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.
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.
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.
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.
No arbitrage holds if a Pareto solution exists for vector-valued utility maximization.
problem Existence of no arbitrage in markets with transaction costs and multiple assets.
method Prove no arbitrage condition equivalent to Pareto solution for vector-valued utility maximization.
result A consistent price process can be constructed from the Pareto maximizer.
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…
Proposes Pareto efficient fairness for supervised learning models.
problem Ensuring fairness in machine learning models without sacrificing accuracy.
method Formulates a bilevel optimization problem to find Pareto efficient classifiers.
result Guaranteed solution on Pareto frontier for convex and non-convex objectives.
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.
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.
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.
Develops a distributed strategy for Pareto optimization of aggregate costs with smoothed regularizers.
problem Optimizing aggregate costs with non-smooth regularizers in a network of agents.
method Distributed strategy using infimal convolution to smooth regularizers, seeking Pareto optimal solution via diffusion.
result Pareto solution of smoothed problem can be made arbitrarily close to original non-smooth problem.
Method orders Pareto solutions using transformed objective scores.
problem Lack of orderability in multi-objective optimization solutions.
method Probability integral transform to map objectives to scores.
result Pareto efficient solutions can be ordered in score space.
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.
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.
Paper approximates solutions for complex decision processes with limited precision.
problem Approximating the set of all solutions for Multi-objective Markov Decision Processes.
method Limited precision approach based on White's multi-objective value-iteration dynamic programming algorithm.
result The number of calculated solutions is tractable and approximates the true 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.
Bayesian method helps decision-makers find preferred solutions in multi-objective optimization.
problem Identifying preferred solutions from the Pareto set in multi-objective optimization problems.
method Bayesian model to estimate decision-maker's utility function based on pairwise comparisons, guided by a principled elicitation strategy.
result Superior performance in finding high-utility solutions with a small number of queries.
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.
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.
SURF steers scalarization weights to uniformly traverse the Pareto front.
problem Non-uniform coverage of the Pareto front when using scalarization weights.
method Geometric analysis and CDF mapping to select weights for uniform coverage.
result SURF converges to uniform Pareto front coverage under provable conditions.
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.
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.
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.
Small parameterized towers improve multi-task learning efficiency and generalization.
problem Balancing Pareto efficiency and generalization in multi-task learning.
method Under-parameterized self-auxiliaries for multi-task models.
result Small parameterized towers enhance Pareto efficiency in various multi-task applications.
This paper analyzes MORL and proposes efficient algorithms to learn Pareto optimal policies.
problem Understanding and efficiently learning Pareto optimal policies in multi-objective reinforcement learning.
method Systematic analysis of optimization targets, reformulation of Tchebycheff scalarization, online UCB-based algorithm, preference-free framework.
result Identification of Tchebycheff scalarization as a favorable method and efficient algorithms for learning Pareto optimal policies.
We present a multi-objective Bayesian optimisation algorithm that allows the user to express preference-order constraints on the objectives of the type "objective A is more important than objective B". These preferences are defined based on the stability of the obtained solutions with respect to preferred objective fun…
The study analyzes the conflict between group fairness and individual fairness in machine learning.
problem The conflict between group fairness (optimal statistical parity) and individual fairness in machine learning.
method Established sufficient conditions for the compatibility between optimal statistical parity and individual fairness requirements.
result Identified regions along the Pareto frontier that satisfy individual fairness requirements.
PAIR optimizes machine learning models to generalize better to out-of-distribution data.
problem Optimization of machine learning models for out-of-distribution (OOD) generalization often leads to compromises that weaken robustness.
method Introduces a multi-objective optimization (MOO) perspective and a new optimization scheme called PAreto Invariant Risk Minimization (PAIR).
result PAIR improves robustness of OOD objectives by cooperatively optimizing with other objectives, yielding top OOD performances.
Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for the entire set. As an end-user would typically prefer a certain part of the objec…
VOGP efficiently identifies Pareto optimal solutions in black-box vector optimization.
problem Black-box vector optimization with incomplete order relations.
method VOGP is an adaptive elimination algorithm using Gaussian process bandits.
result VOGP achieves theoretical guarantees with sample complexity bounds.
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.
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 …
Bayesian optimization with preference learning identifies preferred solutions in multi-objective problems.
problem Optimizing multiple criteria with decision maker preferences in expensive functions.
method Bayesian optimization with interactive preference learning and active acquisition function.
result Identifies the most preferred solution with reduced interaction cost.
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.
A framework for efficient multi-objective optimization using entropy search.
problem Optimizing expensive black-box functions with multiple objectives.
method Output space entropy search (OSE) to minimize resource cost.
result Improves efficiency and accuracy in multi-objective optimization.
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.
Proposes a fair PCA algorithm that balances reconstruction loss and fairness.
problem PCA can be unfair to different groups.
method Adaptive first-order algorithm for Pareto optimality.
result The algorithm finds a fair subspace that minimizes reconstruction loss.
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.
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.
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.
Novel NAS method balances performance and hardware metrics efficiently.
problem Challenging multi-objective optimization in neural architecture search.
method Parameterizes joint architectural distribution via hypernetwork conditioned on hardware features and preferences.
result Zero-shot transferability to new devices with representative and diverse architectures.
BOtied optimizes multiple objectives using copulas and CDF indicators.
problem Joint optimization of multiple competing objectives.
method Proposes BOtied, a new acquisition function based on the CDF.
result BOtied outperforms state-of-the-art MOBO acquisition functions.
Study risk sharing among agents with varying risk preferences.
problem Risk sharing among agents with heterogeneous risk measures.
method Derive explicit solutions for inf-convolution and counter-monotonic inf-convolution under varying risk seeking.
result Explicit solutions for inf-convolution and counter-monotonic inf-convolution can be represented by a generalization of distortion risk measures.