A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper shows how Lagrangian duality improves deep learning for constrained problems.
Paper doubles Hessian estimates for special Lagrangian equation with constraints.
In this study, it is generalized the concept of Lagrangian mechanics with constraints to complex case. To be beginning, it is considered a Kaehlerian manifold as a velocity-phase space. Then a non-holonomic constraint is given by 1-form on it. If the form is closed, it is found that the constraint is (locally) holonomi…
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we give a basis of constraint functions in the Lagrangian and Hamiltonian sides. An ad…
The paper explores solving inverse problems for ODEs with and without constraints.
Proves Hölder-type inequality for Lagrangians' distance.
In recent years, constrained optimization has become increasingly relevant to the machine learning community, with applications including Neyman-Pearson classification, robust optimization, and fair machine learning. A natural approach to constrained optimization is to optimize the Lagrangian, but this is not guarantee…
Geodesic extensions for systems with nonholonomic constraints.
New algorithm reduces regret in CMDPs without cancellation of errors.
Study uses DRL with Lagrangian relaxation to solve temporal control tasks with STL constraints.
New methods for efficient exploration under unknown linear constraints in bandits.
This paper extends the evolution operator to contact mechanics, linking Lagrangian and Hamiltonian formulations.
The time evolution operator is introduced in the graded context and its main properties are discussed. In particular, the operator is used to analize the projectability of constraint functions arising in the Lagrangian formalism for singular Lagrangians.
Survey of Lagrangian reduction for discrete mechanical systems.
In this paper, we propose a geometric integrator for nonholonomic mechanical systems. It can be applied to discrete Lagrangian systems specified through a discrete Lagrangian defined on QxQ, where Q is the configuration manifold, and a (generally nonintegrable) distribution in TQ. In the proposed method, a discretizati…
We derive a Liouville type result for special Lagrangian equations with certain "convexity" and restricted linear growth assumptions on the solutions.
Simplifies neural network models by explicitly enforcing constraints in Cartesian coordinates.
The paper develops methods for time-varying constrained online convex optimization.
In this note we show that the Lagrangian Luttinger surgery preserves the symplectic Kodaira dimension. Some constraints on Lagrangian tori in symplectic four manifolds with non-positive Kodaira dimension are also derived.
Proposes TgNN-LD to improve neural network effectiveness and efficiency.
A parameter-invariant variational problem with a manifestly covariant Lagrangian function of second order is considered, which covers the case of the free relativistic top at constraint manifold of constant acceleration
Given a symplectic manifold M, we consider a category with objects finite ordered families of Lagrangian submanifolds of M (subject to certain additional constraints) and with morphisms Lagrangian cobordisms relating them. We construct a functor that maps this category to a variant of the derived Fukaya category of M i…
Develops a new solver for optimizing with stochastic dominance constraints.
We present a unified approach to constrained implicit Lagrangian and Hamiltonian systems based on the introduced concept of Dirac algebroid. The latter is a certain almost Dirac structure associated with the Courant algebroid on the dual to a vector bundle . If this almost Dirac structure is integrable (Dir…
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago…
Study on relativistic nonholonomic mechanics with time-dependent constraints.
This paper studies special Lagrangian submanifolds and their deformations.
Stochastic approach improves neural network training for kinetic simulations.
An augmented Lagrangian (AL) can convert a constrained optimization problem into a sequence of simpler (e.g., unconstrained) problems, which are then usually solved with local solvers. Recently, surrogate-based Bayesian optimization (BO) sub-solvers have been successfully deployed in the AL framework for a more global …
We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.
Unified Lagrangian-based methods for nonsmooth nonconvex optimization.
New algorithm reduces regret and constraint violation in online convex optimization with predictions.
Minimizing a function over an intersection of convex sets is an important task in optimization that is often much more challenging than minimizing it over each individual constraint set. While traditional methods such as Frank-Wolfe (FW) or proximal gradient descent assume access to a linear or quadratic oracle on the …
Upper bounds for Lagrangian capacities of Liouville domains
Study on volume continuity of Lagrangian submanifolds.
PDCA algorithm learns policies for RL with constraints using a primal-dual approach.
Clean intersections of Lagrangian knots in 3D are impossible.
This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations between symmetries and first integrals. We discuss the so-called nonholonomic Noe…
New algorithm for contextual bandits with linear constraints using regression.
The paper studies bifurcations in Lagrangian systems and geodesics.
The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence of a natural symplectic structure on the cotangent bundle. First it is developed …
LP algorithm optimizes neural networks with architectural constraints.
We give topological obstructions to the existence of a closed exact Lagrangian submanifold in the cotangent bundle of a closed manifold M which is the total space of a fibration over the circle. For instance we show that the fundamental group of such a Lagrangian submanifold cannot be the free product of two non-trivia…
The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian. This problem in the general version remains unsolved. Here, we contribute to it w…
We show that many machine learning goals, such as improved fairness metrics, can be expressed as constraints on the model's predictions, which we call rate constraints. We study the problem of training non-convex models subject to these rate constraints (or any non-convex and non-differentiable constraints). In the non…
We derive constraints on Lagrangian embeddings in completions of certain stable symplectic fillings with semisimple symplectic cohomologies. Manifolds with these properties can be constructed by generalizing the boundary connected sum operation to our setting, and are related to certain birational surgeries like blow-d…
Exact discrete mechanics for nonholonomic systems defined.
A large number of objectives have been proposed to train latent variable generative models. We show that many of them are Lagrangian dual functions of the same primal optimization problem. The primal problem optimizes the mutual information between latent and visible variables, subject to the constraints of accurately …