arXiv research

PureTS uses simple linear models to improve long-term time series forecasting.

Optimizes pure exploration in linear bandits with a new algorithm.

Develops first optimal algorithm for logistic bandits.

We develop algorithms for the numerical computation of the quadratic hedging strategy in incomplete markets modeled by pure jump Markov process. Using the Hamilton-Jacobi-Bellman approach, the value function of the quadratic hedging problem can be related to a triangular system of parabolic partial integro-differential…

New algorithms for model selection in linear bandits adapt to instance complexity.

It is illustrated a methodology to compute the pure premium for the automobile insurance (claim frequency and severity) using generalized linear models. It is obtained the pure premium for the partial damage loss cover (PPD) using a set of automobile insurance policies with an exposition of a year. It is found that the…

Improved confidence bounds for linear logistic model with applications to bandits.

New matrices link point motions to braid groups.

Study pure exploration in high-dimensional feature spaces using adaptive embeddings.

Newly characterizes the Standard Model gauge group using spinors and geometry.

By analyzing known presentations of the pure mapping groups of orientable surfaces of genus $g$ with $b$ boundary components and $n$ punctures, we show that these groups are isomorphic to some groups related to the braid groups and the Artin group of type $D_4$ in the cases when $g=0$ with $b$ and $n$ arbitrary, and wh…

Proposes a new model for time series that considers smooth transitions between states.

Algorithm balances online and offline data for linear bandits.

Improves decision complexity in hybrid environments.

We show that there are not pure $\mathcal{C}^5$ regular y-global Landsberg surfaced. The proof is based on the averaged connection associated with the linear Chern's connection and the classification of irreducibles holonomies of torsion-free affine connections. The structure consists on exausting all the possible case…

Optimal algorithm for identifying best arm in stochastic linear bandits with fixed confidence.

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

We study the Combinatorial Pure Exploration problem with Continuous and Separable reward functions (CPE-CS) in the stochastic multi-armed bandit setting. In a CPE-CS instance, we are given several stochastic arms with unknown distributions, as well as a collection of possible decisions. Each decision has a reward accor…

We propose the first fully-adaptive algorithm for pure exploration in linear bandits---the task to find the arm with the largest expected reward, which depends on an unknown parameter linearly. While existing methods partially or entirely fix sequences of arm selections before observing rewards, our method adaptively c…

We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth. We consider a market model with jumps driven by (multivariate) marked point processes and so-called non-linear wealth dynamics which allows to take …

Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feas…

New methods for efficient exploration under unknown linear constraints in bandits.

In recent years, a market for mortality derivatives began developing as a way to handle systematic mortality risk, which is inherent in life insurance and annuity contracts. Systematic mortality risk is due to the uncertain development of future mortality intensities, or {\it hazard rates}. In this paper, we develop a …

Study of tangent cones at infinity for algebraic sets.

Study optimal execution in financial markets with constraints.

The risk premium of a policy is the sum of the pure premium and the risk loading. In the classification ratemaking process, generalized linear models are usually used to calculate pure premiums, and various premium principles are applied to derive the risk loadings. No matter which premium principle is used, some risk …

Develops a Bayesian non-parametric approach for signal separation with varying components.

The paper tackles combinatorial pure exploration with various feedback structures and proposes efficient algorithms.

In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong connections with generalized linear models, it does not require identifiability of the par…

In this contribution we review results on the kinematics of a quantum system localized on a connected configuration manifold and compatible dynamics for the quantum system including external fields and leading to non-linear Schrödinger equations for pure states.

We prove Birkhoff-type results showing that $L^2$ solutions of the linearized Einstein equations around Riemannian Kottler ("Schwarzschild-anti de Sitter") metrics in arbitrary dimension and horizon topology, which are not controlled by "master functions" are pure gauge. Together with earlier results this implies that …

Full-sampling (e.g., Q-learning) and pure-expectation (e.g., Expected Sarsa) algorithms are efficient and frequently used techniques in reinforcement learning. Q$(σ,λ)$ is the first approach unifies them with eligibility trace through the sampling degree $σ$. However, it is limited to the tabular case, for large-scale …

New method classifies spinor orbits in dimensions up to 14.

The critical locus of the loss function of a neural network is determined by the geometry of the functional space and by the parameterization of this space by the network's weights. We introduce a natural distinction between pure critical points, which only depend on the functional space, and spurious critical points, …

This work introduces a novel estimation method, called LOVE, of the entries and structure of a loading matrix A in a sparse latent factor model X = AZ + E, for an observable random vector X in Rp, with correlated unobservable factors Z \in RK, with K unknown, and independent noise E. Each row of A is scaled and sparse.…

Study optimal strategy for maximizing exponential utility in financial market with linear price impact.

New algorithm reduces privacy breach in posterior sampling.

New method identifies latent causal factors from observational data alone.

Hybrid RL algorithms improve offline and online RL in linear MDPs.

Study improves understanding of network degree distributions using non-linear ERGs.

Develops a method to identify causal effects in linear models with latent variables.

Global fixed points in low-dimensional surface group space correspond to trivial representations.

We propose a new integrated method of exploiting model, batch and domain parallelism for the training of deep neural networks (DNNs) on large distributed-memory computers using minibatch stochastic gradient descent (SGD). Our goal is to find an efficient parallelization strategy for a fixed batch size using $P$ process…

Paper develops a dynamic Bayesian approach for active learning that optimizes exploration-exploitation balance.

We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equation: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge term. We work in a natural wave map/DeTurck gauge and show that the pure gauge term …

This paper presents the solution to a European option pricing problem by considering a regime-switching jump diffusion model of the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure jump process, driving the values of interest rate and volatility coefficient. The p…

Study indifference pricing for insurance policies in a regime-switching market model.

ALEXP improves model selection in linear bandits with exponential regret improvement.