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.
Revisits VIC method to correct intrinsic reward bias in stochastic environments.
Universal AI seeks high-optionality states through empowerment and curiosity.
Exploration in environments with continuous control and sparse rewards remains a key challenge in reinforcement learning (RL). Recently, surprise has been used as an intrinsic reward that encourages systematic and efficient exploration. We introduce a new definition of surprise and its RL implementation named Variation…
In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems. Interesting appli…
It has been established that diverse behaviors spanning the controllable subspace of an Markov decision process can be trained by rewarding a policy for being distinguishable from other policies \citep{gregor2016variational, eysenbach2018diversity, warde2018unsupervised}. However, one limitation of this formulation is …
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new Lagrangian in an extended configuration space ---which we call D'Alambert's--- com…
We discuss intrinsic aspects of Krupka's approach to finite-order variational sequences. We give intrinsic isomorphisms of the quotient subsheaves of the short finite-order variational sequence with sheaves of forms on jet spaces of suitable order, obtaining a new finite-order (short exact) variational sequence which i…
New approach to Lagrangian systems using intrinsic geometry.
We show that in the first sub-Riemannian Heisenberg group there are intrinsic graphs of smooth functions that are both critical and stable points of the sub-Riemannian perimeter under compactly supported variations of contact diffeomorphisms, despite the fact that they are not area-minimizing surfaces. In particular, w…
The mathematical problem concerning intrinsic storage optimisation is formulated and solved by means of variational analysis. The solution, though obtained in implicit form, still sheds light on many important features of the optimal exercise strategy. It is shown how the solution depends on different constraint types …
We prove that, in the first Heisenberg group , an entire locally Lipschitz intrinsic graph admitting vanishing first variation of its sub-Riemannian area and non-negative second variation must be an intrinsic plane, i.e., a coset of a two dimensional subgroup of . Moreover two examples are given…
A new multi-objective RL framework improves intrinsic exploration performance.
A new reinforcement learning method uses mutual information to encourage agents to control their environment.
EXOC framework uses auxiliary variables for counterfactual fairness in machine learning.
We propose a novel framework to identify sub-goals useful for exploration in sequential decision making tasks under partial observability. We utilize the variational intrinsic control framework (Gregor et.al., 2016) which maximizes empowerment -- the ability to reliably reach a diverse set of states and show how to ide…
Exploration in sparse reward reinforcement learning remains an open challenge. Many state-of-the-art methods use intrinsic motivation to complement the sparse extrinsic reward signal, giving the agent more opportunities to receive feedback during exploration. Commonly these signals are added as bonus rewards, which res…
We study the intrinsic structure of parametric minimal discs in metric spaces admitting a quadratic isoperimetric inequality. We associate to each minimal disc a compact, geodesic metric space whose geometric, topological, and analytic properties are controlled by the isoperimetric inequality. Its geometry can be used …
Paper analyzes a new Hopf-Lax semigroup in metric spaces.
Deep neural networks with their large number of parameters are highly flexible learning systems. The high flexibility in such networks brings with some serious problems such as overfitting, and regularization is used to address this problem. A currently popular and effective regularization technique for controlling the…
Derives optimal control conditions using calculus of variations.
New estimators for intrinsic dimension and Wasserstein distance improve OT accuracy.
In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate covariant derivatives, which guarantees that the structure of the equations is invari…
The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples are provided.
Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A popular approach used to reduce gradient's variance involves the use of control varia…
Paper proposes a new method to optimize robot body structure and control policy.
We present an intrinsic formulation of the kinematic problem of two dimensional manifolds rolling one on another without twisting or slipping. We determine the configuration space of the system, which is an dimensional manifold. The conditions of no-twisting and no-slipping are decoded by means of …
This work improves variational inference by reducing gradient variance.
We deal with irregular curves contained in smooth, closed, and compact surfaces. For curves with finite total intrinsic curvature, a weak notion of parallel transport of tangent vector fields is well-defined in the Sobolev setting. Also, the angle of the parallel transport is a function with bounded variation, and its …
New method reduces inference variance for faster optimization.
Study intrinsic volume forms on complex hypersurfaces.
This paper develops scalable control variates for Monte Carlo methods using stochastic optimization.
New method detects anomalies in systems influenced by their environment.
Optimizes MCMC chains with neural control variates.
New algorithm uses control variates to improve multi-armed bandit performance.
This study analyzes VAEs using ID and II, revealing a transition in behaviour and distinct training phases.
Improved confidence interval estimation with control variates.
A new method reduces variance in training discrete latent variable models.
Some intrinsic tools from the formal theory of variational equations are being demonstrated at work in application to one concrete example of the third-order evolution equation of free relativistic top in three-dimensional space-time. The main goal is to introduce a combined approach consisting in the simultaneous util…
This work proposes using zero-variance control variates to reduce variance in pathwise gradient estimators for variational inference.
This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the prism of Riemannian submersions, with shape space metrics being induced from metrics…
We use neural networks as control variates with geometric integration techniques.
Combines control variates and adaptive importance sampling for Monte Carlo integration.
The paper explores how control variates can reduce variance in Monte Carlo simulations, especially for Sobolev functions.
ADAC uses analogous policies to improve RL exploration without sacrificing stability.
Solving tasks with sparse rewards is one of the most important challenges in reinforcement learning. In the single-agent setting, this challenge is addressed by introducing intrinsic rewards that motivate agents to explore unseen regions of their state spaces; however, applying these techniques naively to the multi-age…
An intrinsic description of the Hamilton-Cartan formalism for first-order Berezinian variational problems determined by a submersion of supermanifolds is given. This is achieved by studying the associated higher-order graded variational problem through the Poincaré-Cartan form. Noether theorem and examples from superfi…
Paper improves variance control in importance weighted variational bounds.
A control system is said to be trivializable if there exists local coordinates in which the system is feedback equivalent to a control system of the form . In this paper we characterize trivializable control systems and control systems for which, up to a feedback transformation, a…