On-device research index

arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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48 results for “bounded loss”

More PAC-Bayes bounds: From bounded losses, to losses with general tail behaviors, to anytime validitystat.ML

Paper improves PAC-Bayes bounds for various loss types.

problem Improving PAC-Bayes bounds for different types of losses.

method Introducing new high-probability PAC-Bayes bounds for bounded and general tail behaviors losses, and extending to anytime-valid bounds.

result New fast-rate and mixed-rate bounds for losses with bounded ranges, and parameter-free bounds for losses with general tail behaviors.

PAC-Bayes bounds losses anytime-valid discretization tail behaviors

2023-06-21abs ↗pdf ↗

Establishing Linear Surrogate Regret Bounds for Convex Smooth Losses via Convolutional Fenchel-Young Lossescs.LG

We establish linear regret bounds for convex smooth losses using Fenchel-Young losses.

problem Establishing linear regret bounds for convex smooth losses.

method Constructing a convex smooth surrogate loss using Fenchel-Young losses generated by the convolutional negentropy.

result We derive a smooth loss with a linear surrogate regret bound.

surrogate regret bounds convex smooth losses Fenchel-Young losses convolutional negentropy linear regret bound

2025-05-14abs ↗pdf ↗

A note on generalization bounds for losses with finite momentsstat.ML

The paper improves PAC-Bayes bounds for losses with finite moments.

problem Bounding generalization for losses with heavy tails and finite moments.

method Truncation method and PAC-Bayes bounds for unbounded losses with heavy tails and bounded variance.

result Bounds interpolate between slow and fast rates depending on the moment.

PAC-Bayes generalization truncation losses finite moments

2024-03-25abs ↗pdf ↗

Misclassification excess risk bounds for PAC-Bayesian classification via convexified lossstat.ML

This research improves PAC-Bayesian bounds for classification tasks using convexified loss.

problem Deriving generalization bounds for classification tasks with non-convex loss functions.

method Shift focus to misclassification excess risk bounds for PAC-Bayesian classification using convex surrogate loss and leveraging PAC-Bayesian relative bounds in expectation.

result Improved PAC-Bayesian bounds for classification tasks with convex surrogate loss.

PAC-Bayesian classification convexified loss misclassification excess risk

2024-08-16abs ↗pdf ↗

PAC-Bayes Generalisation Bounds for Heavy-Tailed Losses through Supermartingalesstat.ML

New PAC-Bayes bounds for heavy-tailed losses using supermartingales.

problem Extending PAC-Bayes bounds to heavy-tailed losses.

method Using supermartingales and bounded variance assumption.

result PAC-Bayes generalization bounds for heavy-tailed losses.

PAC-Bayes supermartingales heavy-tailed generalization bounds

2022-10-03abs ↗pdf ↗

H

-Consistency Guarantees for Regressioncs.LG

Study improves $H$ -consistency bounds for regression analysis.

problem Improving

H

-consistency bounds for regression analysis.

method Generalized theorems and novel

H

-consistency bounds for various surrogate loss functions.

result Derives principled surrogate losses for adversarial regression.

$H$-consistency regression surrogate loss adversarial regression Huber loss

2024-03-28abs ↗pdf ↗

Fundamental Novel Consistency Theory:

H

-Consistency Boundscs.LG

Study on $H$ -consistency bounds for machine learning surrogates.

problem Estimating target loss error relative to surrogate loss error in machine learning.

method Developed

H

-consistency bounds for various surrogates and loss functions.

result Stronger guarantees than existing methods, offering distribution-dependent and -independent bounds.

machine learning consistency theory surrogate loss target loss binary classification

2025-12-28abs ↗pdf ↗

Non-exponentially weighted aggregation: regret bounds for unbounded loss functionsstat.ML

New aggregation strategy handles unbounded losses with regret bounds.

problem Online optimization with unbounded loss functions.

method Follow The Regularized Leader (FTRL) with φ-divergence.

result Worst regret bound for unbounded losses with alternative divergences.

online optimization unbounded losses φ-divergence Follow The Regularized Leader regret bounds

2020-09-07abs ↗pdf ↗

A Universal Growth Rate for Learning with Smooth Surrogate Lossescs.LG

Paper establishes a universal growth rate for smooth surrogate losses in classification.

problem Analyzing growth rates of consistency bounds for various surrogate losses.

method Proves square-root growth rate for smooth margin-based losses; extends to multi-class classification.

result Demonstrates a universal square-root growth rate for smooth comp-sum and constrained losses.

growth rate surrogate losses classification minizability gaps excess error bounds

2024-05-09abs ↗pdf ↗

Fast-Rate Loss Bounds via Conditional Information Measures with Applications to Neural Networkscs.LG

New bounds on neural network test loss derived from conditional information measures.

problem Estimating test loss of neural networks trained on limited data.

method Framework based on conditional information density between hypothesis and training set.

result Tail bounds on test loss decay as 1/n, improving over previous 1/sqrt{n} bounds.

