Related papers: Pareto Navigation Gradient Descent: a First-Order …
Post-training of LLMs with RLHF, and subsequently preference optimization algorithms such as DPO, IPO, etc., made a big difference in improving human alignment. However, all such techniques can only work with a single (human) objective. In…
The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points,…
In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…
In general, a multi-objective optimization problem does not have a single optimal solution but a set of Pareto optimal solutions, which forms the Pareto front in the objective space. Various evolutionary algorithms have been proposed to…
We propose a first-order method for convex optimization, where instead of being restricted to the gradient from a single parameter, gradients from multiple parameters can be used during each step of gradient descent. This setup is…
In the imprecise geometry model, the input is an imprecise point set, which is a family of regions $F = (R_1, \ldots,R_n)$, where for each $R_i$ one may retrieve the true point $p_i \in R_i$. By preprocessing $F$, we can construct the…
Although traditional optimization methods focus on finding a single optimal solution, most objective functions in modern machine learning problems, especially those in deep learning, often have multiple or infinite numbers of optima.…
In this article, we propose a Newton-based method for solving multiobjective interval optimization problems (MIOPs). We first provide a connection between weakly Pareto optimal points and Pareto critical points in the context of MIOPs.…
In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…
We introduce \textit{basic inequalities} for first-order iterative optimization algorithms, forming a simple and versatile framework that connects implicit and explicit regularization. While related inequalities appear in the literature, we…
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…
Dynamic programming over tree decompositions is a common technique in parameterized algorithms. In this paper, we study whether this technique can also be applied to compute Pareto sets of multiobjective optimization problems. We first…
Performance optimization of deep learning models is conducted either manually or through automatic architecture search, or a combination of both. On the other hand, their performance strongly depends on the target hardware and how…
In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in…
Offline multi-objective optimization aims to identify Pareto-optimal solutions given a dataset of designs and their objective values. In this work, we propose a preference-guided diffusion model that generates Pareto-optimal designs by…
In multiobjective optimization, most branch and bound algorithms provide the decision maker with the whole Pareto front, and then decision maker could select a single solution finally. However, if the number of objectives is large, the…
A challenging category of robotics problems arises when sensing incurs substantial costs. This paper examines settings in which a robot wishes to limit its observations of state, for instance, motivated by specific considerations of energy…
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…
Multi-objective Bayesian optimization aims to find the Pareto front of trade-offs between a set of expensive objectives while collecting as few samples as possible. In some cases, it is possible to evaluate the objectives separately, and a…
This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier…