相关论文: Exploratory mean-variance portfolio selection with…

Commonly in reinforcement learning (RL), rewards are discounted over time using an exponential function to model time preference, thereby bounding the expected long-term reward. In contrast, in economics and psychology, it has been shown…

In reinforcement learning (RL) algorithms, exploratory control inputs are used during learning to acquire knowledge for decision making and control, while the true dynamics of a controlled object is unknown. However, this exploring property…

We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework…

This paper compares the optimal investment problems based on monotone mean-variance (MMV) and mean-variance (MV) preferences in the L\'{e}vy market with an untradable stochastic factor. It is an open question proposed by Trybu{\l}a and…

This note lays part of the theoretical ground for a definition of differential systems modeling reinforcement learning in continuous time non-Markovian rough environments. Specifically we focus on optimal relaxed control of rough equations…

Experimentally, it has been observed that humans and animals often make decisions that do not maximize their expected utility, but rather choose outcomes randomly, with probability proportional to expected utility. Probability matching, as…

We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…

This work uses the entropy-regularised relaxed stochastic control perspective as a principled framework for designing reinforcement learning (RL) algorithms. Herein agent interacts with the environment by generating noisy controls…

Reinforcement learning (RL) is a machine learning approach that trains agents to maximize cumulative rewards through interactions with environments. The integration of RL with deep learning has recently resulted in impressive achievements…

In reinforcement learning, two objective functions have been developed extensively in the literature: discounted and averaged rewards. The generalization to an entropy-regularized setting has led to improved robustness and exploration for…

Boltzmann exploration is a classic strategy for sequential decision-making under uncertainty, and is one of the most standard tools in Reinforcement Learning (RL). Despite its widespread use, there is virtually no theoretical understanding…

This paper studies an optimal investment-reinsurance problem for an insurer (she) under the Cram\'er--Lundberg model with monotone mean--variance (MMV) criterion. At any time, the insurer can purchase reinsurance (or acquire new business)…

The optimization of a large random portfolio under the Expected Shortfall risk measure with an $\ell_2$ regularizer is carried out by analytical calculation. The regularizer reins in the large sample fluctuations and the concomitant…

We study reinforcement learning (RL) for the same class of continuous-time stochastic linear--quadratic (LQ) control problems as in \cite{huang2024sublinear}, where volatilities depend on both states and controls while states are…

In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is…

We study expected utility maximization problem with constant relative risk aversion utility function in a complete market under the reinforcement learning framework. To induce exploration, we introduce the Tsallis entropy regularizer, which…

The mathematical theory of reproducing kernel Hilbert spaces (RKHS) provides powerful tools for minimum variance estimation (MVE) problems. Here, we extend the classical RKHS based analysis of MVE in several directions. We develop a…

In this paper, we investigate mean-variance (MV) portfolio selection problems with jumps in a regime-switching financial model. The novelty of our approach lies in allowing not only the market parameters -- such as the interest rate,…

We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min-max…

Latent variable models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet…