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This paper develops a quantized Q-learning algorithm for the optimal control of controlled diffusion processes on $\mathbb{R}^d$ under both discounted and ergodic (average) cost criteria. We first establish near-optimality of finite-state…
This paper is concerned with the maximum principle and dynamic programming principle for mean-variance portfolio selection of jump diffusions and their relationship. First, the optimal portfolio and efficient frontier of the problem are…
Recent advances in reinforcement learning (RL) have achieved great successes by leveraging the multimodality and exploration capability of diffusion policies. Among these approaches, one representative branch focuses on the sampling-based…
Distributional reinforcement learning (RL) is a powerful framework increasingly adopted in safety-critical domains for its ability to optimize risk-sensitive objectives. However, the role of the discount factor is often overlooked, as it is…
Research in quantitative finance has demonstrated that reinforcement learning (RL) methods have delivered promising outcomes in the context of hedging financial portfolios. For example, hedging a portfolio of European options using RL…
Reinforcement learning has become a central paradigm for improving LLM reasoning, but most existing methods optimize policies over discrete token sequences. This creates a mismatch between the optimization space and the structure of…
Real-world applications require RL algorithms to act safely. During learning process, it is likely that the agent executes sub-optimal actions that may lead to unsafe/poor states of the system. Exploration is particularly brittle in…
As a paradigm for sequential decision making in unknown environments, reinforcement learning (RL) has received a flurry of attention in recent years. However, the explosion of model complexity in emerging applications and the presence of…
Sequential decision making in the presence of uncertainty and stochastic dynamics gives rise to distributions over state/action trajectories in reinforcement learning (RL) and optimal control problems. This observation has led to a variety…
Reinforcement Learning (RL) of robotic manipulation skills, despite its impressive successes, stands to benefit from incorporating domain knowledge from control theory. One of the most important properties that is of interest is control…
Linear dynamical systems that obey stochastic differential equations are canonical models. While optimal control of known systems has a rich literature, the problem is technically hard under model uncertainty and there are hardly any…
Reinforcement Learning (RL) has proven effective in solving complex decision-making tasks across various domains, but challenges remain in continuous-time settings, particularly when state dynamics are governed by stochastic differential…
Much research has been done to analyze the stock market. After all, if one can determine a pattern in the chaotic frenzy of transactions, then they could make a hefty profit from capitalizing on these insights. As such, the goal of our…
We introduce Random Reward Perturbation (RRP), a novel exploration strategy for reinforcement learning (RL). Our theoretical analyses demonstrate that adding zero-mean noise to environmental rewards effectively enhances policy diversity…
Risk-sensitive reinforcement learning (RL) is crucial for maintaining reliable performance in high-stakes applications. While traditional RL methods aim to learn a point estimate of the random cumulative cost, distributional RL (DRL) seeks…
Reinforcement learning (RL) is a powerful machine learning technique that has been successfully applied to a wide variety of problems. However, it can be unpredictable and produce suboptimal results in complicated learning environments.…
In complex environments with large discrete action spaces, effective decision-making is critical in reinforcement learning (RL). Despite the widespread use of value-based RL approaches like Q-learning, they come with a computational burden,…
In domains such as finance, healthcare, and robotics, managing worst-case scenarios is critical, as failure to do so can lead to catastrophic outcomes. Distributional Reinforcement Learning (DRL) provides a natural framework to incorporate…
Offline reinforcement learning (RL), which aims to learn an optimal policy using a previously collected static dataset, is an important paradigm of RL. Standard RL methods often perform poorly in this regime due to the function…
In finance, sequential decision problems are often faced, for which reinforcement learning (RL) emerges as a promising tool for optimisation without the need of analytical tractability. However, the objective of classical RL is the expected…