Neural Networks Loss Bounds Conditional Information PAC-Bayesian Tail Probability

2020-10-22abs ↗pdf ↗

A note on large deviations in life insurancemath.PR

Study large deviations in life insurance portfolios without identical distributions.

problem Large deviations in life insurance portfolios with bounded losses and variances.

method Upper bound from standard large deviations, counterexample for full large deviation principle.

result Exponential bound for average loss exceeding a threshold.

life insurance large deviations non-identical distributions bounded losses bounded variances

2020-09-03abs ↗pdf ↗

Contextual bandits with surrogate losses: Margin bounds and efficient algorithmscs.LG

We use surrogate losses to obtain several new regret bounds and new algorithms for contextual bandit learning. Using the ramp loss, we derive new margin-based regret bounds in terms of standard sequential complexity measures of a benchmark class of real-valued regression functions. Using the hinge loss, we derive an ef…

2018-06-28abs ↗pdf ↗

Calibrated Surrogate Losses for Classification with Label-Dependent Costsstat.ML

We present surrogate regret bounds for arbitrary surrogate losses in the context of binary classification with label-dependent costs. Such bounds relate a classifier's risk, assessed with respect to a surrogate loss, to its cost-sensitive classification risk. Two approaches to surrogate regret bounds are developed. The…

2010-09-14abs ↗pdf ↗

Cross-Entropy Loss Functions: Theoretical Analysis and Applicationscs.LG

Theoretical analysis of cross-entropy loss functions and their robustness.

problem Guarantees for using cross-entropy as a surrogate loss function.

method Theoretical analysis of a broad family of loss functions, including cross-entropy.

result First

H

-consistency bounds for comp-sum losses and smooth adversarial comp-sum losses.

cross-entropy loss functions theoretical analysis consistency bounds adversarial robustness

2023-04-14abs ↗pdf ↗

Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functionscs.LG

The paper sets lower bounds for adversarial robustness in multiclass classification.

problem Adversarial robustness in multiclass classification with arbitrary loss functions.

method Dual and barycentric reformulations for robust risk minimization.

result Sharp lower bounds for adversarial risks are computed efficiently.

adversarial robustness multiclass classification arbitrary loss functions lower bounds robust risk minimization

2025-10-02abs ↗pdf ↗

Lower-Bounded Proper Losses for Weakly Supervised Classificationstat.ML

Paper develops proper, lower-bounded losses for weakly supervised classification.

problem Weakly supervised classification with corrupted labels.

method Representation theorem for proper losses, derived condition for lower-boundedness, generalized logit squeezing.

result Proper and lower-bounded losses for weak-label learning.

weakly supervised classification proper losses lower-boundedness label corruption class-probability estimation

2021-03-04abs ↗pdf ↗

Multi-Label Learning with Stronger Consistency Guaranteescs.LG

Unified surrogate loss framework for multi-label learning with strong consistency guarantees.

problem Improving consistency and accounting for label correlations in multi-label learning.

method Introducing multi-label logistic loss and extending it to comprehensive multi-label comp-sum losses, proving strong consistency guarantees for any multi-label loss.

result Unified surrogate loss framework benefiting from strong consistency guarantees for any multi-label loss.

multi-label learning surrogate losses consistency guarantees logistic loss label correlations

2024-07-18abs ↗pdf ↗

Excess Risk Bounds for Exponentially Concave Lossescs.LG

The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, a…

2014-01-18abs ↗pdf ↗

PAC-Bayes unleashed: generalisation bounds with unbounded lossesstat.ML

New PAC-Bayes bounds for unbounded loss functions.

problem Generalization bounds for learning problems with unbounded loss functions.

method Introducing HYPE, a new notion for loss range, and deriving a novel PAC-Bayesian generalization bound.

result PAC-Bayes framework extended to unbounded loss functions.

