Study risk-sensitive reinforcement learning with Lipschitz dynamic risk measures, establishing regret bounds.
problem Risk-sensitive reinforcement learning in Markov decision processes.
method Two model-based algorithms for Lipschitz dynamic risk measures, focusing on regret bounds.
result Upper bounds demonstrate optimal dependencies on actions and episodes, reflecting risk sensitivity vs. sample complexity trade-off.
Paper provides new bounds for risk aggregation and sharing.
problem Quantitative risk management and robust risk aggregation with dependence uncertainty.
method Established new inequality for RVaR, derived extended convolution bounds, and analyzed risk sharing for averaged quantiles.
result Extended convolution bounds for robust risk aggregation and risk sharing, providing sharpness conditions and explicit expressions.
We estimate risk measures in Markov cost processes with lower and upper bounds.
problem Estimating risk measures in infinite-horizon discounted costs within Markov processes.
method Truncation scheme and lower/upper bounds for CVaR and variance estimation.
result Upper and lower bounds for CVaR and variance estimation match up to logarithmic factors.
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.
New risk measures control subgroup imbalances, improving PAC-Bayesian bounds.
problem Insufficient risk bounds for subgroup imbalances in data.
method Introduce constrained f-entropic risk measures and derive PAC-Bayesian bounds.
result First disintegrated PAC-Bayesian guarantees beyond standard risks.
The paper analyzes risk estimation methods and derives bounds for OCE risk.
problem Estimating the Optimized Certainty Equivalent (OCE) risk from samples.
method Derives mean-squared error and concentration bounds for SAA of OCE, and analyzes an efficient stochastic approximation-based estimator.
result Finite sample bounds and mis-identification probability bounds for the efficient estimator.
We derive bounds for a notion of adversarial risk, designed to characterize the robustness of linear and neural network classifiers to adversarial perturbations. Specifically, we introduce a new class of function transformations with the property that the risk of the transformed functions upper-bounds the adversarial r…
This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introduced include as special cases well known risk measures from the finance literature such as condition…
Study risk-sensitive reinforcement learning with entropic risk measures and generative models.
problem Risk-sensitive reinforcement learning in discounted MDPs with recursive entropic risk measures.
method Introduced Model-Based ERM Q-Value Iteration (MB-RS-QVI) and derived PAC bounds on sample complexity for value and policy learning. result PAC bounds show exponential dependence on ∣β∣/(1−γ), with tight bounds in S and A. ERTS uses Thompson sampling for Gaussian entropic risk bandits, achieving regret bounds.
problem Risk in decision making complicates reward maximization in MAB problems.
method ERTS (Entropic Risk Thompson Sampling) using Thompson sampling with an entropic risk measure.
result Regret bounds for ERTS under entropic risk measure provided.
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.
The paper bounds payoffs and option prices in discrete models.
problem Measuring risk in discrete models and incomplete markets.
method Analytical and simulated bounds for payoff functions and option prices.
result Analytical and simulated bounds for European and American options.
The paper calculates MES bounds for systemic risk contributions under uncertain dependence.
problem Measuring systemic risk contributions of financial firms under uncertainty in dependence structure.
method Derives worst-case and best-case bounds for MES under known individual firm risks and partial dependence information.
result Improved MES bounds derived for various types of dependence models.
This paper unifies risk-averse Thompson sampling for continuous risk functionals.
problem Designing and analyzing risk-averse Thompson sampling algorithms for continuous risk functionals.
method Developed analytical toolkits to prove asymptotically optimal regret bounds for various risk measures.
result Proved asymptotic optimality of ρ-MTS for Bernoulli distributions and a class of risk measures. For a risk vector V, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by Value-at-Risk or Conditional Tail Expectation. We assume Pareto tails for the componen…
Paper bounds convergence rate of adversarial surrogate risk.
problem Vulnerability of binary classification models to adversarial attacks.
method Characterizes conditions for adversarial consistency and provides surrogate risk bounds.
result Surrogate risk bounds quantify the rate of convergence of adversarial classification risk.
Study gap-dependent regret bounds for risk-sensitive RL.
problem Risk-sensitive reinforcement learning with entropic risk measure.
method Propose cascaded gaps to adapt to problem structures, derive regret bounds.
result Exponential improvement over existing bounds in appropriate settings.
Improved risk-sensitive RL with exponential Bellman equation and better regret bounds.
problem Exponential gap between upper and lower bounds in risk-sensitive RL.
method Identified and addressed deficiencies in existing algorithms and analysis; developed novel analysis and exploration mechanism.
result Improved regret upper bounds over existing ones.
Prove non-asymptotic bounds for minimal risk in statistical learning
problem Estimating minimal risk in statistical learning
method Using concentration inequalities
result Non-asymptotic bounds for minimal risk
The risk premium is one of main concepts in mathematical finance. It is a measure of the trade-offs investors make between return and risk and is defined by the excess return relative to the risk-free interest rate that is earned from an asset per one unit of risk. The purpose of this article is to determine upper and …
Study minimax linear regression under quantile risk, improving existing bounds and providing new results.
problem Designing minimax procedures in linear regression under quantile risk.
method Analyzes realizable setting with Gaussian noise, extends to all p-th power error functions, develops new lower and upper bounds.
result Proves minimaxity of a variant of the min-max regression procedure for all p-th power error functions.
Sharp bounds found for various risk measures using generalized FGM copulas.
problem Finding sharp bounds for risk measures in high dimensions.
method Proved that generalized FGM copulas form a convex polytope, used this structure to find bounds for risk measures.
result Sharp analytical bounds for convex risk measures in the class of generalized FGM copulas.
The paper establishes risk bounds for PU learning with label noise.
problem Finding a classifier in PU learning with label noise.
method Establishes risk bounds under the assumption of label selection randomness.
result Proves that the upper bound on minimax risk is almost optimal.
