arXiv research

New offline RL method works with limited data and function approximators.

New PAC-Bayesian bounds explain few-shot learning performance gaps.

Logarithmic regret achieved in RL with linear function approximation.

This note removes technical assumptions and characterizes relatively dominated representations.

New study shows exponential lower bound for RL even with constant suboptimality gap.

Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for Ricci-flat manifolds, removing the volume growth assumptions in known results.

New algorithm reduces regret in combinatorial causal bandits without graph structure.

Estimates the mass gap for domains with integral Ricci curvature bounds.

In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, f…

Estimates scalar curvature without nonnegativity, showing gap phenomenon on manifolds.

This work closes the theory-practice gap for distributed optimization methods by introducing a new regularity condition.

In this paper we first use the result in $[12]$ to remove the assumption of the $L^2$ boundedness of Weyl curvature in the gap theorem in $[9]$ and then obtain a gap theorem for a class of conformally compact Einstein manifolds with very large renormalized volume. We also uses the blow-up method to derive curvature est…

Develops finite-gap solutions for Pohlmeyer--Lund--Regge equation and Lund--Regge curve evolution.

A new neural network model predicts inflation and output gap more accurately.

WR-CP reduces prediction set size and coverage gap under distribution shift.

In this paper we study some new von Neumann spectral invariants associated to the Laplacian acting on L^2 differential forms on the universal cover of a closed manifold. These invariants coincide with the Novikov-Shubin invariants whenever there is no spectral gap in the spectrum of the Laplacian, and are homotopy inva…

Let F be a family of Borel measurable functions on a complete separable metric space. The gap (or fat-shattering) dimension of F is a combinatorial quantity that measures the extent to which functions f in F can separate finite sets of points at a predefined resolution gamma > 0. We establish a connection between the g…

We give a reduction from {\sc clique} to establish that sparse PCA is NP-hard. The reduction has a gap which we use to exclude an FPTAS for sparse PCA (unless P=NP). Under weaker complexity assumptions, we also exclude polynomial constant-factor approximation algorithms.

New framework improves restless bandit policies for large numbers of arms.

The paper studies 4D Ricci flow manifolds with curvature constraints.

Stable commutator length scl_G(g) of an element g in a group G is an invariant for group elements sensitive to the geometry and dynamics of G. For any group G acting on a tree, we prove a sharp bound scl_G(g)>=1/2 for any g acting without fixed points, provided that the stabilizer of each edge is relatively torsion-fre…

New empirical PAC-Bayes bound for Markov chains with finite state space.

The paper studies eigenvalues in gaps of the essential spectrum of a Bochner-Schrödinger operator.

In this paper we discuss the asymptotic entropy for ancient solutions to the Ricci flow. We prove a gap theorem for ancient solutions, which could be regarded as an entropy counterpart of Yokota's work. In addition, we prove that under some assumptions on one time slice of a complete ancient solution with nonnegative c…

The paper analyzes Q-learning in 2-player Markov games and provides gap-dependent logarithmic regret bounds.

In this paper, we study the combinatorial multi-armed bandit problem (CMAB) with probabilistically triggered arms (PTAs). Under the assumption that the arm triggering probabilities (ATPs) are positive for all arms, we prove that a class of upper confidence bound (UCB) policies, named Combinatorial UCB with exploration …

The paper analyzes risk bounds and Rademacher complexity in batch RL.

New method uses kernel methods to approximate ground states of quantum Hamiltonians efficiently.

New method explains ML performance gaps without causal knowledge.

In this paper, we will prove a gap theorem for four-dimensional gradient shrinking soliton. More precisely, we will show that any complete four-dimensional gradient shrinking soliton with nonnegative and bounded Ricci curvature, satisfying a pinched Weyl curvature, either is flat, or $λ_1 + λ_2\ge c_0 R>0$ everywhere f…

Method constrains spectral gaps of hyperbolic spin surfaces using identities and semidefinite programming.

In an effort to better understand the different ways in which the discount factor affects the optimization process in reinforcement learning, we designed a set of experiments to study each effect in isolation. Our analysis reveals that the common perception that poor performance of low discount factors is caused by (to…

New framework for RL with linear-convex models reduces performance gap.

Unified parametric assumption improves convergence guarantees for nonconvex optimization.

Epoch gradient descent method (a.k.a. Epoch-GD) proposed by Hazan and Kale (2011) was deemed a breakthrough for stochastic strongly convex minimization, which achieves the optimal convergence rate of $O(1/T)$ with $T$ iterative updates for the {\it objective gap}. However, its extension to solving stochastic min-max pr…

Study proposes worst+gap measure for better DG evaluation.

Study on geodesics on high genus expander surfaces, proving filling and non-simple properties.

Understanding generalization in reinforcement learning (RL) is a significant challenge, as many common assumptions of traditional supervised learning theory do not apply. We focus on the special class of reparameterizable RL problems, where the trajectory distribution can be decomposed using the reparametrization trick…

New theorem shows gaps in magnetic Schrödinger operator spectra for large coupling.

Paper establishes a universal growth rate for smooth surrogate losses in classification.

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis technique provides a fresh perspective on Nesterov's excessive gap te…

New insights link diverse statistical problems via secret leakage planted clique.

A modern aircraft may require on the order of thousands of custom shims to fill gaps between structural components in the airframe that arise due to manufacturing tolerances adding up across large structures. These shims are necessary to eliminate gaps, maintain structural performance, and minimize pull-down forces req…

Gluon optimizes LMO-based methods for large-scale tasks, improving performance and theory-practice gap.

Paper tackles fast convergence for non-convex strongly-concave min-max problems.

The paper analyzes the latent geometry of generative diffusion models.

New RL method tackles sim-to-real gap using interactive data collection.

The trace set of a Fuchsian group $Γ$ ist the set of length of closed geodesics in the surface $Γ\backslash \mathbb{H}$. Luo and Sarnak showed that the trace set of a cofinite arithmetic Fuchsian group satisfies the bounded clustering property. Sarnak then conjectured that the B-C property actually characterizes arithm…