PAC-Bayes generalization unbounded loss HYPE learning problems

2020-06-12abs ↗pdf ↗

PAC-Bayes-Chernoff bounds for unbounded lossesstat.ML

New PAC-Bayes bounds for unbounded losses using Cramér-Chernoff techniques.

problem Developing bounds for unbounded losses in PAC-Bayesian settings.

method Introducing a new PAC-Bayes oracle bound using Cramér-Chernoff bounds and controlling random variable tails.

result Our bounds generalize and improve upon previous results, providing more informative and potentially tighter bounds.

PAC-Bayes Cramér-Chernoff unbounded losses bounds random variables

2024-01-02abs ↗pdf ↗

\mathscr{H}

-Consistency Estimation Error of Surrogate Loss Minimizerscs.LG

Study of estimation errors in surrogate loss minimizers, providing stronger guarantees than existing methods.

problem Estimation errors in surrogate loss minimizers for various hypothesis sets.

method Detailed study of

\mathscr{H}

-consistency estimation error bounds, proving general theorems for distribution-dependent and independent settings.

result Explicit bounds for zero-one and adversarial losses, showing enhancements under distributional assumptions.

estimation errors surrogate loss minimizers hypothesis set distribution-dependent distribution-independent

2022-05-16abs ↗pdf ↗

The Benefits of Being Distributional: Small-Loss Bounds for Reinforcement Learningcs.LG

This paper explains why distributional reinforcement learning is better than vanilla RL using small-loss bounds.

problem Understanding when and why distributional reinforcement learning (DistRL) is superior to vanilla reinforcement learning (RL).

method The paper uses small-loss bounds to explain the benefits of DistRL, proposing algorithms and proving bounds for different RL settings.

result Distributional reinforcement learning (DistRL) outperforms vanilla RL when optimal costs are small, as shown by small-loss bounds.

distributional reinforcement learning small-loss bounds contextual bandits online reinforcement learning offline reinforcement learning

2023-05-25abs ↗pdf ↗

Surrogate Regret Bounds for Polyhedral Lossescs.LG

New bounds show polyhedral surrogates are optimal for generalization.

problem Proving generalization rates for polyhedral loss functions.

method Developed two general results for polyhedral surrogates.

result Polyhedral surrogates provide linear surrogate regret bounds, translating directly to target rates.

surrogate risk minimization polyhedral losses excess risk bounds generalization rates

2021-10-26abs ↗pdf ↗

A Second-order Bound with Excess Lossesstat.ML

We study online aggregation of the predictions of experts, and first show new second-order regret bounds in the standard setting, which are obtained via a version of the Prod algorithm (and also a version of the polynomially weighted average algorithm) with multiple learning rates. These bounds are in terms of excess l…

2014-02-10abs ↗pdf ↗

PAC-Bayesian Generalization Bounds for MultiLayer Perceptronscs.LG

PAC-Bayesian bounds for MLPs with cross entropy loss validated.

problem Generalization bounds for MLPs with cross entropy loss.

method Introduced probabilistic explanations and proved PAC-Bayesian bounds using ELBO.

result MLPs with cross entropy loss inherently guarantee PAC-Bayesian generalization bounds.

PAC-Bayesian MultiLayer Perceptrons Cross Entropy Generalization Probabilistic Foundations

2020-06-16abs ↗pdf ↗

Enhanced

H

-Consistency Boundscs.LG

Enhanced $H$ -consistency bounds derived under relaxed conditions.

problem Quantifying the relationship between zero-one estimation error and surrogate loss estimation error.

method Relaxing the condition on the surrogate loss conditional regret and presenting a general framework for establishing enhanced

H

-consistency bounds.

result Derivation of more favorable

H

-consistency bounds in various scenarios.

$H$-consistency bounds surrogate losses conditional regrets multi-class classification binary classification

2024-07-18abs ↗pdf ↗

On the Importance of Gradient Norm in PAC-Bayesian Boundscs.LG

New bound relaxes uniform gradient norm assumptions for PAC-Bayesian bounds.

problem Generalization bounds with strict assumptions like uniformly bounded loss.

method Relax uniform bounds assumptions to on-average bounded loss and gradient norm.

result Proposes a new generalization bound with a surrogate of model complexity.

