirical risk, leveraging rate-distortion theory.
result Significant improvements in domain generalization performance across multiple methods.
New method improves model risk prediction using cross-audit projection.
problem Over-optimism in K K K -fold CV for binary classification. method Cross-audit projection (CAP) procedure combining resampling and asymptotic bias correction.
result CAP estimator achieves second-order asymptotic unbiasedness.
Paper studies convergence rates from surrogate risk minimizers to Bayes optimal classifier.
problem Analyzing the convergence rates of surrogate risk minimizers to the Bayes optimal classifier.
method Introducing consistency intensity to characterize surrogate loss functions and using it to derive convergence rates.
result Empirical surrogate risk minimizers converge faster to the Bayes optimal classifier under certain conditions.
Paper tackles heavy-tailed data without finite variance, proposing robust risk minimization.
problem Empirical risk minimization under heavy-tailed data with finite p p p -th moment. method Minimizes risk values robustly estimated via Catoni's method, using generalized generic chaining.
result Shows better performance of optimizer based on empirical risks via Catoni-style estimation.
Optimizes bilevel empirical risk minimization with improved oracle calls.
problem Optimizing bilevel empirical risk minimization problems.
method Proposes a bilevel extension of the SARAH algorithm.
result Demonstrates improved oracle calls to achieve stationarity.
The paper tackles spurious local minima in empirical risk and proposes an SGD-based algorithm to find ε ε ε -approximate local minima of the underlying function.
problem Spurious local minima in empirical risk for nonconvex nonsmooth losses.
method A simple SGD-based algorithm on a smoothed version of the empirical risk function.
result The algorithm finds ε ε ε -approximate local minima of the underlying function F F F while avoiding shallow local minima arising from the tolerance ν ν ν . A new framework tightens risk measure confidence bounds.
problem Improving confidence bounds for various risk measures.
method Distribution optimization framework with two estimation schemes based on concentration bounds.
result Consistently tighter confidence bounds compared to previous methods.
The study reveals traders' risk aversion and a new risk premium from market volumes.
problem Understanding traders' rationality and risk aversion from market volumes.
method Optimal Merton dynamics model to estimate average risk aversion and price of risk.
result Validation of the proposed trading strategy model on real data.
New algorithms achieve uniform stability for empirical risk minimization.
problem Designing uniformly stable optimization algorithms for empirical risk minimization.
method Black-box conversion of smooth optimization algorithms and development of Mirror Descent for smooth optimization.
result Optimal algorithms with uniform stability and convergence rates for smooth optimization.
Optimal algorithm identifies best arm for risk measures in heavy-tailed distributions.
problem Identifying the arm with smallest CVaR, VaR, or weighted sum of CVaR and mean from heavy-tailed distributions.
method Multi-armed bandit best-arm identification framework, solving non-convex optimization problem.
result Optimal δ-correct algorithm with matching lower bound on expected samples.
Paper analyzes time series prediction using empirical risk minimization.
problem Optimizing 1-step-ahead prediction for time series.
method Empirical risk minimization applied to recursive algorithms for time series forecasting.
result Empirical risk minimization achieves optimal predictive performance.
Unified framework for risk-aware policy learning in contextual bandits.
problem Optimizing decision rules in high-stakes domains with adverse outcomes.
method Distributional framework for Lipschitz-continuous risk functionals, with novel empirical concentration inequalities.
result Data-dependent suboptimality bounds with an i l d e O ( 1 / n ) ilde{\mathcal{O}}(1/\sqrt{n}) i l d e O ( 1/ n ) rate, matching risk-neutral offline policy optimization. We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach builds off of techniques for distributionally robust optimization and Owen's empiric…
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.
A new SGD framework reduces empirical risk by favoring higher loss observations.
problem Minimizing empirical risk in machine learning problems.
method Develops a biased gradient estimator for stochastic optimization.
result Minimizes an ordered modification of the empirical average loss.
New measure quantifies function similarity for optimization.
problem Measuring similarity between functions for optimization.
method Quantifies sub-optimality gaps and operation rules.
result Unified measure for various functional similarities.
