New multivariate distribution for financial risk measurement.
problem Modeling dependent heavy-tailed risks in finance.
method Introduced a new absolutely continuous multivariate distribution with positively dependent Pareto margins.
result The new distribution is useful for describing dependent heavy-tailed risks in insurance.
PFES uses entropy of Pareto-frontier for multi-objective Bayesian optimization.
problem Bayesian optimization for multi-objective problems, especially trade-off among objectives.
method Pareto-frontier entropy search (PFES) incorporating trade-off relation.
result PFES effectively incorporates dependency among objectives conditioned on Pareto-frontier.
New algorithms for learning under s-concave distributions, including Pareto and t-distributions.
problem Learning under broad and natural generalizations of log-concave distributions, including fat-tailed ones.
method Introduce new convex geometry tools to study s s s -concave distributions and use these properties to provide bounds on learning quantities. result Significantly generalize prior results for margin-based, disagreement-based, and passive learning of intersections of halfspaces.
Study optimizes fairness in predictive models by balancing utility and separation.
problem Balancing fairness and utility in predictive models.
method Information-theoretic approach using conditional mutual information (CMI).
result Reduces separation violations while maintaining or improving utility.
MBPEP algorithm improves uncertainty prediction for unknown input distributions.
problem Difficulty in providing high-quality machine learning solutions for unknown input distributions.
method Margin-based Pareto deep ensemble pruning (MBPEP) model using deep ensemble networks and unique loss functions.
result Achieves small prediction interval width and high confidence of prediction interval coverage probability.
New MRF structures extend CreditRisk+ for modeling default and insurance risks.
problem Modeling default and insurance risks with multiple factors and heavy tails.
method Introducing MRF dependence structures that extend CreditRisk+ and model Pareto-distributed risks.
result MRF structures can model default and insurance risks with dependent and heavy-tailed components.
This work explores adaptive strategies for multi-armed bandits with causal structure, achieving optimal regret bounds.
problem Adapting to causal structure in multi-armed bandits with additional observed variables.
method Reduction to linear bandits and establishment of Pareto optimal frontier of adaptive rates.
result Established upper and lower bounds on adaptive rates, resolving open questions.
A new algorithm THV-UCB reduces regret in multi-objective bandit problems.
problem Maintaining a small set of actions that jointly approximate the Pareto frontier in multi-objective slate selection.
method THV-UCB, an optimistic algorithm that selects arms based on optimistic estimates of their marginal hypervolume contributions.
result The algorithm achieves a gap-free regret bound of i l d e O ( d n k T ) ilde{O}(d\sqrt{nkT}) i l d e O ( d nk T ) and a gap-dependent bound of i l d e O ( n k 2.5 / Δ min ) ilde{O}(nk^{2.5}/Δ_{\min}) i l d e O ( n k 2.5 / Δ m i n ) . Triangle fees adjust fees based on trade size and price movement, improving price accuracy and revenue.
problem Price staleness and low fee revenue in AMMs.
method Decreasing marginal fees proportional to price movement, creating incentives for price accuracy.
result Triangle fees strictly improve the Pareto frontier of price accuracy versus losses.
This paper applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that r…
The paper optimizes reinsurance under uncertain dependence among insurers.
problem Designing Pareto-optimal reinsurance contracts in a market with uncertain dependence.
method Robust optimization approach assuming known marginal distributions and unspecified dependence structure.
result Characterization of optimal indemnity schedules under worst-case scenario and derivation of optimal two-parameter layer contracts for independent risks.
Study of insurance market equilibria with risk-averse policyholders.
problem Analyzing optimal insurance contracts in a monopoly market with risk-averse policyholders.
method Modeling Stackelberg equilibria with a profit-maximizing insurer and a risk-averse policyholder.
result Equilibrium contracts exhibit a layer-type structure, providing full insurance over pessimistic loss layers and no coverage over optimistic ones.
We improve generative models for heavy-tailed multivariate data using an invariant statistical loss.
problem Traditional generative models struggle with heavy-tailed and multivariate data, leading to unstable training and mode dropping.
method We extend the invariant statistical loss method to handle heavy-tailed and multivariate data using a Pareto-ISL generator trained with input noise from a generalised Pareto distribution.
result Pareto-ISL accurately models the tails of heavy-tailed distributions while capturing central characteristics.
New method finds exact Pareto front for MO-MDPs efficiently.
problem Finding the exact Pareto front for MO-MDPs is challenging.
method Investigates geometric structure, develops efficient algorithm.
result Pareto front is on boundary of convex polytope of deterministic policies.