PAC-Bayesian bounds gradient norm generalization Bayesian deep nets log-Sobolev inequalities

2022-10-12abs ↗pdf ↗

Optimal Dimension-Free Sampling for Regularized Classificationcs.LG

Optimal sampling bounds for various classification losses under different regularization terms.

problem Achieving optimal sampling complexity for classification losses under different regularization terms.

method Proved optimal sampling bounds for a broad class of Lipschitz continuous classification loss functions under various regularization terms.

result Proved

k^2/\varepsilon^2

upper and lower bounds for

\|\cdot\|_2/k

regularization, and

k/\varepsilon^2

upper and lower bounds for

\|\cdot\|_1/k

regularization.

classification sampling regularization loss functions upper bounds

2026-05-22abs ↗pdf ↗

When Lower-Order Terms Dominate: Adaptive Expert Algorithms for Heavy-Tailed Lossescs.LG

New algorithms avoid a dominant lower-order term in heavy-tailed loss settings.

problem Prediction with heavy-tailed losses without prior knowledge.

method Adaptive algorithms that avoid the maximum of losses as a lower-order term in regret.

result Improved regret bounds of

\mathcal{O}(\sqrt{θT\log(K)})

and

\mathcal{O}(θ\log(KT)/Δ_{\min})

heavy-tailed losses adaptive algorithms regret bounds lower-order term squared loss

2025-06-02abs ↗pdf ↗

Multiclass Classification Calibration Functionsstat.ML

In this paper we refine the process of computing calibration functions for a number of multiclass classification surrogate losses. Calibration functions are a powerful tool for easily converting bounds for the surrogate risk (which can be computed through well-known methods) into bounds for the true risk, the probabili…

2016-09-20abs ↗pdf ↗

Exploring Local Norms in Exp-concave Statistical Learningcs.LG

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 )

excess risk bound.

stochastic convex optimization exp-concave losses Empirical Risk Minimization local norms geometric assumption

2023-02-21abs ↗pdf ↗

Fast Rates for General Unbounded Loss Functions: from ERM to Generalized Bayescs.LG

We present new excess risk bounds for general unbounded loss functions including log loss and squared loss, where the distribution of the losses may be heavy-tailed. The bounds hold for general estimators, but they are optimized when applied to $η$ -generalized Bayesian, MDL, and empirical risk minimization estimators. …

2016-05-01abs ↗pdf ↗

Theoretical Analysis of Divide-and-Conquer ERM: Beyond Square Loss and RKHScs.LG

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.

distributed learning empirical risk minimization general loss functions hypothesis spaces risk bounds

2020-03-09abs ↗pdf ↗

A Closer Look at Small-loss Bounds for Bandits with Graph Feedbackcs.LG

We study small-loss bounds for adversarial multi-armed bandits with graph feedback, that is, adaptive regret bounds that depend on the loss of the best arm or related quantities, instead of the total number of rounds. We derive the first small-loss bound for general strongly observable graphs, resolving an open problem…

2020-02-02abs ↗pdf ↗

Orthogonal Statistical Learning with Self-Concordant Lossstat.ML

Improves statistical learning bounds with self-concordant losses.

problem Statistical prediction with nuisance components.

method Orthogonal statistical learning with self-concordant loss.

result Non-asymptotic bounds on excess risk improved by a dimension factor.

statistical learning self-concordant loss excess risk two-stage prediction nuisance component

2022-04-30abs ↗pdf ↗

Unconstrained Online Learning with Unbounded Lossescs.LG

New algorithms for online learning without boundedness or Lipschitz loss assumptions.

problem Online learning with unbounded domains and non-Lipschitz losses.

method Developed an algorithm with a specific regret bound and used it for saddle-point optimization.

result First algorithm achieving non-trivial dynamic regret in an unbounded domain for non-Lipschitz losses.

online learning unbounded domains non-Lipschitz losses saddle-point optimization dynamic regret

2023-06-08abs ↗pdf ↗

Quantile Risk Control: A Flexible Framework for Bounding the Probability of High-Loss Predictionscs.LG

Flexible framework for bounding high-loss predictions using quantiles.

problem Need for rigorous guarantees in risk-sensitive applications.

method Order statistics of loss values, flexible quantile-based metrics.

result Ability to rigorously control loss quantiles on real-world datasets.

quantile risk control predictive algorithms order statistics loss distribution quantile-based metrics

2022-12-27abs ↗pdf ↗

An Improved Privacy and Utility Analysis of Differentially Private SGD with Bounded Domain and Smooth Lossescs.LG

Paper improves privacy and utility of SGD with bounded domain and smooth losses.

problem Lack of tight privacy bounds and practical assumptions in DPSGD.

method Rigorous privacy characterization for DPSGD with general L-smooth and non-convex loss functions, tracking privacy loss over iterations.

result Privacy loss converges without convexity assumption for bounded domain, improving utility.

