Related papers: Improved sample complexity bound for sample-based …
We investigate the sample complexity of bounded two-layer neural networks using different activation functions. In particular, we consider the class $$ \mathcal{H} = \left\{\textbf{x}\mapsto \langle \textbf{v}, \sigma \circ W\textbf{b} +…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We study the sample complexity of differentially private optimization of quasi-concave functions. For a fixed input domain $\mathcal{X}$, Cohen et al. (STOC 2023) proved that any generic private optimizer for low sensitive quasi-concave…
We consider infinite-horizon $\gamma$-discounted (linear) constrained Markov decision processes (CMDPs) where the objective is to find a policy that maximizes the expected cumulative reward subject to expected cumulative constraints. Given…
We develop an optimal control algorithm for robust quantum gate preparation in open environments with the state of the quantum system represented using the Lindblad master equation. The algorithm is based on adaptive linearization and…
Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in…
The generalized smooth condition, $(L_{0},L_{1})$-smoothness, has triggered people's interest since it is more realistic in many optimization problems shown by both empirical and theoretical evidence. Two recent works established the…
The Normalized Maximum Likelihood (NML) codelength, or stochastic complexity, represents a principled criterion for universal coding. While recent coarea-based formulations provided a calculation method for smooth models, this framework…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
We consider the algorithm by Ferson et al. (Reliable computing 11(3), p. 207-233, 2005) designed for solving the NP-hard problem of computing the maximal sample variance over interval data, motivated by robust statistics (in fact, the…
We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…
Sampling from high-dimensional probability distributions is fundamental in machine learning and statistics. As datasets grow larger, computational efficiency becomes increasingly important, particularly in reducing adaptive complexity,…
We study the optimal sample complexity in large-scale Reinforcement Learning (RL) problems with policy space generalization, i.e. the agent has a prior knowledge that the optimal policy lies in a known policy space. Existing results show…
We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain $D$ of ${\mathbb R}^n$ for a second order parameter-dependent elliptic differential operator $A (x,\partial, \lambda)$ with complex-valued essentially…
We present a robust method for quantum process tomography, which yields a set of Lindblad operators that optimally fit the measured density operators at a sequence of time points. The benefits of this method are illustrated using a set of…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…
We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…
This work considers the sample complexity of obtaining an $\varepsilon$-optimal policy in an average reward Markov Decision Process (AMDP), given access to a generative model (simulator). When the ground-truth MDP is weakly communicating,…
In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees…
Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, the theoretical underpinnings governing the conditions for efficient operator learning remain…