In this paper, we present a novel algorithm, `uniINF`, for the Heavy-Tailed Multi-Armed Bandits (HTMAB) problem, demonstrating robustness and adaptability in both stochastic and adversarial environments. Unlike the stochastic MAB setting where loss distributions are stationary with time, our study extends to the adversarial setup, where losses are generated from heavy-tailed distributions that depend on both arms and time. Our novel algorithm `uniINF` enjoys the so-called Best-of-Both-Worlds (BoBW) property, performing optimally in both stochastic and adversarial environments *without* knowing the exact environment type. Moreover, our algorithm also possesses a Parameter-Free feature, *i.e.*, it operates *without* the need of knowing the heavy-tail parameters $(\sigma, \alpha)$ a-priori. To be precise, `uniINF` ensures nearly-optimal regret in both stochastic and adversarial environments, matching the corresponding lower bounds when $(\sigma, \alpha)$ is known (up to logarithmic factors). To our knowledge, `uniINF` is the first parameter-free algorithm to achieve the BoBW property for the heavy-tailed MAB problem. Technically, we develop innovative techniques to achieve BoBW guarantees for Parameter-Free HTMABs, including a refined analysis for the dynamics of log-barrier, an auto-balancing learning rate scheduling scheme, an adaptive skipping-clipping loss tuning technique, and a stopping-time analysis for logarithmic regret.

The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions. However, prior analyses of this framework have primarily focused on the continuous-time setting, assuming perfect solution of the underlying equations. In this work, we present the first discrete-time analysis of the stochastic interpolant framework, where we introduce a innovative discrete-time sampler and derive a finite-time upper bound on its distribution estimation error. Our result provides a novel quantification on how different factors, including the distance between source and target distributions and estimation accuracy, affect the convergence rate and also offers a new principled way to design efficient schedule for convergence acceleration. Finally, numerical experiments are conducted on the discrete-time sampler to corroborate our theoretical findings.

Risk-sensitive reinforcement learning (RL) aims to optimize policies that balance the expected reward and risk. In this paper, we present a novel risk-sensitive RL framework that employs an Iterated Conditional Value-at-Risk (CVaR) objective under both linear and general function approximations, enriched by human feedback. These new formulations provide a principled way to guarantee safety in each decision making step throughout the control process. Moreover, integrating human feedback into risk-sensitive RL framework bridges the gap between algorithmic decision-making and human participation, allowing us to also guarantee safety for human-in-the-loop systems. We propose provably sample-efficient algorithms for this Iterated CVaR RL and provide rigorous theoretical analysis. Furthermore, we establish a matching lower bound to corroborate the optimality of our algorithms in a linear context.

In the realm of reinforcement learning (RL), accounting for risk is crucial for making decisions under uncertainty, particularly in applications where safety and reliability are paramount. In this paper, we introduce a general framework on Risk-Sensitive Distributional Reinforcement Learning (RS-DisRL), with static Lipschitz Risk Measures (LRM) and general function approximation. Our framework covers a broad class of risk-sensitive RL, and facilitates analysis of the impact of estimation functions on the effectiveness of RSRL strategies and evaluation of their sample complexity. We design two innovative meta-algorithms: RS-DisRL-M, a model-based strategy for model-based function approximation, and RS-DisRL-V, a model-free approach for general value function approximation. With our novel estimation techniques via Least Squares Regression (LSR) and Maximum Likelihood Estimation (MLE) in distributional RL with augmented Markov Decision Process (MDP), we derive the first $\widetilde{\mathcal{O}}(\sqrt{K})$ dependency of the regret upper bound for RSRL with static LRM, marking a pioneering contribution towards statistically efficient algorithms in this domain.

This work pioneers regret analysis of risk-sensitive reinforcement learning in partially observable environments with hindsight observation, addressing a gap in theoretical exploration. We introduce a novel formulation that integrates hindsight observations into a Partially Observable Markov Decision Process (POMDP) framework, where the goal is to optimize accumulated reward under the entropic risk measure. We develop the first provably efficient RL algorithm tailored for this setting. We also prove by rigorous analysis that our algorithm achieves polynomial regret $\tilde{O}\left(\frac{e^{|{\gamma}|H}-1}{|{\gamma}|H}H^2\sqrt{KHS^2OA}\right)$, which outperforms or matches existing upper bounds when the model degenerates to risk-neutral or fully observable settings. We adopt the method of change-of-measure and develop a novel analytical tool of beta vectors to streamline mathematical derivations. These techniques are of particular interest to the theoretical study of reinforcement learning.

