This paper introduces the hypervolume maximization with a single solution as an alternative to the mean loss minimization. The relationship between the two problems is proved through bounds on the cost function when an optimal solution to one of the problems is evaluated on the other, with a hyperparameter to control t…
This work improves GAN training by optimizing multiple discriminator losses.
problem Training GANs with multiple discriminators using single-objective methods.
method Formulates multi-objective optimization of multiple discriminator losses.
result Hypervolume maximization outperforms previous methods in sample quality and computational cost.
This paper introduces a new scalarization method for multi-objective optimization.
problem Efficiently optimizing multiple conflicting objectives in black box settings.
method Introduces a novel hypervolume scalarization function and uses it to approximate the hypervolume indicator metric.
result Provable convergence to the entire Pareto frontier using random scalarizations and Bayesian optimization.
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 ) . Simulated annealing improves candidate optimization for multi-objective Bayesian optimization.
problem Efficient candidate optimization for multi-objective acquisition functions in Bayesian optimization.
method Simulated annealing-based approach for batch acquisition function optimization.
result Simulated annealing outperforms SLSQP in most multi-objective optimization problems, achieving higher hypervolume values and better convergence characteristics.
This paper calculates the exact probability distribution of hypervolume improvement for bi-objective problems.
problem Calculating the exact probability distribution of hypervolume improvement in bi-objective problems.
method Cell partition-based method to derive the probability distribution of hypervolume improvement from a bi-variate Gaussian random variable.
result The proposed ε \varepsilon ε -PoHVI acquisition function outperforms other related functions in Bayesian optimization. Parallel Bayesian optimization tackles noisy multi-objective problems.
problem Optimizing multiple objectives with noisy data.
method NEHVI and q q q NEHVI acquisition functions, integrating Bayesian treatment over uncertainty. result Parallel q q q NEHVI is one-step Bayes-optimal and robust to noise. 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 scalarizing functions improve multi-objective Bayesian optimisation.
problem Improving multi-objective Bayesian optimisation efficiency.
method Comparing two infill criteria based on hypervolume improvement.
result Effective scalarizing functions enhance hypervolume maximisation.
An efficient algorithm calculates exact EHVI values for multi-objective optimization problems.
problem Efficient computation of EHVI values for multi-objective optimization problems.
method Partitioning the integration volume into axis-parallel slices and using a new hyperbox decomposition technique.
result Theoretical time complexity improved to Θ ( n log n ) Θ(n\log n) Θ ( n log n ) , asymptotically optimal. A new parallel BO method with exact gradients for multi-objective optimization.
problem Efficiently optimizing multiple objectives in a sample-efficient manner.
method Derive q-Expected Hypervolume Improvement (qEHVI) for parallel, constrained evaluation.
result qEHVI is computationally tractable and outperforms state-of-the-art methods.
Bayesian optimization algorithm with preference constraints on objectives.
problem Finding Pareto-optimal solutions with user-defined preference over objectives.
method A multi-objective Bayesian optimization algorithm that incorporates user-defined preference constraints on objectives. The algorithm selects Pareto-optimal points that satisfy these constraints and uses a new acquisition function based on expected improvement in dominated hypervolume (EHI).
result The algorithm efficiently explores the Pareto front satisfying user-defined preference constraints.
Student- t t t processes have recently been proposed as an appealing alternative non-parameteric function prior. They feature enhanced flexibility and predictive variance. In this work the use of Student- t t t processes are explored for multi-objective Bayesian optimization. In particular, an analytical expression for the h…
TAMO optimizes multiple objectives in-context using transformers.
problem Balancing competing objectives in expensive, black-box problems.
method Fully amortized, transformer-based policy for multi-objective optimization.
result Significant speedup in proposal time with improved Pareto quality.
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…
Pessimistic estimator improves multi-objective policy optimization.
problem Optimizing multi-objective policies from existing data.
method Pessimistic estimator based on inverse propensity scores (IPS).
result Pessimistic estimator outperforms naive IPS estimator in theory and experiments.
A new method for multi-objective Bayesian optimization.
problem Finding optimal compromises between competing objectives.
method Joint Entropy Search (JES) acquisition function for multi-objective Bayesian optimization.
result JES outperforms existing methods in terms of hypervolume and its variants.
FlexiBO optimizes deep neural networks by balancing cost and performance.
problem Optimizing deep neural networks for multiple objectives incurs high costs.
method Decouples and weights cost in multi-objective Bayesian optimization.
result FlexiBO discovers designs with lower hypervolume error.
Much of the focus in machine learning research is placed in creating new architectures and optimization methods, but the overall loss function is seldom questioned. This paper interprets machine learning from a multi-objective optimization perspective, showing the limitations of the default linear combination of loss f…
MO-CBO optimizes multiple outcomes in causal systems with minimal data.
problem Optimizing multiple outcomes in causal systems with limited data.
method Decomposes MO-CBO into multi-objective optimization tasks and uses relative hypervolume improvement for sequential intervention balancing.
result MO-CBO outperforms traditional multi-objective Bayesian optimization in causal settings.
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.
In multi-objective Bayesian optimization and surrogate-based evolutionary algorithms, Expected HyperVolume Improvement (EHVI) is widely used as the acquisition function to guide the search approaching the Pareto front. This paper focuses on the exact calculation of EHVI given a nondominated set, for which the existing …
Bayesian optimization improves DRL for ESG portfolio management.
problem Optimizing hyperparameters of DRL agents for ESG metrics.
method Bayesian optimization for noisy, expensive-to-evaluate functions.
result Multi-objective optimization yields optimal Pareto set of portfolios.
Adaptive algorithm for multi-objective optimization with binary constraints.
problem Optimization of black-box problems with binary constraints.
method Bayesian optimization using regression and classification models.
result Significantly faster expected hypervolume calculation.
EHVI outperforms scalarized EI in MOBO for molecule design.
problem Benchmarking MOBO strategies for molecule design.
method Compared EHVI against fixed-weight scalarized EI in MOBO.
result EHVI consistently outperforms scalarized EI in molecular optimization tasks.
A new Adamize method improves multi-objective recommender systems.
problem Improving recommendation systems with multiple conflicting objectives.
method Developed a multi-objective model-agnostic Adamize method that corrects and stabilizes gradients.
result Significant improvements in recommendation systems, measured by hypervolume, coverage, and spacing.
PRISM integrates diverse rewards in MORL, improving sample efficiency and Pareto coverage.
problem Heterogeneous MORL where dense objectives dominate, leading to poor sample efficiency.
method PRISM uses reflectional symmetry and ReSymNet to reconcile temporal-frequency mismatches and accelerate exploration.
result PRISM consistently outperforms sparse-reward baselines and oracles, achieving significant Pareto gains.
LogEI improves Bayesian optimization by simplifying numerical computation of EI and related functions.
problem Numerical pathologies in optimizing EI and related acquisition functions.
method Proposes LogEI, a family of acquisition functions that simplify numerical optimization.
result LogEI members improve optimization performance and match or exceed state-of-the-art methods.
New method ranks multivariate distributions in SMOOP using q-dominance.
problem Lack of reliable methods to rank multivariate distributions in SMOOP.
method Introduces center-outward q-dominance and develops empirical test procedures.
result Proves q-dominance implies FSD and establishes a sample size threshold.
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.
Multi-objective optimization is a crucial matter in computer systems design space exploration because real-world applications often rely on a trade-off between several objectives. Derivatives are usually not available or impractical to compute and the feasibility of an experiment can not always be determined in advance…
MO-PaDGAN improves multi-objective optimization by generating diverse and high-performing designs.
problem Challenges in parameterizing engineering designs for multi-objective optimization.
method MO-PaDGAN uses a generative adversarial network with a Determinantal Point Processes loss function to address these challenges.
result MO-PaDGAN generates designs with improved performance and coverage, even surpassing training data.
This work improves molecular design by efficiently selecting diverse candidate molecules.
problem Designing molecules that satisfy multiple conflicting objectives.
method A modular 'generate-then-optimize' framework using generative models and a novel acquisition function.
result Significant improvements in sample efficiency across synthetic and application-driven tasks.