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.
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.
Lower bounds on Bayes risk for realizable models derived using information theory.
problem Deriving lower bounds on Bayes risk for realizable machine learning models.
method Information-theoretic analysis using rate-distortion theory and mutual information.
result Lower bounds on Bayes risk for realizable models, matching known bounds up to logarithmic factors.
We consider a problem of risk estimation for large-margin multi-class classifiers. We propose a novel risk bound for the multi-class classification problem. The bound involves the marginal distribution of the classifier and the Rademacher complexity of the hypothesis class. We prove that our bound is tight in the numbe…
The paper improves risk certificate tightness for neural networks using PAC-Bayes bounds.
problem Improving the usability of risk certificates for neural networks based on PAC-Bayes bounds.
method Theoretical contributions including KL divergence bounds, efficient methodology for optimization, and methods for optimizing non-differentiable objectives.
result First non-vacuous generalization bounds on CIFAR-10 for neural networks.
Develops bounds for deep learning risk via Hilbert coresets.
problem Risk estimation for complex deep learning models.
method Hilbert coreset approach for transductive risk bounds.
result Effective and meaningful bounds for deep neural networks.
In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation ineq…
The study establishes risk bounds for distributional regression estimators.
problem Estimating distributional regression models with nonparametric methods.
method Theoretical bounds for CRPS and MSE are derived for convex and non-convex constraints.
result Theoretical risk bounds are validated through experiments on simulated and real data.
Paper improves risk bounds for nonconvex-strongly-concave minimax problems.
problem Achieving sharper risk bounds for nonconvex-strongly-concave minimax problems.
method Using uniform localized convergence to derive high probability generalization error bounds.
result Derives n times faster excess primal risk bounds for popular algorithms.
Estimating and assessing the risk of a large portfolio is an important topic in financial econometrics and risk management. The risk is often estimated by a substitution of a good estimator of the volatility matrix. However, the accuracy of such a risk estimator for large portfolios is largely unknown, and a simple ine…
We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized …
Paper extends learning theory to dependent data with uniform risk bounds.
problem Learning with dependent data sequences.
method Derives uniform risk bounds for dependent data using VC-dimension and Rademacher complexity.
result Standard classification risk bounds hold for dependent data, same as for independent data.
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. Novel MOBO method for risk measures under input uncertainty.
problem Efficiently identifying Pareto front for black-box functions with input uncertainty.
method Assumes Gaussian process model and constructs bounding boxes for risk measures.
result The method can return an arbitrary-accurate solution with high probability.
Quantum reservoirs risk bounds are analyzed using Rademacher complexity.
problem Bounding generalization errors of quantum reservoirs.
method Using Rademacher complexity, specific bounds are derived for quantum reservoir classes.
result Risk bounds converge with increasing training samples and qubits.
New bounds for quantile aggregation unify and clarify existing methods.
problem Analytical bounds for quantile aggregation with dependence uncertainty.
method Using inf-convolution of quantile-based risk measures, establish new analytical bounds called convolution bounds.
result Convolution bounds are the best available and provide sharp results in many cases.
In this paper, we study the statistical properties of kernel k-means and obtain a nearly optimal excess clustering risk bound, substantially improving the state-of-art bounds in the existing clustering risk analyses. We further analyze the statistical effect of computational approximations of the Nyström kernel k-m…
Optimizes shortfall risk using gradient-based methods.
problem Optimizing utility-based shortfall risk measures.
method Gradient-based stochastic optimization, non-asymptotic bounds derivation.
result Non-asymptotic convergence rate for optimizing UBSR.
The paper analyzes risk bounds and Rademacher complexity in batch RL.
problem Estimating/minimizing Bellman error with general value function approximation.
method Characterizes generalization performance using Rademacher complexities of function classes.
result Risk bounds and Rademacher complexities provide insights into batch RL.
Deep linear networks can closely approximate interpolants without improving risk.
problem Understanding the risk bounds of deep linear networks compared to minimum ℓ2-norm solutions. method Bounding excess risk of interpolating deep linear networks trained using gradient flow.
result Deep linear networks can closely approximate or match minimum ℓ2-norm solutions in terms of risk. Study non-asymptotic bounds for robust estimators under misspecified models.
problem Evaluate performance of robust estimators under adversarial conditions.
method Propose a general approach to adversarial risk analysis, including investigations on generalization and approximation errors.
result Establish non-asymptotic upper bounds for adversarial excess risk under Lipschitz loss functions.
We shall provide in this paper good deal pricing bounds for contingent claims induced by the shortfall risk with some loss function. Assumptions we impose on loss functions and contingent claims are very mild. We prove that the upper and lower bounds of good deal pricing bounds are expressed by convex risk measures on …
The paper addresses human-like decision-making in multi-agent systems using bounded risk-sensitive Markov Games.
problem Modeling human-like decision-making in multi-agent systems with risk-seeking and loss-aversion behaviors.
method Forward policy design and inverse reward learning with iterative reasoning and cumulative prospect theory.
result The proposed algorithms demonstrate both risk-averse and risk-seeking behaviors in multi-agent systems.
Sharp risk bounds for early-stopping in Gaussian linear regression are derived.
problem Minimizing in-sample mean squared error in high-dimensional Gaussian linear regression.
method Early-stopped mirror descent (ESMD) with local Gaussian width bounds.
result Sharp risk bounds extend to early-stopped mirror descent for least squares estimator (LSE).
Unified bounds for DP risks reduce noise and improve accuracy.
problem Difficult interpretation and calibration of DP mechanisms.
method Hypothesis-testing interpretation of DP (f-DP) and unified bounds. result Unified bounds are tighter and tunable for specific risks.