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Stochastic multi-armed bandits (MABs) provide a fundamental reinforcement learning model to study sequential decision making in uncertain environments. The upper confidence bounds (UCB) algorithm gave birth to the renaissance of bandit…
In many applications of Reinforcement Learning (RL), it is critically important that the algorithm performs safely, such that instantaneous hard constraints are satisfied at each step, and unsafe states and actions are avoided. However,…
We study online reinforcement learning for finite-horizon deterministic control systems with {\it arbitrary} state and action spaces. Suppose that the transition dynamics and reward function is unknown, but the state and action space is…
Reinforcement Learning (RL) has gained substantial attention across diverse application domains and theoretical investigations. Existing literature on RL theory largely focuses on risk-neutral settings where the decision-maker learns to…
This paper addresses the average cost minimization problem for discrete-time systems with multiplicative and additive noises via reinforcement learning. By using Q-function, we propose an online learning scheme to estimate the kernel matrix…
We study the reinforcement learning (RL) problem in a constrained Markov decision process (CMDP), where an agent explores the environment to maximize the expected cumulative reward while satisfying a single constraint on the expected total…
Partial observability is a common challenge in many reinforcement learning applications, which requires an agent to maintain memory, infer latent states, and integrate this past information into exploration. This challenge leads to a number…
We study time-inhomogeneous episodic reinforcement learning (RL) under general function approximation and sparse rewards. We design a new algorithm, Variance-weighted Optimistic $Q$-Learning (VO$Q$L), based on $Q$-learning and bound its…
Reinforcement learning (RL) with linear function approximation has received increasing attention recently. However, existing work has focused on obtaining $\sqrt{T}$-type regret bound, where $T$ is the number of interactions with the MDP.…
This paper presents a discrete-time option pricing model that is rooted in Reinforcement Learning (RL), and more specifically in the famous Q-Learning method of RL. We construct a risk-adjusted Markov Decision Process for a discrete-time…
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…
We study reinforcement learning (RL) for a class of continuous-time linear-quadratic (LQ) control problems for diffusions, where states are scalar-valued and running control rewards are absent but volatilities of the state processes depend…
We study how a central bank should dynamically set short-term nominal interest rates to stabilize inflation and unemployment when macroeconomic relationships are uncertain and time-varying. We model monetary policy as a sequential…
We consider online reinforcement learning in episodic Markov decision process (MDP) with unknown transition function and stochastic rewards drawn from some fixed but unknown distribution. The learner aims to learn the optimal policy and…
Offline inverse reinforcement learning (IRL) aims to recover a reward function that explains expert behavior using only fixed demonstration data, without any additional online interaction. We propose BiCQL-ML, a policy-free offline IRL…
In this paper, we investigate the problem of \textit{episodic reinforcement learning} with quantum oracles for state evolution. To this end, we propose an \textit{Upper Confidence Bound} (UCB) based quantum algorithmic framework to…
Multi-action restless multi-armed bandits (RMABs) are a powerful framework for constrained resource allocation in which $N$ independent processes are managed. However, previous work only study the offline setting where problem dynamics are…
Learning Markov decision processes (MDPs) in the presence of the adversary is a challenging problem in reinforcement learning (RL). In this paper, we study RL in episodic MDPs with adversarial reward and full information feedback, where the…
We study risk-sensitive Reinforcement Learning (RL), where we aim to maximize the Conditional Value at Risk (CVaR) with a fixed risk tolerance $\tau$. Prior theoretical work studying risk-sensitive RL focuses on the tabular Markov Decision…
In real-world tasks, reinforcement learning (RL) agents frequently encounter situations that are not present during training time. To ensure reliable performance, the RL agents need to exhibit robustness against worst-case situations. The…