Study finds Hilbert square of real surfaces can be maximal even when the surface has disconnected real locus.
problem Exploring conditions for maximality of Hilbert square of real surfaces.
method Analyzing Hilbert square of maximal real surfaces and examining specific examples.
result Hilbert square can be maximal even for surfaces with disconnected real locus.
Maximal knotless graphs have at least 74% of their vertices' edges.
problem Characterizing maximal knotless graphs and understanding their edge constraints.
method Analyzing edge maximality and constructing graphs to meet constraints.
result There exists an infinite family of maximal knotless graphs with fewer edges than previously thought.
Maximizing margins leads to lossless compression of training data.
problem Generalization in supervised learning.
method Information-theoretic interpretation of margin maximization.
result Margin maximization is a form of lossless maximal compression.
The study classifies area-maximizing hypersurfaces with singularities and exterior domains.
problem Classifying area-maximizing hypersurfaces with singularities and exterior domains.
method Complete classification for entire area maximizing hypersurfaces with isolated singularities. Construction of an example. Partial result on asymptotic behavior for exterior domains. Solvability of exterior Dirichlet problems.
result Complete classification and partial results on asymptotic behavior for area maximizing hypersurfaces.
Maximal acceleration metrics limit spacetime curvature.
problem Bounding spacetime curvature under maximal acceleration.
method Developed a geometric framework for maximal acceleration metrics and associated connections, proving curvature bounds.
result Uniform bounds on curvature components follow from uniform bounds on maximal acceleration.
RFMS optimizes model hyperparameters across remote sites for high-dimensional data.
problem Training machine learning models on remote data sites due to privacy and trust concerns.
method Bayesian Optimization for multi-objective hyperparameter tuning.
result Multi-objective Bayesian Optimization improves model performance across multiple data sites.
The paper finds maximal metrics on Euclidean spaces.
problem Finding maximal elements in moduli spaces of Riemannian metrics.
method Defining a preorder on moduli space by isometry groups and identifying maximal elements.
result Constructs many examples of maximal metrics on Euclidean spaces.
Survey on geometry and topology of maximal antipodal sets.
problem Maximal antipodal sets on Riemannian manifolds.
method Comprehensive survey of existing research.
result Relation to various mathematical areas.
New bounds on maximal linkless graphs with improved edge-to-vertex ratios.
problem Finding maximal linklessly embeddable graphs with improved edge-to-vertex ratios.
method Constructing families of graphs and proving necessary and sufficient conditions for clique sums.
result Improved edge-to-vertex ratios for maximal linklessly embeddable graphs.
New maximally linkless graphs found with fewer edges.
problem Finding graphs without any links in 3D space.
method Demonstrated new maximally linkless graphs with improved edge count.
result Found maximally linkless graphs with m ≤ 14 5 n m\le \frac{14}{5}n m ≤ 5 14 n edges. Study examines maximal domains of radial harmonic functions across different curvature types.
problem Understanding maximal domains of radial harmonic functions in various curvature settings.
method Analysis of harmonic spaces with positive, zero, and negative curvature.
result Characterization of maximal domains for radial harmonic functions in different curvature contexts.
The paper explores reflection principles for lightlike line segments on maximal surfaces.
problem Reflection property does not hold for lightlike line segments on maximal surfaces.
method Analyzes reflection properties for lightlike line segments connecting shrinking singularities.
result Shows a kind of reflection principle for lightlike line segments on maximal surfaces.
We shall investigate maximal surfaces in Minkowski 3-space with singularities. Although the plane is the only complete maximal surface without singular points, there are many other complete maximal surfaces with singularities and we show that they satisfy an Osserman-type inequality.
New maximal surfaces solve Bernstein problems.
problem Bernstein problems in centroaffine geometry.
method Calabi affine maximal surfaces and orthonormal frame fields.
result Complete centroaffine extremal hypersurfaces solve all Bernstein problems.
The study finds that maximizing median returns is the only viable strategy in portfolio selection.
problem Difficulties in studying optimal portfolio strategies due to discontinuity and time inconsistency in maximizing median and quantile returns.
method Used intra-personal equilibrium approach to analyze portfolio selection under median and quantile maximization.
result Median maximization is the only viable strategy, with no investment in risky assets for other quantiles.