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.
Bayesian nonparametrics improves data-driven risk optimization under distributional uncertainty.
problem Improving out-of-sample performance in machine learning models due to distributional uncertainty.
method Combining Bayesian nonparametric theory and decision-theoretic preferences to propose a robust optimization criterion.
result The proposed robust optimization procedure provides favorable statistical guarantees and tractable approximations.
New method turns optimization algorithms into uniformly stable learning algorithms for non-Euclidean norms.
problem Non-Euclidean norms in binary classification problems.
method Black-box reduction method using uniformly convex regularizers.
result Achieves optimal statistical risk bounds on excess risk for non-Euclidean norms.
The paper analyzes the performance of empirical risk minimization for p p p -norm linear regression.
problem Empirical risk minimization on p p p -norm linear regression. method Analyzes performance under various conditions and moment assumptions.
result High probability excess risk bounds for empirical risk minimizer, matching asymptotic rates.
Paper shows robust estimators converge to true risk minimizers at optimal rates.
problem Understanding asymptotic properties of robust risk minimizers.
method Investigates robust analogues of empirical risk minimization, focusing on median of means estimator.
result Robust minimizers converge to true minimizers at optimal rates and have similar asymptotic variance.
Optimizes exp-concave losses with a new risk bound.
problem Optimizing exp-concave losses with stochastic convex optimization.
method Empirical Risk Minimization with a unified geometric assumption and local norms.
result Provides an O ( d / n + log ( 1 / δ ) / n ) O( d / n + \log( 1 / δ) / n ) O ( d / n + log ( 1/ δ ) / n ) excess risk bound. Simplified screening tests for data points in optimization.
problem Discarding irrelevant data points in empirical risk minimization.
method Designing loss functions and regularizing convex losses to induce sparsity, using ellipsoidal approximations.
result Automatic discarding of data samples without losing optimization guarantees.
Optimal private ERM and SCO with subquadratic gradient complexity.
problem Private optimization of non-smooth convex functions.
method Subquadratic gradient complexity algorithm using subsampling and smoothing.
result Achieved optimal excess empirical risk and population loss.
PF-based FSO methods improve on SGD and IPM for large-scale empirical risk minimization.
problem Optimizing large-scale empirical risk minimization problems efficiently.
method Developed PF-based stochastic optimizers (PFSOs) based on FSO methods.
result PFSOs outperform SGD, vanilla IPM, and KF-type FSO methods in stability, speed, and flexibility.
Optimizes differentially private kernel learning with random projection.
problem Privacy-preserving learning algorithms with optimal performance.
method Differentially private kernel ERM algorithm based on random projection in reproducing kernel Hilbert space.
result Achieves minimax-optimal excess risk rates for various loss functions.
New framework for optimizing machine learning risks.
problem Optimizing non-decomposable machine learning objectives.
method Empirical X-risk minimization (EXM) framework with algorithmic techniques.
result Developed algorithms for solving EXM with smooth non-convex objectives.
Mitigates overfitting in UU classification from two unlabeled datasets.
problem Overfitting in the UU classification method.
method Wrapping negative empirical risk terms with correction functions and proving consistency.
result Successfully mitigates overfitting and improves classification accuracy.
Paper improves privacy in ERM with faster algorithms and broader applicability.
problem Privacy-preserving machine learning with empirical risk minimization.
method Develops faster algorithms for differentially private ERM in various settings.
result Achieves optimal or near-optimal utility bounds with less gradient complexity.
In stochastic optimization, the population risk is generally approximated by the empirical risk. However, in the large-scale setting, minimization of the empirical risk may be computationally restrictive. In this paper, we design an efficient algorithm to approximate the population risk minimizer in generalized linear …
Deep neural network with l_1-regularization achieves nearly optimal risk bounds.
problem Achieving optimal risk bounds in deep learning.
method Empirical risk minimization with l_1-regularization.
result Adaptively nearly-minimax risk bound across various function classes.
