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.
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.
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 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.
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.
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…
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.
Multi-task learning is a powerful method for solving multiple correlated tasks simultaneously. However, it is often impossible to find one single solution to optimize all the tasks, since different tasks might conflict with each other. Recently, a novel method is proposed to find one single Pareto optimal solution with…
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.
PALS extends PAL for optimizing stochastic simulators efficiently.
problem Optimizing stochastic simulators with high output variance and expensive evaluations.
method Bayesian optimization with probabilistic models, extending PAL for stochastic settings.
result PALS outperforms other methods in optimizing stochastic simulators.
Algorithm identifies Pareto optimal designs efficiently for noisy, multi-objective functions.
problem Optimizing multi-objective functions with noisy data and large design spaces.
method Adaptive discretization and tree-based approach to identify Pareto optimal designs.
result Algorithm identifies Pareto optimal designs with fewer evaluations than exhaustive search.
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.
New method for identifying best designs in vector optimization with uncertain feedback.
problem Optimizing vector-valued outcomes with uncertain preferences.
method Stochastic bandit feedback, polyhedral ordering cone, (ε,δ)-PAC Pareto set identification. result Sample complexity characterized and matched by the naïve elimination algorithm.
SVH-PSL uses Stein Variational Gradient Descent and Hypernetworks to improve Pareto set learning for expensive MOO.
problem Fragmented surrogate models and pseudo-local optima in expensive multi-objective optimization problems.
method SVH-PSL integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks to address fragmentation and pseudo-local optima.
result SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive MOO.
This work fills the gap in understanding multi-objective learning generalization.
problem Lack of statistical learning theory insights into multi-objective learning generalization.
method Established generalization bounds and excess bounds for multi-objective learning.
result Showed that all Pareto-optimal solutions can be approximated by empirically Pareto-optimal ones, but not vice versa.
This paper studies an entropy-based multi-objective Bayesian optimization (MBO). The entropy search is successful approach to Bayesian optimization. However, for MBO, existing entropy-based methods ignore trade-off among objectives or introduce unreliable approximations. We propose a novel entropy-based MBO called Pare…
New method finds all Nash equilibria via vector optimization.
problem Finding all Nash equilibria in games.
method Formulate vector optimization problem to find Pareto optimal solutions.
result Characterize set of all Nash equilibria as Pareto optimal solutions.
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.
The paper tackles identifying Pareto Set with constraints using bandit feedback.
problem Identifying the Pareto Set under feasibility constraints in a multivariate bandit setting.
method Fixed-confidence identification algorithm that outperforms existing methods.
result The sample complexity of the proposed algorithm is near-optimal.
The paper proposes a new method to learn choice functions using Pareto-embeddings.
problem Learning subset choices from feature vectors.
method Embedding choice alternatives into a higher-dimensional utility space and identifying choice sets with Pareto-optimal points. Minimizing a differentiable loss function.
result The feasibility of learning a Pareto-embedding demonstrated on benchmark datasets.
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
Optimal algorithms identify non-dominated arms in multi-output linear bandit models.
problem Identifying the Pareto Set in multi-output linear bandit models.
method Design-based algorithms for Pareto Set Identification (PSI) in a structured multi-output linear bandit model.
result Nearly optimal guarantees in both fixed-budget and fixed-confidence settings.
Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the evaluation of the functions in question are expensive. Traditional methods for mult…
Optimizing nonlinear systems involving expensive computer experiments with regard to conflicting objectives is a common challenge. When the number of experiments is severely restricted and/or when the number of objectives increases, uncovering the whole set of Pareto optimal solutions is out of reach, even for surrogat…
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.
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.
MOBO-OSD optimizes multi-objective functions using orthogonal search directions.
problem Challenging multi-objective optimization problem.
method Solves multiple constrained optimization problems along orthogonal search directions.
result Consistently outperforms state-of-the-art algorithms.
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.
A multiobjective optimization problem is simplicial if the Pareto set and front are homeomorphic to a simplex and, under the homeomorphisms, each face of the simplex corresponds to the Pareto set and front of a subproblem. In this paper, we show that strongly convex problems are simplicial under a mild assumption on th…
New ABC method improves Bézier simplex fitting for noisy data.
problem Overfitting in Bézier simplex fitting when sample points are not on the Pareto set.
method Extended Bézier simplex model to a probabilistic one and proposed a new learning algorithm based on approximate Bayesian computation (ABC) with Wasserstein distance.
result The new algorithm converges on a finite sample and outperforms deterministic methods on noisy instances.