Paper proposes Adaptive Pareto Exploration for identifying Pareto optimal arms in multi-objective scenarios.
problem Identifying Pareto optimal arms in multi-objective scenarios with relaxed constraints.
method Adaptive Pareto Exploration strategy for different relaxations of Pareto Set Identification.
result Reduction in sample complexity when identifying at most k Pareto optimal arms.
GFlowNets sample diverse candidates in active learning.
problem Sampling diverse candidates in active learning.
method Generative Flow Networks (GFlowNets) for proportional sampling.
result GFlowNets estimate joint and marginal distributions.
Diversification improves profits for heavy-tailed investments.
problem Investment portfolios of Pareto-distributed returns.
method Stochastic dominance and majorization order.
result Diversification increases first-order stochastic dominance for heavy-tailed returns.
We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. Th…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance of the estimation of the shape parameter of generalized Pareto distributed using …
We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk ma…
In order to study the phenomenon in detail that income distribution follows Pareto law, we analyze the database of high income companies in Japan. We find a quantitative relation between the average capital of the companies and the Pareto index. The larger the average capital becomes, the smaller the Pareto index becom…
Pareto optimal centralized risk sharing with multiple agents
problem Centralized risk sharing with endogenous prices
method Inclusive and fair Pareto optimality
result Equivalence between inclusive and fair Pareto optimality and balanced sequential optimization
Study on Pareto optimality in multi-objective bandit problems.
problem Pareto optimality in multi-objective multi-armed bandit problems.
method Formulated adversarial multi-objective multi-armed bandit, defined Pareto regrets, presented algorithms, established upper and lower bounds.
result New algorithms are optimal in adversarial settings and nearly optimal in stochastic settings.
New Bayesian method improves Pareto front estimation in multitask finetuning.
problem Efficiently estimating Pareto fronts for multitask finetuning.
method Variational Model Merging using non-Gaussian posteriors.
result More flexible posteriors lead to better Pareto front estimates.
This paper develops a method to approximate the whole Pareto set for expensive multi-objective optimization.
problem Finding an approximate Pareto front with limited expensive evaluations.
method A novel learning-based method to approximate the whole Pareto set for multi-objective Bayesian optimization (MOBO).
result The method approximates the whole Pareto set, not just a finite set, for MOBO.
This paper solves aggregation of Pareto optimal models by using Bayesian priors and weighted averaging.
problem How to rationally aggregate Pareto optimal models while preserving Pareto efficiency.
method Four logical steps: 1) Bayesian models, 2) Prior as preference ranking, 3) Consistent aggregation, 4) Weighted average of priors.
result All rational/consistent aggregation rules follow a generalized hierarchical Bayesian model.
Agents prefer non-diversification in markets with extreme losses.
problem Optimal risk allocation and equilibria in markets with extremely heavy-tailed losses.
method Analysis of super-Pareto loss distributions and stochastic dominance.
result Non-diversification is preferred in markets with super-Pareto losses.
Pareto MTL finds optimal solutions for multiple tasks with different trade-offs.
problem Finding a single optimal solution for multiple conflicting tasks.
method Formulate multi-task learning as multiobjective optimization, decompose into subproblems, solve in parallel.
result Generates well-representative Pareto optimal solutions for different trade-offs.
This research extends the Pareto/NBD model using neural networks for better out-of-sample predictions.
problem The limitations of the Pareto/NBD model in predicting out-of-sample data.
method A neural network-based extension of the Pareto/NBD model.
result The proposed method shows extraordinary predictability on repeat purchases at individual and aggregate levels.
Unexpectedly, weighted Pareto variables are stochastically dominant.
problem Understanding stochastic dominance in Pareto distributions.
method Analyzing weighted averages of Pareto random variables with infinite mean.
result The weighted average of Pareto variables is stochastically dominant.
New method generates continuous Pareto sets for multi-task learning.
problem Challenges in finding optimal solutions for correlated multi-task learning problems.
method Efficiently generates locally continuous Pareto sets and fronts in multi-objective optimization problems.
result Demonstrates continuous analysis of Pareto optimal solutions in machine learning problems.
The univariate piecing-together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. We propose a multivariate extension. First it is shown that an arbitrary copula is in the domain of attraction of a multivariate extreme value …
Paper proves Pareto efficient insurance for multiple entities.
problem Optimizing insurance for multiple policyholders and insurers.
method Sum-minimization characterization and pairwise implementability analysis.
result Characterization of Pareto efficient insurance arrangements.
A-GPS learns to generate Pareto sets efficiently with user preferences.
problem Online discrete multi-objective optimization with user preferences.
method Generative model with class probability estimator (CPE) for non-dominance and preference alignment.
result Amortized generative model for efficient Pareto set approximation.