Improved sample complexity for diffusion models without needing empirical risk minimizers.
problem Theoretical limitations in sample complexity for diffusion models.
method Structured decomposition of score estimation error, eliminating dependence on neural network parameters.
result Achieved sample complexity bound of O(ε^(-4)) without empirical risk minimizer access.
Wide deep neural networks are easy to optimize without constraints.
problem Optimizing wide deep neural networks.
method Analysis of optimization landscapes and empirical-risk minimization.
result Wide neural networks have no confined points, making optimization easier.
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.
New learning algorithm for real analytic functions without gradient descent.
problem Learning real analytic functions without gradient descent.
method Taylor approximation and sampling data distribution.
result Nonuniform learning result for real analytic functions.
Simple analysis for fast rates in empirical minimization with concave losses and convex regularization.
problem Fast rates in empirical minimization with concave losses and convex regularization.
method Simple analysis using covering number and concentration inequality.
result First result of fast rates with high probability for exponential concave empirical risk minimization.
The article analyzes high-dimensional classification using empirical risk minimization with precise error predictions.
problem Classifying high-dimensional data with Gaussian mixture models.
method Theoretical analysis of ridge-regularized and unregularized empirical risk minimization for high-dimensional Gaussian mixture separation.
result The square loss is optimal for high-dimensional classification in both ridge-regularized and unregularized cases.
ERM performs well in feature learning with minimal feature maps.
problem Empirical risk minimization in feature learning with square loss.
method Asymptotic and non-asymptotic analysis of ERM performance.
result Excess risk quantiles of ERM match those of oracle procedure under certain conditions.
New algorithms minimize risk in MNL bandits, achieving near-optimal performance.
problem Minimizing risk in multi-armed bandit problems.
method Designing algorithms for various risk criteria (e.g., CVaR, Sharpe ratio, entropy risk).
result Near-optimal regret for the designed algorithms.
Modern portfolio theory(MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk, conflating uncertainty with risk. There have been many subsequent attempts to al…
A method to optimize deep networks by sequentially minimizing risk functions.
problem Optimizing deep networks during training to find global optima.
method Surfing: Iterative optimization over incrementally trained deep networks.
result The method can find global optima and improve compressed sensing performance.
New method corrects bias in estimating entropic risk for better decision-making.
problem Underestimation of entropic risk when data are limited.
method Parametric bootstrap procedure to overestimate entropic risk.
result Corrected method provides better risk estimates, leading to improved decision-making.
The paper analyzes the generalization performance of spectral clustering algorithms and proposes new methods to improve their effectiveness.
problem Theoretical analysis of spectral clustering's generalization performance.
method Theoretical analysis and development of new spectral clustering algorithms.
result The excess risk bounds of spectral clustering algorithms have a O ( 1 / n ) \mathcal{O}(1/\sqrt{n}) O ( 1/ n ) convergence rate. We study the Stochastic Gradient Langevin Dynamics (SGLD) algorithm for non-convex optimization. The algorithm performs stochastic gradient descent, where in each step it injects appropriately scaled Gaussian noise to the update. We analyze the algorithm's hitting time to an arbitrary subset of the parameter space. Two…
Efficiently computes optimal policies for Entropic Risk Measures.
problem Optimizing risk-sensitive metrics in MDPs is computationally expensive.
method Uses Entropic Risk Measures and novel structural analysis for efficient computation.
result Achieves strong performance in various decision-making scenarios.
The paper provides theoretical guarantees for neural network-based anomaly detection.
problem Theoretical guarantees for unsupervised neural network-based anomaly detection.
method Casting anomaly detection as a binary classification problem, establishing non-asymptotic upper bounds and convergence rates.
result The convergence rate on the excess risk matches the minimax optimal rate.
Develops neural network framework for risk-reward optimization problems.
problem Multi-period risk-reward optimization with constrained policies.
method Neural network framework with two coupled feedforward networks, parametrizing two-step policies.
result Empirical optimum converges to true optimal value as network capacity and training size increase.