Related papers: Generalized Optimization Modulo Theories
Satisfiability Modulo Theories (SMT) refers to the problem of deciding the satisfiability of a formula with respect to certain background first order theories. In this paper, we focus on Satisfiablity Modulo Integer Arithmetic, which is…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
The study of theory combination in Satisfiability Modulo Theories (SMT) involves various model theoretic properties (e.g., stable infiniteness, smoothness, etc.). We show that such properties can be partly captured by the natural density of…
Numerical global optimization methods are often very time consuming and could not be applied for high-dimensional nonconvex/nonsmooth optimization problems. Due to the nonconvexity/nonsmoothness, directly solving the primal problems…
Solving nonlinear SMT problems over real numbers has wide applications in robotics and AI. While significant progress is made in solving quantifier-free SMT formulas in the domain, quantified formulas have been much less investigated. We…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
Optimization modeling is one of the most crucial but technical parts of operations research (OR). To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps…
Machine learning has achieved tremendous success in a variety of domains in recent years. However, a lot of these success stories have been in places where the training and the testing distributions are extremely similar to each other. In…
Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…
While the optimal transport (OT) problem was originally formulated as a linear program, the addition of entropic regularization has proven beneficial both computationally and statistically, for many applications. The Sinkhorn fixed-point…
Out-of-Distribution (OOD) generalization in machine learning is a burgeoning area of study. Its primary goal is to enhance the adaptability and resilience of machine learning models when faced with new, unseen, and potentially adversarial…
Answer Set Programming Modulo Theories (ASPMT) is a new framework of tight integration of answer set programming (ASP) and satisfiability modulo theories (SMT). Similar to the relationship between first-order logic and SMT, it is based on a…
Optimizing the performance of many objectives (instantiated by tasks or clients) jointly with a few Pareto stationary solutions (models) is critical in machine learning. However, previous multi-objective optimization methods often focus on…
Learning-to-optimize leverages machine learning to accelerate optimization algorithms. While empirical results show tremendous improvements compared to classical optimization algorithms, theoretical guarantees are mostly lacking, such that…
This paper presents a framework to solve constrained optimization problems in an accelerated manner based on High-Order Tuners (HT). Our approach is based on reformulating the original constrained problem as the unconstrained optimization…
We introduce the framework of qualitative optimization problems (or, simply, optimization problems) to represent preference theories. The formalism uses separate modules to describe the space of outcomes to be compared (the generator) and…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
Rapidly growing product lines and services require a finer-granularity forecast that considers geographic locales. However the open question remains, how to assess the quality of a spatio-temporal forecast? In this manuscript we introduce a…
Given samples from two joint distributions, we consider the problem of Optimal Transportation (OT) between them when conditioned on a common variable. We focus on the general setting where the conditioned variable may be continuous, and the…
Can transformers generalize efficiently on problems that require dealing with examples with different levels of difficulty? We introduce a new task tailored to assess generalization over different complexities and present results that…