Related papers: Learning Fast Monomial Orders for Gr\"obner Basis …

Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…

Recent advances in reinforcement learning with verifiable rewards (RLVR) show that large language models enhance their reasoning abilities when trained with verifiable signals. However, due to reward sparsity, effectiveness depends heavily…

We present an approach to make molecular optimization more efficient. We infer a hypergraph replacement grammar from the ChEMBL database, count the frequencies of particular rules being used to expand particular nonterminals in other rules,…

In this article, we investigate the cardinality of Groebner bases under various monomial orderings. We identify a family of polynomials F and a criterion such that the reduced Groebner basis of F is double exponential in cardinality with…

Sequence prediction models can be learned from example sequences with a variety of training algorithms. Maximum likelihood learning is simple and efficient, yet can suffer from compounding error at test time. Reinforcement learning such as…

Greedy algorithms have long been a workhorse for learning graphical models, and more broadly for learning statistical models with sparse structure. In the context of learning directed acyclic graphs, greedy algorithms are popular despite…

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To…

Reinforcement learning synthesizes controllers without prior knowledge of the system. At each timestep, a reward is given. The controllers optimize the discounted sum of these rewards. Applying this class of algorithms requires designing a…

Despite the numerous advances, reinforcement learning remains away from widespread acceptance for autonomous controller design as compared to classical methods due to lack of ability to effectively tackle the reality gap. The reliance on…

This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…

We show a new algorithm and its implementation for multiplying bit-polynomials of large degrees. The algorithm is based on evaluating polynomials at a specific set comprising a natural set for evaluation with additive FFT and a high order…

Policy gradient methods are powerful reinforcement learning algorithms and have been demonstrated to solve many complex tasks. However, these methods are also data-inefficient, afflicted with high variance gradient estimates, and frequently…

We study reinforcement learning with linear function approximation and finite-memory approximations for partially observed Markov decision processes (POMDPs). We first present an algorithm for the value evaluation of finite-memory feedback…

Learning heuristics for combinatorial optimization problems through graph neural networks have recently shown promising results on some classic NP-hard problems. These are single-level optimization problems with only one player. Multilevel…

We discuss efficient conversion algorithms for orthogonal polynomials. We describe a known conversion algorithm from an arbitrary orthogonal basis to the monomial basis, and deduce a new algorithm of the same complexity for the converse…

We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving…

We consider large-scale Markov decision processes (MDPs) with an unknown cost function and employ stochastic convex optimization tools to address the problem of imitation learning, which consists of learning a policy from a finite set of…

Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…

The numerical construction of polynomials in the product representation (as used for instance in variants of the multiboson technique) can become problematic if rounding errors induce an imprecise or even unstable evaluation of the…

We focus on Gr\"obner bases for modules of univariate polynomial vectors over a ring. We identify a useful property, the "predictable leading monomial (PLM) property" that is shared by minimal Gr\"{o}bner bases of modules in F[x]^q, no…