arXiv research

Paper shows FB and FC are equally hard up to logarithmic factors.

Study hypothesis testing under quantized samples with communication constraints, achieving near-optimal sample complexity.

Improved model-free RL algorithm with reduced sample complexity.

Improved uniform convergence bound with fat-shattering dimension reduces sample complexity gap.

Study shows sample complexity for learning optimal policies in SSP with generative model.

Study examines sample complexity for RL with safety constraints.

Improved sampling for high-dimensional posteriors with underdamped Langevin.

Optimal unimodal fitting for linear loss functions in a sequential, efficient manner.

Transformers capture combinatorial tasks with bounded error and logarithmic sample dependence.

The paper analyzes the statistical cost of tuning kernel hyperparameters in robust regression.

Optimal ReLU networks can memorize any separable set of points with a small number of parameters.

This paper improves system identification by reducing sample complexity for high-dimensional linear dynamical systems.

ULA estimates covariance of log-concave distributions efficiently.

Logarithmic connections on complex manifolds with trivial tangent bundle.

Long horizon reinforcement learning is as hard as short horizon learning.

In the Best-$k$-Arm problem, we are given $n$ stochastic bandit arms, each associated with an unknown reward distribution. We are required to identify the $k$ arms with the largest means by taking as few samples as possible. In this paper, we make progress towards a complete characterization of the instance-wise sample…

We investigate the statistical complexity of estimating the parameters of a discrete-state Markov chain kernel from a single long sequence of state observations. In the finite case, we characterize (modulo logarithmic factors) the minimax sample complexity of estimation with respect to the operator infinity norm, while…

This work improves the convergence theory of diffusion models for generating samples from complex distributions.

We study the sample complexity of private synthetic data generation over an unbounded sized class of statistical queries, and show that any class that is privately proper PAC learnable admits a private synthetic data generator (perhaps non-efficient). Previous work on synthetic data generators focused on the case that …

New Thompson sampling algorithm for stochastic partial monitoring achieves logarithmic regret.

The paper extends statistical estimation techniques under differential privacy.

We pursue the study of holomorphic Cartan geometry with singularities. We introduce the notion of logarithmic Cartan geometry on a complex manifold, with polar part supported on a normal crossing divisor. In particular, we show that the push-forward of a Cartan geometry constructed using a finite Galois ramified coveri…

Polynomial mixing times for simulated tempering in mixture sampling problems.

New algorithm reduces sample and communication complexities in federated Q-learning.

Self-attention prefers sparse functions of input sequences, reducing sample complexity.

Efficient algorithms for sparse parameter recovery in mixture models.

VA-LUCB identifies best arm with variance constraint, achieving optimal sample complexity.

We shall introduce the notion of $C^\infty$ logarithmic symplectic structures on a differentiable manifold which is an analog of the one of logarithmic symplectic structures in the holomorphic category. We show that the generalized complex structure induced by a $C^\infty$ logarithmic symplectic structure has unobstruc…

Causal discovery from empirical data is a fundamental problem in many scientific domains. Observational data allows for identifiability only up to Markov equivalence class. In this paper we first propose a polynomial time algorithm for learning the exact correctly-oriented structure of the transitive reduction of any c…

We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or $\varepsilon$-far from a given reference chain. We obtain nearly matching (up to logarithmic factors) upper and lower sample complexity bounds for our notion of distance, which is bas…

Study shows exponential gap in sample complexity between noisy and non-noisy recurrent neural networks.

We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might yield useful information about other, unobserved, parts of the MDP. We present a…

We revisit the inductive matrix completion problem that aims to recover a rank-$r$ matrix with ambient dimension $d$ given $n$ features as the side prior information. The goal is to make use of the known $n$ features to reduce sample and computational complexities. We present and analyze a new gradient-based non-convex…

Improved sampling from high-dimensional Gaussians using smoothed scores.

We present a new method to solve certain $\bar{\partial}$-equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. The result can be considered as a $\bar{\partial}$-lemma for logarithmic forms. As applications, we generalize the result of Deligne about closedness…

It is widely believed that the practical success of Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) owes to the fact that CNNs and RNNs use a more compact parametric representation than their Fully-Connected Neural Network (FNN) counterparts, and consequently require fewer training examples to…

Online change detection algorithm using random Fourier features.

Research examines correlations of complex logarithms of lattice points, showing level repulsion and Poissonian behavior.

In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, it induces a differential complex from which we derive the notio…

Paper analyzes sample complexity of offline MABs with KL regularization.

A new algorithm improves sample complexity for thresholding in Monte Carlo Tree Search.

Behavior cloning can achieve horizon-independent sample complexity in offline imitation learning.

New Q-learning method achieves optimal sample complexity for average-reward problems.

SCAFFLSA reduces communication complexity for federated learning with heterogeneous clients.

New algorithm reduces online logistic regression regret without exponential constant.

Polynomial-time DP algorithm for learning Gaussians with matching sample complexity.

Algorithm identifies Pareto front using multiple context directions and reuses exploration samples.

Optimizes ICA performance in high dimensions with computational constraints.