Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.
problem Adversarial online nonparametric regression with general convex losses.
method Parameter-free learning algorithm leveraging chaining trees to compete against H{ö}lder functions, dynamically tracking and adapting to local smoothness variations.
result First computationally efficient algorithm with locally adaptive optimal rates for online regression in an adversarial setting.
Study approximates unknown function levels with queries.
problem Approximating unknown function levels through sequential queries.
method Introduce Bisect and Approximate algorithms to reduce to local function approximation.
result Rate-optimal sample complexity guarantees for H{ö}lder functions.
Explains Gromov's and Rumin's work on Carnot manifolds.
problem Hölder equivalence problem for Carnot manifolds
method PDE techniques and Rumin's complex
result Both methods yield similar conclusions for the H{ö}lder equivalence problem
Paper offers a new method to solve risk-sharing problems in Principal-Agent models.
problem Risk-sharing in Principal-Agent models with CARA utilities.
method Optimal decomposition of expected utility using Reverse-H{ö}lder inequality.
result Proof of existence and uniqueness of the solution under general assumptions.
Study on Hölder-equivalence problem for Carnot groups, with partial result.
problem Hölder-equivalence problem for Carnot groups.
method General coarea inequality for packing energies of maps.
result Partial result given for the problem.
New algorithm adapts to unknown smoothness in stochastic bandits with polynomial cost.
problem Adapting to unknown smoothness in stochastic bandits.
method Reconsidered Locatelli and Carpentier's lower bound, defined admissible rate functions, and developed a new algorithm.
result New algorithm matches minimal rate functions and provides polynomial cost of adaptation.
Let S be a closed oriented surface of genus at least 2, and denote by T(S) its Teichm{ü}ller space. For any isotopy class of closed curves γ, we compute the first three derivatives of the length function ℓ_γ:T(S)→R_+ in the shearing coordinates associated to a maxim…
We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a non-constructive fashion by Rakhlin and Sridharan (2014). Our regret bound is expre…
Study of finite energy quasiplurisubharmonic functions on toric Kähler manifolds.
problem Characterizing and understanding finite energy quasiplurisubharmonic functions on toric Kähler manifolds.
method Characterization through convex functions and integrability properties of Legendre transforms.
result Log-Lipschitz convex functions on Delzant polytopes correspond to toric quasiplurisubharmonic functions with exponential integrability.
Validates economic scenarios using statistical tests on stochastic processes.
problem Ensuring the accuracy of real-world economic scenario models.
method Applies Chevyrev and Oberhauser's (2022) signature and maximum mean distance test to various stochastic processes.
result Demonstrates the test's effectiveness across different path properties relevant to financial modeling.
Study shows zero-shot super-resolution in neural operators is impossible in many cases.
problem Understanding the theoretical limits of zero-shot super-resolution in neural operators.
method Systematic theoretical study including information-theoretic and generalization bounds analysis.
result Zero-shot super-resolution is information-theoretically impossible in many settings.
Local Ricci flow under negative curvature conditions, with applications to metric space smoothing.
problem Finding solutions to Ricci flow under local negative curvature conditions.
method Local solution to Ricci flow equation with uniform existence time and bounded curvature.
result Local Ricci flow exists for a uniform time with bounded curvature, generalizing previous results.
Efficient algorithms for contextual bandits with smooth regret in continuous action spaces.
problem Efficient learning in large or continuous action spaces.
method Smooth regret notion and efficient algorithms for general function approximation.
result Statistically and computationally efficient algorithms for contextual bandits with smooth regret.
General lower bounds on neural network approximation in L^p norm.
problem Fundamental limits of neural network expressivity.
method General lower bound proof on approximation in L^p norm, applied to feed-forward neural networks.
result Neural networks can't approximate certain functions as well as previously thought.
This paper selects features in deep neural networks with theoretical guarantees.
problem Feature selection in deep neural networks with unknown nonlinear functions.
method Reformulate neural networks as index models, estimate feature sets using Stein's formula, and apply screening-and-selection mechanism.
result Consistent feature selection with theoretical guarantees, even in high-dimensional settings.
New algorithms for interactive learning match minimax bounds efficiently.
problem Interactive learning in the realizable setting with computational efficiency.
method General framework, computationally efficient algorithms, Monte Carlo hit-and-run sampling.
result Sample complexities quantifiable in terms of combinatorial quantities, computationally efficient.
Introduces a space of almost complex structures for complex Lie group bundles.
problem Integrability of almost complex structures on complex Lie group bundles.
method Introduces a space of bundle almost complex structures and studies their properties.
result Locally pseudo-holomorphic sections exist if and only if the obstruction form is zero.