相关论文: Sharper lower bounds on the performance of the emp…

Exponential tilting is a technique commonly used in fields such as statistics, probability, information theory, and optimization to create parametric distribution shifts. Despite its prevalence in related fields, tilting has not seen…

In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling…

In this work, we present the first finite-time analysis of Q-learning with time-varying learning policies (i.e., on-policy sampling) for discounted Markov decision processes under minimal assumptions, requiring only the existence of a…

We study robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the…

We consider the teacher-student setting of learning shallow neural networks with quadratic activations and planted weight matrix $W^*\in\mathbb{R}^{m\times d}$, where $m$ is the width of the hidden layer and $d\le m$ is the data dimension.…

We present a quantum algorithm that analyzes risk more efficiently than Monte Carlo simulations traditionally used on classical computers. We employ quantum amplitude estimation to evaluate risk measures such as Value at Risk and…

Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software and hardware developments. Similarly to the classical setting,…

In this paper, our aim is to analyse the generalization capabilities of first-order methods for statistical learning in multiple, different yet related, scenarios including supervised learning, transfer learning, robust learning and…

In low-depth implementations of the Quantum Approximate Optimization Algorithm (QAOA), the dominant cost is often the number of objective evaluations rather than circuit depth. We introduce a graph-conditioned trust-region method for…

Many modern computational approaches to classical problems in quantitative finance are formulated as empirical loss minimization (ERM), allowing direct applications of classical results from statistical machine learning. These methods,…

The theoretical and empirical performance of Empirical Risk Minimization (ERM) often suffers when loss functions are poorly behaved with large Lipschitz moduli and spurious sharp minimizers. We propose and analyze a counterpart to ERM…

We propose a new simple and natural algorithm for learning the optimal Q-value function of a discounted-cost Markov Decision Process (MDP) when the transition kernels are unknown. Unlike the classical learning algorithms for MDPs, such as…

This paper investigates the finite-sample prediction risk of the high-dimensional least squares estimator. We derive the central limit theorem for the prediction risk when both the sample size and the number of features tend to infinity.…

We examine the relationship between the mutual information between the output model and the empirical sample and the generalization of the algorithm in the context of stochastic convex optimization. Despite increasing interest in…

Exploration in unknown environments is a fundamental problem in reinforcement learning and control. In this work, we study task-guided exploration and determine what precisely an agent must learn about their environment in order to complete…

We present an optimistic Q-learning algorithm for regret minimization in average reward reinforcement learning under an additional assumption on the underlying MDP that for all policies, the time to visit some frequent state $s_0$ is finite…

The entropic risk measure is widely used in high-stakes decision-making across economics, management science, finance, and safety-critical control systems because it captures tail risks associated with uncertain losses. However, when data…

In this paper, we derive rates of convergence in the high-dimensional central limit theorem for Polyak--Ruppert averaged iterates generated by entropy-regularized asynchronous Q-learning with linear function approximation and a polynomial…

We present an information-theoretic lower bound for the problem of parameter estimation with time-uniform coverage guarantees. Via a new a reduction to sequential testing, we obtain stronger lower bounds that capture the hardness of the…

The optimality and sensitivity of the empirical risk minimization problem with relative entropy regularization (ERM-RER) are investigated for the case in which the reference is a sigma-finite measure instead of a probability measure. This…