A new method for diverse Pareto solutions in multi-objective learning.
problem Maximizing diversity while maximizing hypervolume in Pareto solutions.
method Annealed Stein Variational Gradient Descent (SVGD) with diverse gradient directions.
result SVH-MOL achieves superior performance in multi-objective and multi-task learning.
Proposes a new way to represent and analyze Pareto front surfaces.
problem Identifying and analyzing Pareto front surfaces in multi-objective optimization.
method Parameterizes Pareto front surfaces using polar coordinates and scalar-valued length functions.
result Derives statistics of Pareto front surfaces and develops visualisation techniques.
Employing profits data of Japanese companies in 2002 and 2003, we confirm that Pareto's law and the Pareto index are derived from the law of detailed balance and Gibrat's law. The last two laws are observed beyond the region where Pareto's law holds. By classifying companies into job categories, we find that companies …
The paper tackles the trade-off between fairness and accuracy in machine learning models.
problem Ensuring fairness in machine learning often reduces model accuracy.
method The paper introduces formal tools for reconciling the fairness-accuracy tension using Pareto optimality from multi-objective optimization.
result The Chebyshev scalarization scheme is superior for finding Pareto optimal solutions compared to the linear scalarization scheme.
Algorithm identifies Pareto front in multi-objective bandits efficiently.
problem Sequentially learning the Pareto front in multi-objective bandits.
method Efficient algorithm achieving optimal sample complexity.
result Correct answer with high probability in minimal rounds.
A new method for multi-objective Bayesian optimization using entropy search and variational lower bound maximization.
problem Efficiently optimizing multiple objectives in continuous domains.
method Approximates the Pareto-frontier using a mixture distribution and optimizes the balance through variational lower bound maximization.
result Demonstrated effectiveness especially with many objective functions.
The paper simplifies strongly convex problems to simplicial structures.
problem Strongly convex problems with C r C^r C r smoothness. method Generic linear perturbations and singularity theory.
result Strongly convex C 1 C^1 C 1 problems are C 0 C^0 C 0 simplicial. Study on efficiency in economies with risk-averse agents, finding Pareto optima.
problem Efficiency in economies with risk-averse agents.
method Analysis of utility functionals, existence and characterization of Pareto optima.
result Existence and comonotone characterization of Pareto optima for risk-averse agents.
MOL-TS uses Thompson Sampling for multi-objective linear bandits with Pareto guarantees.
problem Optimizing multiple conflicting objectives in linear contextual bandits.
method Proposes MOL-TS, a Thompson Sampling algorithm with Pareto regret guarantees.
result Achieves a worst-case Pareto regret bound of O ~ ( d 3 / 2 T ) \widetilde{O}(d^{3/2}\sqrt{T}) O ( d 3/2 T ) . Study dynamic Pareto-optimal allocations in multi-period economies with time-consistent risk measures.
problem Optimal allocation in multi-period pure-exchange economies with stochastic endowments and time-consistent risk measures.
method Introduced dynamic Pareto-optimal allocation processes and derived recursive and comonotone improvement theorems.
result Dynamic Pareto-optimal allocation processes can be constructed recursively and are comonotone.
Algorithm identifies Pareto front using multiple context directions and reuses exploration samples.
problem Identifying a set of arms with undominated mean reward vectors in linear bandits.
method Proposes a new estimator that updates estimates along multiple context directions and reuses exploration samples.
result Optimal sample complexity and logarithmic regret compared to optimal algorithms.
This work improves cost-aware Bayesian optimization by introducing Pareto-efficient acquisition functions.
problem Cost variability in hyperparameter evaluations affects the efficiency of Bayesian optimization.
method Reformulated cost-aware Bayesian optimization as Pareto efficiency, proposing a novel Pareto-efficient expected improvement.
result Pareto-efficient acquisition functions significantly outperform previous solutions, providing finer control over cost-accuracy trade-offs.
This research focuses on optimizing expensive computer experiments with multiple objectives, targeting the central part of the Pareto front.
problem Optimizing complex systems with limited experiments and conflicting objectives.
method A Bayesian multi-objective optimization method that directs the search towards the central part of the Pareto front.
result The method, C-EHI, better locates the central part of the Pareto front compared to state-of-the-art algorithms.
New algorithms identify Pareto optimal sets in multi-objective bandit problems.
problem Identifying Pareto optimal sets in multi-objective bandit problems.
method Empirical Gap Elimination (EGE) algorithms combining hardness estimation and elimination schemes.
result Two EGE algorithms have exponentially decaying error probabilities with budget.