Differentially Private SGD Privacy Utility Trade-off Bounded Domain Smooth Losses Convergence Analysis

2025-02-25abs ↗pdf ↗

Risk Bounds and Calibration for a Smart Predict-then-Optimize Methodcs.LG

This paper improves risk bounds and calibration for smart predict-then-optimize method.

problem Improving risk bounds and calibration for smart predict-then-optimize method.

method Develops risk bounds and uniform calibration results for the SPO+ loss relative to the SPO loss.

result Empirical minimizer of the SPO+ loss achieves low excess true risk with high probability.

predict-then-optimize SPO loss SPO+ loss risk bounds calibration

2021-08-19abs ↗pdf ↗

Demystifying Diffusion Objectives: Reweighted Losses are Better Variational Boundscs.LG

New reweighted losses improve diffusion model training and image quality.

problem Training and improving diffusion models for image generation.

method Constructing a cascade of time-dependent variational lower bounds.

result Significant improvements in pixel-space image modeling quality.

diffusion models variational bounds image generation reweighted losses

2025-11-24abs ↗pdf ↗

Relative Loss Bounds for On-line Density Estimation with the Exponential Family of Distributionscs.LG

We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an average of the past examples. After receiving an example the algorithm incurs a loss which is the negative log-likelihood…

2013-01-23abs ↗pdf ↗

The Central Role of the Loss Function in Reinforcement Learningstat.ML

The paper explores how different loss functions impact reinforcement learning algorithms.

problem Improving reinforcement learning algorithms by optimizing loss functions.

method Comprehensive survey on loss functions in reinforcement learning, proving the benefits of specific loss functions.

result Binary cross-entropy loss leads to first-order bounds and is more efficient than squared loss.

reinforcement learning loss functions binary cross-entropy squared loss distributional RL

2024-09-19abs ↗pdf ↗

Comparing Comparators in Generalization Boundscs.LG

The study optimizes bounds for comparing training and population loss.

problem Optimizing bounds for comparing training and population loss.

method Derives generic information-theoretic and PAC-Bayesian generalization bounds using convex comparator functions.

result The tightest possible bound is obtained with the comparator being the convex conjugate of the CGF of the bounding distribution.

generalization bounds PAC-Bayesian information theory cumulant-generating function convex functions

2023-10-16abs ↗pdf ↗

Revisiting Projection-Free Online Learning with Time-Varying Constraintscs.LG

Improved online learning with time-varying constraints for complex domains.

problem Constrained online convex optimization with time-varying constraints.

method Constructing a composite surrogate loss and using the online Frank-Wolfe method.

result Novel regret and cumulative constraint violation bounds for strongly convex losses.

online learning constrained optimization time-varying constraints composite surrogate loss Frank-Wolfe method

2025-01-27abs ↗pdf ↗

Optimal Multiclass U-Calibration Error and Beyondstat.ML

Optimal multiclass U-calibration error found to be Θ(√KT).

problem Online multiclass U-calibration with low regret for all bounded proper losses.

method Follow-the-Perturbed-Leader algorithm and lower bound construction.

result Optimal U-calibration error is Θ(√KT).

U-calibration online learning regret proper losses Follow-the-Perturbed-Leader

2024-05-28abs ↗pdf ↗

Uniform Deviation Bounds for Unbounded Loss Functions like k-Meansstat.ML

Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss…

2017-02-27abs ↗pdf ↗

Relative Deviation Margin Boundscs.LG

New margin-based learning guarantees improve generalization bounds.

problem Improving generalization bounds for machine learning models.

method Relative deviation margin bounds using empirical margin loss and Rademacher complexity.

result Distribution-dependent generalization bounds for unbounded loss functions.

margin-based learning generalization bounds Rademacher complexity unbounded loss functions

2020-06-26abs ↗pdf ↗

Minimizing The Misclassification Error Rate Using a Surrogate Convex Losscs.LG

We carefully study how well minimizing convex surrogate loss functions, corresponds to minimizing the misclassification error rate for the problem of binary classification with linear predictors. In particular, we show that amongst all convex surrogate losses, the hinge loss gives essentially the best possible bound, o…

2012-06-27abs ↗pdf ↗