Paper proposes PSIPS for identifying Pareto set with correlated objectives.
problem Identifying the best answer among items with multiple conflicting metrics.
method Posterior sampling in stopping and sampling rules for structure and correlation.
result PSIPS is asymptotically optimal and demonstrates good empirical performance.
The paper analyzes reinsurance strategies in peer-to-peer insurance schemes.
problem Strategic interaction between plan managers and reinsurers in P2P insurance.
method Develops two game-theoretic contract designs: Pareto and Bowley designs, deriving optimal contracts and analyzing their welfare effects.
result The Bowley design yields a unique optimal contract, while the Pareto design allows for multiple Pareto-optimal contracts.
In this paper we propose the multi-objective contextual bandit problem with similarity information. This problem extends the classical contextual bandit problem with similarity information by introducing multiple and possibly conflicting objectives. Since the best arm in each objective can be different given the contex…
Pareto Testing optimizes model performance under multiple constraints.
problem Optimizing machine learning models with multiple conflicting objectives.
method Two-stage process combining optimization and statistical testing.
result Models can be configured to satisfy multiple statistical guarantees and objectives.
Bayesian method reduces misclassification errors in ranking Pareto-optimal solutions.
problem Identifying true Pareto-optimal solutions in noisy multiobjective optimization.
method Sequential allocation of extra samples using stochastic kriging to build predictive distributions.
result The proposed method outperforms existing algorithms in reducing misclassification errors.
A multiobjective optimization problem is Cr simplicial if the Pareto set and the Pareto front are Cr diffeomorphic to a simplex and, under the Cr diffeomorphisms, each face of the simplex corresponds to the Pareto set and the Pareto front of a subproblem, where 0≤r≤∞. In the paper titled "Topolo…
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.
We solve a portfolio selection problem with four objectives, finding convex scalarizations for part of the Pareto front.
problem Portfolio selection with four objectives: mean, variance, skewness, and kurtosis.
method Linearly scalarize MVSK objectives into a convex polynomial Fλ over the probability simplex, compute optimizers for each λ. result Identify a set of hyper-parameters for which the scalarization is convex, allowing computation of part of the Pareto front.
This paper surveys gradient-based multi-objective deep learning methods.
problem Balancing multiple conflicting objectives in deep learning models.
method Gradient-based techniques adapted from Multi-Objective Optimization.
result Comprehensive survey of gradient-based multi-objective deep learning algorithms.
The paper addresses risk sharing and variability measures among agents with general risk preferences.
problem Risk sharing and variability measures among agents with general risk preferences.
method Characterizes Pareto-optimal allocations using Gini deviation, mean-median deviation, and inter-quantile difference as variability measures.
result Optimal allocations are not comonotonic and feature a mixture of pairwise counter-monotonic structures.
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.
This paper improves fraud prevention rule sets in fintech by generating diverse rules and finding Pareto-optimal subsets.
problem Improving the quality and flexibility of fraud prevention rule sets in fintech.
method Introducing SpectralRules for generating diverse rules, and PORS for finding Pareto-optimal subsets.
result SpectralRules generates diverse rules that improve the quality of final rule subsets.
Proposes MOGFNs for generating diverse Pareto optimal solutions in multi-objective optimization.
problem Generating diverse candidates in multi-objective optimization with conflicting objectives.
method Introduces MOGFNs based on GFlowNets, with two variants: MOGFN-PC and MOGFN-AL.
result Improved candidate diversity compared to existing methods.
FraPPE efficiently identifies Pareto optimal arms in multi-objective bandits.
problem Efficiently identifying Pareto optimal arms in multi-objective bandits with confidence.
method Deriving structural properties and using Frank-Wolfe optimisation to solve the maxmin optimisation problem.
result FraPPE achieves optimal sample complexity and identifies the exact Pareto set.
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 studies risk-sharing allocations for risk-seeking agents using a common distortion risk measure.
problem Characterizing Pareto-optimal risk-sharing allocations for risk-seeking agents.
method Modeling preferences with a common distortion risk measure and analyzing three settings: risk-averse, risk-seeking, and inverse S-shaped distortion.
result Pareto-optimal allocations for risk-seeking agents are counter-monotonic, not comonotonic.
Study optimal risk sharing in decentralized peer-to-peer markets with robust risk measures.
problem Optimizing risk sharing in decentralized markets with non-convex risk measures.
method Characterization of Pareto-optimal allocations using robust distortion risk measures and probabilistic risk aversion.
result Shape of allocations depends on agents' tail risk assessments.
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.