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Some quality indicators have been proposed for benchmarking preference-based evolutionary multi-objective optimization algorithms using a reference point. Although a systematic review and analysis of the quality indicators are helpful for…
We study the problem of multivariate $L_2$-approximation of functions in a weighted Korobov space using a median lattice-based algorithm recently proposed by the authors. In the original work, the algorithm requires knowledge of the…
Leveraging visual priors from pre-trained text-to-image (T2I) generative models has shown success in dense prediction. However, dense prediction is inherently an image-to-image task, suggesting that image editing models, rather than T2I…
Real-world problems often involve the optimization of several objectives under multiple constraints. An example is the hyper-parameter tuning problem of machine learning algorithms. In particular, the minimization of the estimation of the…
Augmented Lagrangian and optimistic primal--dual methods stabilize equality-constrained optimization through seemingly different mechanisms: the former adds constraint-dependent primal curvature, while the latter adds dual memory. Recent…
This paper addresses the problem of constrained multi-objective optimization over black-box objective functions with practitioner-specified preferences over the objectives when a large fraction of the input space is infeasible (i.e.,…
Bayesian optimization (BO) algorithm is very popular for solving low-dimensional expensive optimization problems. Extending Bayesian optimization to high dimension is a meaningful but challenging task. One of the major challenges is that it…
Extending Bayesian optimization to batch evaluation can enable the designer to make the most use of parallel computing technology. However, most of current batch approaches do not scale well with the batch size. That is, their performances…
We introduce a new incremental preference elicitation procedure able to deal with noisy responses of a Decision Maker (DM). The originality of the contribution is to propose a Bayesian approach for determining a preferred solution in a…
We consider the problem of learning an $\varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Given access to a generative model, we achieve rate-optimal sample…
The complexity of Pareto fronts imposes a great challenge on the convergence analysis of multi-objective optimization methods. While most theoretical convergence studies have addressed finite-set and/or discrete problems, others have…
Many modern datasets consist of multiple related matrices measured on a common set of units, where the goal is to recover the shared low-dimensional subspace. While the Angle-based Joint and Individual Variation Explained (AJIVE) framework…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification…
Our main contribution is a concentration inequality for the symmetric volume difference of a $ C^2 $ convex body with positive Gaussian curvature and a circumscribed random polytope with a restricted number of facets, for any probability…
This paper studies the continuous-time dynamics of primal-dual algorithms for linearly constrained convex optimization problems and provides a quantitative convergence analysis using the Lyapunov functions. With the growing prevalence of…
We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…
The lack of proper class discrimination among the Hyperspectral (HS) data points poses a potential challenge in HS classification. To address this issue, this paper proposes an optimal geometry-aware transformation for enhancing the…
Mixed H2/H-infinity control balances performance and robustness by minimizing an H2 cost bound subject to an H-infinity constraint. However, classical Riccati/LMI solutions offer limited insight into the nonconvex optimization landscape and…
We present an analytical-numerical method providing robust upper estimates for the topological entropy or, more generally, uniform volume growth exponents of differentiable mappings. By introducing varying metrics, we simplify the analysis…