Multi-user delay-constrained scheduling is a crucial challenge in various real-world applications, such as wireless communication, live streaming, and cloud computing. The scheduler must make real-time decisions to guarantee both delay and resource constraints simultaneously, without prior information on system dynamics that can be time-varying and challenging to estimate. Additionally, many practical scenarios suffer from partial observability issues due to sensing noise or hidden correlation. To address these challenges, we propose a deep reinforcement learning (DRL) algorithm called Recurrent Softmax Delayed Deep Double Deterministic Policy Gradient ($\mathtt{RSD4}$) (https://github.com/hupihe/RSD4), which is a data-driven method based on a Partially Observed Markov Decision Process (POMDP) formulation.$\mathtt{RSD4}$guarantees resource and delay constraints by Lagrangian dual and delay-sensitive queues, respectively. It also efficiently handles partial observability with a memory mechanism enabled by the recurrent neural network (RNN). Moreover, it introduces user-level decomposition and node-level merging to support large-scale multihop scenarios. Extensive experiments on simulated and real-world datasets demonstrate that$\mathtt{RSD4}$is robust to system dynamics and partially observable environments and achieves superior performance over existing methods.

We study reinforcement learning with linear function approximation where the transition probability and reward functions are linear with respect to a feature mapping $\boldsymbol{\phi}(s,a)$. Specifically, we consider the episodic inhomogeneous linear Markov Decision Process (MDP), and propose a novel computation-efficient algorithm, LSVI-UCB$^+$, which achieves an $\widetilde{O}(Hd\sqrt{T})$ regret bound where $H$ is the episode length, $d$ is the feature dimension, and $T$ is the number of steps. LSVI-UCB$^+$ builds on weighted ridge regression and upper confidence value iteration with a Bernstein-type exploration bonus. Our statistical results are obtained with novel analytical tools, including a new Bernstein self-normalized bound with conservatism on elliptical potentials, and refined analysis of the correction term. To the best of our knowledge, this is the first minimax optimal algorithm for linear MDPs up to logarithmic factors, which closes the $\sqrt{Hd}$ gap between the best known upper bound of $\widetilde{O}(\sqrt{H^3d^3T})$ in \cite{jin2020provably} and lower bound of $\Omega(Hd\sqrt{T})$ for linear MDPs.

Multi-user delay constrained scheduling is important in many real-world applications including wireless communication, live streaming, and cloud computing. Yet, it poses a critical challenge since the scheduler needs to make real-time decisions to guarantee the delay and resource constraints simultaneously without prior information of system dynamics, which can be time-varying and hard to estimate. Moreover, many practical scenarios suffer from partial observability issues, e.g., due to sensing noise or hidden correlation. To tackle these challenges, we propose a deep reinforcement learning (DRL) algorithm, named Recurrent Softmax Delayed Deep Double Deterministic Policy Gradient (RSD4)1, which is a data-driven method based on a Partially Observed Markov Decision Process (POMDP) formulation. RSD4 guarantees resource and delay constraints by Lagrangian dual and delay-sensitive queues, respectively. It also efficiently tackles partial observability with a memory mechanism enabled by the recurrent neural network (RNN) and introduces user-level decomposition and node-level merging to ensure scalability. Extensive experiments on simulated/real-world datasets demonstrate that RSD4 is robust to system dynamics and partially observable environments, and achieves superior performances over existing DRL and non-DRL-based methods.

As the Industry 4.0 or Internet of Things (IoT) era begins, security plays a key role in the Industry Internet of Things (IIoT) due to various threats, which include escape or Distributed Denial of Service (DDoS) attackers in the virtualization layer and vulnerability exploiters in the device layer. A successful cross-VM escape attack in the virtualization layer combined with cross-layer penetration in the device layer, which we define as an Advanced Persistent Escaper (APE), poses a great threat. Therefore, the development of detection and rejection methods for APEs across multiple layers in IIoT is an open issue. To the best of our knowledge, less effective methods are established, especially for vulnerability exploitation in the virtualization layer and backdoor leverage in the device layer. On the basis of this, we propose Escaper Cops (EscaperCOP), a detection method for cross-VM escapers in the virtualization layer and cross-layer penetrators in the device layer. In particular, a new detection method for guest-to-host escapers is proposed for the virtualization layer. Finally, a novel encryption method based on Identity-based Broadcast Encryption (IBBE) is proposed to protect the critical components in EscaperCOP, detection library, and control command library. To verify our method, experimental tests are performed for a large number of APEs in an IIoT framework. The test results have demonstrated the proposed method is effective with an acceptable level of detection ratio.