Related papers: Computing a partition function of a generalized pa…
Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…
Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. This paper introduces a novel formalism for a prominent problem in…
We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…
Post-training compression of large language models (LLMs) often relies on low-rank weight approximations that represent each column of the weight matrix in a shared low-dimensional subspace. This strategy is computationally efficient but…
Categorical regressor variables are usually handled by introducing a set of indicator variables, and imposing a linear constraint to ensure identifiability in the presence of an intercept, or equivalently, using one of various coding…
For many applications of reinforcement learning it can be more convenient to specify both a reward function and constraints, rather than trying to design behavior through the reward function. For example, systems that physically interact…
We study the Stable Fixtures problem, a many-to-many generalisation of the classical non-bipartite Stable Roommates matching problem. Building on the foundational work of Tan on stable partitions, we extend his results to this significantly…
A Constraint Satisfaction Problem (CSP) is a framework used for modeling and solving constrained problems. Tree-search algorithms like backtracking try to construct a solution to a CSP by selecting the variables of the problem one after…
We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides…
In order to give appropriate semantics to qualitative conditionals of the form "if A then normally B", ordinal conditional functions (OCFs) ranking the possible worlds according to their degree of plausibility can be used. An OCF accepting…
This paper focuses on the branching process for solving any constraint satisfaction problem (CSP). A parametrised schema is proposed that (with suitable instantiations of the parameters) can solve CSP's on both finite and infinite domains.…
In this paper, we study the conditional stochastic optimization (CSO) problem which covers a variety of applications including portfolio selection, reinforcement learning, robust learning, causal inference, etc. The sample-averaged gradient…
Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical…
Constraint satisfaction problems form a nicely behaved class of problems that lends itself to complexity classification results. From the point of view of parameterized complexity, a natural task is to classify the parameterized complexity…
Finite valued constraint satisfaction problems are a formalism for describing many natural optimization problems, where constraints on the values that variables can take come with rational weights and the aim is to find an assignment of…
The input in the Minimum-Cost Constraint Satisfaction Problem (MinCSP) over the Point Algebra contains a set of variables, a collection of constraints of the form $x < y$, $x = y$, $x \leq y$ and $x \neq y$, and a budget $k$. The goal is to…
We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…
Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem…
Existing Reinforcement Learning with Verifiable Rewards (RLVR) algorithms, such as GRPO, rely on rigid, uniform, and symmetric trust region mechanisms that are fundamentally misaligned with the complex optimization dynamics of Large…
Support vector machine is an important and fundamental technique in machine learning. Soft-margin SVM models have stronger generalization performance compared with the hard-margin SVM. Most existing works use the hinge-loss function which…