Study good-deal hedging under uncertain market prices, reducing speculative components.
problem Good-deal valuation under model uncertainty and speculative risk.
method Robust approach using backward stochastic differential equations.
result Reduction or elimination of speculative components in good-deal hedging.
New theory tackles AGI by breaking data constraints and minimizing global risk.
problem Current AI's limitations in handling complex real-world data and making reasonable judgments.
method Developed subjectivity learning theory to break data constraints and minimize global risk.
result Subjectivity learning holds a lower risk bound than traditional machine learning.
GIANT optimizes distributed computing by improving Newton method efficiency.
problem Efficiently solving empirical risk minimization problems in distributed environments.
method GIANT combines local ANT directions to form a GIANT direction, averaging communications and computations.
result GIANT achieves faster convergence compared to first-order and existing Newton-type methods.
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.
This paper tackles minimizing clipped convex functions with heuristics and mixed-integer convex programming.
problem Minimizing a sum of clipped convex functions.
method Heuristics and mixed-integer convex programming.
result Heuristics can find good solutions, and the perspective transformation yields tractable lower bounds.
A new distributed optimization method for ERM problems.
problem Efficiently solving ERM problems with nonsmooth regularization in a distributed setting.
method Second-order distributed optimization using successive quadratic approximations and Hessian approximation.
result Global linear convergence for a broad range of non-strongly convex problems.
A new framework for bilevel optimization tackles stochastic and global variance reduction.
problem Bilevel optimization challenges in large-scale empirical risk minimization.
method Introducing a novel framework where inner and main variables evolve simultaneously, leading to unbiased estimates and global variance reduction algorithms.
result SABA algorithm achieves $O( rac{1}{T})$ convergence rate and linear convergence under Polyak-Lojasciewicz assumption.
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.
Recurring international financial crises have adverse socioeconomic effects and demand novel regulatory instruments or strategies for risk management and market stabilization. However, the complex web of market interactions often impedes rational decisions that would absolutely minimize the risk. Here we show that, for…
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.
Sharp asymptotics reveal how network width controls learnability in quadratic neural networks.
problem Understanding learnability in overparameterized quadratic neural networks.
method Mapping ERM to convex matrix sensing with nuclear norm penalization.
result Characterization of global minima and precise generalization thresholds.
Study on double descent behavior in two-layer neural networks for binary classification.
problem Understanding the double descent phenomenon in model test error.
method Two-layer neural network with ReLU activation for binary classification. Quantified model size by sample-to-dimension ratio. Empirical risk minimization using Convex Gaussian Min Max Theorem.
result Observed and investigated the double descent behavior of model test error.
The paper learns sensor trees to minimize costs and improve classification accuracy.
problem Learning sensor trees to minimize costs and improve classification accuracy during test time.
method The problem is posed as empirical risk minimization over tree structures and node decision rules. The combinatorial part is solved using linear programming, while the continuous part is approximated with convex surrogate loss functions.
result The approach outperforms state-of-the-art methods on benchmark datasets.
We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization allows to handle under extre…
Study risk-minimizing insurance investments with taxes and expenses.
problem Determining optimal insurance investments in the presence of taxes and expenses.
method Introduced tax- and expense-modified risk-minimization, derived strategies, linked to decompositions, and established equivalence to artificial market approach.
result Equivalence to artificial market approach and consistency with classic risk-minimization.
Efficient distributed algorithm for ERM with nonsmooth regularizers.
problem Solving Empirical Risk Minimization problems with nonsmooth regularization in a distributed setting.
method A distributed quasi-Newton algorithm using successive quadratic approximations and efficient subproblem solving.
result Global linear convergence for a broad range of non-strongly convex problems, reducing communication complexity.
New method ISR improves domain generalization with provable guarantees.
problem Achieving reliable performance across unseen environments.
method Invariant-feature Subspace Recovery (ISR) algorithms.
result ISR can achieve provable domain generalization with fewer training environments.
Paper improves learning efficiency by focusing on effective dimensionality.
problem Dimensionality bottleneck in modern learning tasks.
method Developed tools to reduce dimensional costs using effective dimensionality.
result Uniform concentration bounds involving effective dimensionality, improving over existing results.
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.
A method for hedging defaultable claims using locally risk-minimizing in a structural model.
problem Hedging defaultable claims in a structural model with jumps and non-risk-neutral probabilities.
method Locally risk-minimizing approach in a structural model with finite variation Levy process.
result Derivation of Follmer-Schweizer decompositions for hedging.
New optimization for federated learning with local models.
problem Training models with private data from multiple devices.
method Proposes a new optimization formulation and efficient SGD variants.
result Local steps can improve communication for heterogeneous data.
PDA method optimizes neural networks with global convergence rate analysis.
problem Quantitative convergence rate for neural network optimization in mean field regime.
method Particle dual averaging (PDA) method, combining Langevin algorithm and outer loop optimization.
result Established quantitative global convergence for two-layer mean field neural networks.
The paper explores risk-minimization for exponential additive models, providing mathematical expressions and numerical examples.
problem Risk-minimization in incomplete markets for exponential additive models.
method Derive explicit mathematical expressions for local risk-minimization strategies in exponential additive models.
result Provide necessary conditions for deriving expressions and confirm integrability conditions for specific models.
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.
We extend the well-known BFGS quasi-Newton method and its memory-limited variant LBFGS to the optimization of nonsmooth convex objectives. This is done in a rigorous fashion by generalizing three components of BFGS to subdifferentials: the local quadratic model, the identification of a descent direction, and the Wolfe …
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.
The paper proves convex risk minimization selects a unique conditional probability model.
problem General conditional probability estimation in various settings.
method Convex risk minimization and empirical risk minimization.
result The unique conditional probability model is selected by convex risk minimization.
We obtain explicit representations of locally risk-minimizing strategies of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein--Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for Levy processes, Arai and Suzuki (2015) obtained a formula for locally risk-minimiz…
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.
Develops a convex surrogate for variance in risk minimization.
problem Balancing approximation and estimation error in optimization.
method Combines distributionally robust optimization and empirical likelihood.
result Shows faster convergence rates than empirical risk minimization.
Novel Newton method for large-scale kernel methods using random features.
problem Efficiently solving large-scale finite-sum minimization problems in RKHS.
method Randomized feature-based Newton method for empirical risk minimization.
result Local superlinear and global linear convergence of the method.
The paper analyzes the performance of empirical risk minimization for p-norm linear regression.
problem Empirical risk minimization on 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.
New approach improves model robustness and calibration in latent space.
problem Improving model robustness and calibration under input perturbations.
method VarMixup (Variational Mixup) in latent space of VAEs.
result Models trained with VarMixup in latent space are more robust and calibrated.
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.
Paper extends chaining technique for empirical risk minimization bounds.
problem Empirical risk minimization with unbounded noise and estimates.
method Chaining technique applied to random design settings, proving excess risk bounds.
result Proves upper bounds for empirical risk minimization with sub-Gaussian or subexponential noise.
Solves risk minimization problem with SSD constraints.
problem Finding SSD-minimal quantile function under mixed constraints.
method Explicitly works out SSD-minimal solution and relates to Skorokhod problem.
result Explicit solution to risk minimizing problem.
Efficiently learns decision rules for sensor selection in classification systems.
problem Reducing test-time acquisition costs in classification systems.
method Modeling as a directed acyclic graph (DAG) and using dynamic programming for efficient optimization.
result Proven guarantees of convergence to the optimal system for a fixed architecture.
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of "2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization" by V. Koltchinskii [arXiv:0708.0083]
Study of regularized least squares in RKKS with indefinite kernels.
problem Asymptotic properties of regularized least squares with indefinite kernels in RKKS.
method Introducing a bounded hyper-sphere constraint, theoretical demonstration of globally optimal solution, modified error decomposition techniques, matrix perturbation theory.
result Derivation of learning rates in RKKS, same as RKHS under certain conditions.
Auto-regressive models learn latent states from partially observed linear dynamical systems.
problem Understanding how auto-regressive models learn latent representations from partially observed linear dynamical systems.
method Empirical risk minimization on partially observed linear dynamical systems.
result Two-layer linear auto-regressive models learn to approximate Kalman filtering, coinciding with optimal state estimates.
Study on estimating class probabilities using empirical risk minimization.
problem Estimating class probabilities within binary classification.
method Empirical risk minimization (ERM) for class probability estimation.
result The estimator converges to true class probabilities under certain conditions.
Proposes a new framework for learning image augmentations to improve classification performance.
problem Improving classification performance with a given class of predictors.
method Transformed Risk Minimization (TRM) framework that optimizes both predictive models and data transformations.
result Performance of TRM with SCALE algorithm compares favorably to prior methods on CIFAR10/100.
IRM learns representations invariant to training distributions for better generalization.
problem Learning generalizable models across different training distributions.
method IRM learns a data representation that remains consistent across multiple training distributions, ensuring an optimal classifier matches across them.
result IRM enables out-of-distribution generalization by learning invariant correlations.
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.