Related papers: Improved sample complexity bound for sample-based …
Distributed data analysis is a large and growing field driven by a massive proliferation of user devices, and by privacy concerns surrounding the centralised storage of data. We consider two \emph{adaptive} algorithms for estimating one…
We derive approximation bounds for learning single neuron models using thresholded gradient descent when both the labels and the covariates are possibly corrupted adversarially. We assume the data follows the model $y =…
Conventional wisdom in the sampling literature, backed by a popular diffusion scaling limit, suggests that the mixing time of the Metropolis-Adjusted Langevin Algorithm (MALA) scales as $O(d^{1/3})$, where $d$ is the dimension. However, the…
We study the sample complexity of learning an $\varepsilon$-optimal policy in an average-reward Markov decision process (MDP) under a generative model. For weakly communicating MDPs, we establish the complexity bound…
We study a class of optimization problems on Riemannian manifolds, where the objective function consists of a smooth term and quasi-norm type penalties with exponent $p \in (0, 1]$. The essential difficulty lies in the fact that the…
The Lindblad equation determines the time evolution of the density operator of open quantum systems. While valid for any system size, its use is, in practice, restricted to prototype/surrogate models with the aim of tackling specific…
A new method for stochastic unraveling of general time-local quantum master equations (QME) which involve the reduced density operator at time t only is proposed. The present kind of jump algorithm enables a numerically efficient treatment…
Adaptive importance samplers are adaptive Monte Carlo algorithms to estimate expectations with respect to some target distribution which \textit{adapt} themselves to obtain better estimators over a sequence of iterations. Although it is…
Matrix multiplication is a fundamental classical computing operation whose efficiency becomes a major challenge at scale, especially for machine learning applications. Quantum computing, with its inherent parallelism and exponential storage…
Markovian open quantum systems are governed by the Lindblad master equation where the dissipation contains two parts, i.e., the anti-Hermitian operator and the quantum jumps, which share a common dissipation rate. We generalize the Lindblad…
A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications,…
We present a two-step protocol for quantum measurement tomography that is light on classical co-processing cost and still achieves optimal sample complexity in the system dimension. Given measurement data from a known probe state ensemble,…
Let $\mathcal{O} \subset \mathbb{R}^d$ be a bounded domain of class $C^2$. In the Hilbert space $L_2(\mathcal{O};\mathbb{C}^n)$, we consider a matrix elliptic second order differential operator $\mathcal{A}_{D,\varepsilon}$ with the…
Model-based reinforcement learning (RL) is considered to be a promising approach to reduce the sample complexity that hinders model-free RL. However, the theoretical understanding of such methods has been rather limited. This paper…
Verifying uniform conditions over continuous spaces through random sampling is fundamental in machine learning and control theory, yet classical coverage analyses often yield conservative bounds, particularly at small failure probabilities.…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…
Convex composition optimization is an emerging topic that covers a wide range of applications arising from stochastic optimal control, reinforcement learning and multi-stage stochastic programming. Existing algorithms suffer from…
For the problem of task-agnostic reinforcement learning (RL), an agent first collects samples from an unknown environment without the supervision of reward signals, then is revealed with a reward and is asked to compute a corresponding…
We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…
Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron…