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Found 19 papers, 0 papers with code
On Bellman equations for continuous-time policy evaluation I: discretization and approximation
We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process.
Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency
When it is violated, the classical semi-parametric efficiency bound can easily become infinite, so that the instance-optimal risk depends on the function class used to model the regression function.
Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiency
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures.
Optimal variance-reduced stochastic approximation in Banach spaces
We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space.
Optimal and instance-dependent guarantees for Markovian linear stochastic approximation
We then prove a non-asymptotic instance-dependent bound on a suitably averaged sequence of iterates, with a leading term that matches the local asymptotic minimax limit, including sharp dependence on the parameters $(d, t_{\mathrm{mix}})$ in the higher order terms.
Optimal oracle inequalities for solving projected fixed-point equations
Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations.
ROOT-SGD: Sharp Nonasymptotics and Near-Optimal Asymptotics in a Single Algorithm
We study the problem of solving strongly convex and smooth unconstrained optimization problems using stochastic first-order algorithms.
On the Sample Complexity of Reinforcement Learning with Policy Space Generalization
To avoid such undesirable dependence on the state and action space sizes, this paper proposes a new notion of eluder dimension for the policy space, which characterizes the intrinsic complexity of policy learning in an arbitrary Markov Decision Process (MDP).
On Linear Stochastic Approximation: Fine-grained Polyak-Ruppert and Non-Asymptotic Concentration
When the matrix $\bar{A}$ is Hurwitz, we prove a central limit theorem (CLT) for the averaged iterates with fixed step size and number of iterations going to infinity.
Sampling for Bayesian Mixture Models: MCMC with Polynomial-Time Mixing
We study the problem of sampling from the power posterior distribution in Bayesian Gaussian mixture models, a robust version of the classical posterior.
An Efficient Sampling Algorithm for Non-smooth Composite Potentials
We consider the problem of sampling from a density of the form $p(x) \propto \exp(-f(x)- g(x))$, where $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a smooth and strongly convex function and $g: \mathbb{R}^d \rightarrow \mathbb{R}$ is a convex and Lipschitz function.
High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm
We propose a Markov chain Monte Carlo (MCMC) algorithm based on third-order Langevin dynamics for sampling from distributions with log-concave and smooth densities.
Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity
We present an improved analysis of the Euler-Maruyama discretization of the Langevin diffusion.
Dropout Training, Data-dependent Regularization, and Generalization Bounds
We study the problem of generalization guarantees for dropout training.
Differentially Private Clustering in High-Dimensional Euclidean Spaces
We study the problem of clustering sensitive data while preserving the privacy of individuals represented in the dataset, which has broad applications in practical machine learning and data analysis tasks.
Generalization Bounds of SGLD for Non-convex Learning: Two Theoretical Viewpoints
This is the first algorithm-dependent result with reasonable dependence on aggregated step sizes for non-convex learning, and has important implications to statistical learning aspects of stochastic gradient methods in complicated models such as deep learning.
Collect at Once, Use Effectively: Making Non-interactive Locally Private Learning Possible
For learning with smooth generalized linear losses, we propose an approximate stochastic gradient oracle estimated from non-interactive LDP channel, using Chebyshev expansion.
Efficient Private ERM for Smooth Objectives
For strongly convex and smooth objectives, we prove that gradient descent with output perturbation not only achieves nearly optimal utility, but also significantly improves the running time of previous state-of-the-art private optimization algorithms, for both $\epsilon$-DP and $(\epsilon, \delta)$-DP.
Stable Memory Allocation in the Hippocampus: Fundamental Limits and Neural Realization
In Valiant's neuroidal model, the hippocampus was described as a randomly connected graph, the computation on which maps input to a set of activated neuroids with stable size.
