Related papers: Exploratory mean-variance portfolio selection with…

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The…

Reinforcement learning with verifiable rewards (RLVR) is a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs), yet its success hinges on effective exploration. An ideal exploration strategy must…

We consider the use of extreme learning machines (ELM) for computational partial differential equations (PDE). In ELM the hidden-layer coefficients in the neural network are assigned to random values generated on $[-R_m,R_m]$ and fixed,…

We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…

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…

An important question in constructing Cross Validation (CV) estimators of the generalization error is whether rules can be established that allow "optimal" selection of the size of the training set, for fixed sample size $n$. We define the…

The classical Markowitz mean-variance model uses variance as a risk measure and calculates frontier portfolios in closed form by using standard optimization techniques. For general mean-risk models such closed form optimal portfolios are…

Estimation of the mean and covariance functions is a fundamental problem in functional data analysis, particularly for discretely observed functional data. In this work, we study a regularization-based framework for estimating the mean and…

Equivariant and invariant deep learning models have been developed to exploit intrinsic symmetries in data, demonstrating significant effectiveness in certain scenarios. However, these methods often suffer from limited representation…

Following the recent resurgence in establishing linear control theoretic benchmarks for reinforcement leaning (RL)-based policy optimization (PO) for complex dynamical systems with continuous state and action spaces, an optimal control…

Reinforcement Learning (RL) remains a central optimisation framework in machine learning. Although RL agents can converge to optimal solutions, the definition of ``optimality'' depends on the environment's statistical properties. The…

This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation…

Reasoning ability has become a defining capability of Large Language Models (LLMs), with Reinforcement Learning with Verifiable Rewards (RLVR) emerging as a key paradigm to enhance it. However, RLVR training often suffers from policy…

Reinforcement learning (RL) methods often rely on massive exploration data to search optimal policies, and suffer from poor sampling efficiency. This paper presents a mixed reinforcement learning (mixed RL) algorithm by simultaneously using…

Safe exploration is crucial for the real-world application of reinforcement learning (RL). Previous works consider the safe exploration problem as Constrained Markov Decision Process (CMDP), where the policies are being optimized under…

This paper establishes a new and comprehensive theoretical analysis for the application of reinforcement learning (RL) in high-frequency market making. We bridge the modern RL theory and the continuous-time statistical models in…

Ensemble Kalman Sampler (EKS) is a method to find approximately $i.i.d.$ samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. The continuous version of the algorithm is a set of…

This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be…

The optimal execution problem has always been a continuously focused research issue, and many reinforcement learning (RL) algorithms have been studied. In this article, we consider the execution problem of targeting the volume weighted…

Resolving the exploration-exploitation trade-off remains a fundamental problem in the design and implementation of reinforcement learning (RL) algorithms. In this paper, we focus on model-free RL using the epsilon-greedy exploration policy,…