Reinforcement Learning (RL) agents often struggle with inefficient exploration, particularly in environments with sparse rewards. Traditional exploration strategies can lead to slow learning and suboptimal performance because agents fail to systematically build on previously successful experiences, thereby reducing sample efficiency. To tackle this issue, we propose a self-imitating on-policy algorithm that enhances exploration and sample efficiency by leveraging past high-reward state-action pairs to guide policy updates. Our method incorporates self-imitation by using optimal transport distance in dense reward environments to prioritize state visitation distributions that match the most rewarding trajectory. In sparse-reward environments, we uniformly replay successful self-encountered trajectories to facilitate structured exploration. Experimental results across diverse environments demonstrate substantial improvements in learning efficiency, including MuJoCo for dense rewards and the partially observable 3D Animal-AI Olympics and multi-goal PointMaze for sparse rewards. Our approach achieves faster convergence and significantly higher success rates compared to state-of-the-art self-imitating RL baselines. These findings underscore the potential of self-imitation as a robust strategy for enhancing exploration in RL, with applicability to more complex tasks.

We study infinite-horizon Constrained Markov Decision Processes (CMDPs) with general policy parameterizations and multi-layer neural network critics. Existing theoretical analyses for constrained reinforcement learning largely rely on tabular policies or linear critics, which limits their applicability to high-dimensional and continuous control problems. We propose a primal-dual natural actor-critic algorithm that integrates neural critic estimation with natural policy gradient updates and leverages Neural Tangent Kernel (NTK) theory to control function-approximation error under Markovian sampling, without requiring access to mixing-time oracles. We establish global convergence and cumulative constraint violation rates of 𝒪̃(T^-1/4) up to approximation errors induced by the policy and critic classes. Our results provide the first such guarantees for CMDPs with general policies and multi-layer neural critics, substantially extending the theoretical foundations of actor-critic methods beyond the linear-critic regime.

This paper addresses the challenge of achieving optimal sample complexity in reinforcement learning for Markov Decision Processes (MDPs) with general policy parameterization and multi-layer neural network critics. Existing approaches either fail to achieve the optimal rate or require impractical assumptions, such as access to knowledge of mixing times or the linearity of the critic. We introduce the Natural Actor-Critic with Data Drop (NAC-DD) algorithm, which integrates Natural Policy Gradient methods with a Data Drop technique to mitigate statistical dependencies inherent in Markovian sampling. NAC-DD achieves an optimal sample complexity of (O) over tilde (1/epsilon(2)), marking a significant improvement over the previous state-of-the-art guarantee of (O) over tilde (1/epsilon(3)). The algorithm employs a multi-layer neural network critic with differentiable activation functions, aligning with real-world applications where tabular policies and linear critics are insufficient. Our work represents the first to achieve order-optimal sample complexity for actor-critic methods with neural function approximation, continuous state and action spaces, and Markovian sampling. Empirical evaluations on benchmark tasks confirm the theoretical findings, demonstrating the practical efficacy of the proposed method.

This work examines average-reward reinforcement learning with general policy parametrization. Existing state-of-the-art (SOTA) guarantees for this problem are either suboptimal or hindered by several challenges, including poor scalability with respect to the size of the state-action space, high iteration complexity, and a significant dependence on knowledge of mixing times and hitting times. To address these limitations, we propose a Multi-level Monte Carlo-based Natural Actor-Critic (MLMC-NAC) algorithm. Our work is the first to achieve a global convergence rate of (O) over tilde (1/root T) for average-reward Markov Decision Processes (MDPs) (where T is the horizon length), using an Actor-Critic approach. Moreover, the convergence rate does not scale with the size of the state space, therefore even being applicable to infinite state spaces.

We present the first finite-sample analysis of policy evaluation in robust average-reward Markov Decision Processes (MDPs). Prior work in this setting have established only asymptotic convergence guarantees, leaving open the question of sample complexity. In this work, we address this gap by showing that the robust Bellman operator is a contraction under a carefully constructed semi-norm, and developing a stochastic approximation framework with controlled bias. Our approach builds upon Multi-Level Monte Carlo (MLMC) techniques to estimate the robust Bellman operator efficiently. To overcome the infinite expected sample complexity inherent in standard MLMC, we introduce a truncation mechanism based on a geometric distribution, ensuring a finite expected sample complexity while maintaining a small bias that decays exponentially with the truncation level. Our method achieves the order-optimal sample complexity of $\tilde{\mathcal{O}}(\epsilon^{-2})$ for robust policy evaluation and robust average reward estimation, marking a significant advancement in robust reinforcement learning theory.

This paper investigates infinite-horizon average reward Constrained Markov Decision Processes (CMDPs) under general parametrized policies with smooth and bounded policy gradients. We propose a Primal-Dual Natural Actor-Critic algorithm that adeptly manages constraints while ensuring a high convergence rate. In particular, our algorithm achieves global convergence and constraint violation rates of $\tilde{\mathcal{O}}(1/\sqrt{T})$ over a horizon of length $T$ when the mixing time, $\tau_{\mathrm{mix}}$, is known to the learner. In absence of knowledge of $\tau_{\mathrm{mix}}$, the achievable rates change to $\tilde{\mathcal{O}}(1/T^{0.5-\epsilon})$ provided that $T \geq \tilde{\mathcal{O}}\left(\tau_{\mathrm{mix}}^{2/\epsilon}\right)$. Our results match the theoretical lower bound for Markov Decision Processes and establish a new benchmark in the theoretical exploration of average reward CMDPs.

We present two Policy Gradient-based methods with general parameterization in the context of infinite horizon average reward Markov Decision Processes. The first approach employs Implicit Gradient Transport for variance reduction, ensuring an expected regret of the order $\tilde{\mathcal{O}}(T^{3/5})$. The second approach, rooted in Hessian-based techniques, ensures an expected regret of the order $\tilde{\mathcal{O}}(\sqrt{T})$. These results significantly improve the state of the art of the problem, which achieves a regret of $\tilde{\mathcal{O}}(T^{3/4})$.

In this paper, we consider an infinite horizon average reward Markov Decision Process (MDP). Distinguishing itself from existing works within this context, our approach harnesses the power of the general policy gradient-based algorithm, liberating it from the constraints of assuming a linear MDP structure. We propose a vanilla policy gradient-based algorithm and show its global convergence property. We then prove that the proposed algorithm has O(T^3/4) regret. Remarkably, this paper marks a pioneering effort by presenting the first exploration into regret bound computation for the general parameterized policy gradient algorithm in the context of average reward scenarios.

This paper presents a conditional generative adversarial network (cGAN) that translates base station location (BSL) information of any Region-of-Interest (RoI) to location-dependent coverage probability values within a subset of that region, called the region-of-evaluation (RoE). We train our network utilizing the BSL data of India, the USA, Germany, and Brazil. In comparison to the state-of-the-art convolutional neural networks (CNNs), our model improves the prediction error (L_1 difference between the coverage manifold generated by the network under consideration and that generated via simulation) by two orders of magnitude. Moreover, the cGAN-generated coverage manifolds appear to be almost visually indistinguishable from the ground truth.

We consider a constrained Markov Decision Problem (CMDP) where the goal of an agent is to maximize the expected discounted sum of rewards over an infinite horizon while ensuring that the expected discounted sum of costs exceeds a certain threshold. Building on the idea of momentum-based acceleration, we develop the Primal-Dual Accelerated Natural Policy Gradient (PD-ANPG) algorithm that ensures an $\epsilon$ global optimality gap and $\epsilon$ constraint violation with $\tilde{\mathcal{O}}((1-\gamma)^{-7}\epsilon^{-2})$ sample complexity for general parameterized policies where $\gamma$ denotes the discount factor. This improves the state-of-the-art sample complexity in general parameterized CMDPs by a factor of $\mathcal{O}((1-\gamma)^{-1}\epsilon^{-2})$ and achieves the theoretical lower bound in $\epsilon^{-1}$.

We consider the problem of designing sample efficient learning algorithms for infinite horizon discounted reward Markov Decision Process. Specifically, we propose the Accelerated Natural Policy Gradient (ANPG) algorithm that utilizes an accelerated stochastic gradient descent process to obtain the natural policy gradient. ANPG achieves $\mathcal{O}({\epsilon^{-2}})$ sample complexity and $\mathcal{O}(\epsilon^{-1})$ iteration complexity with general parameterization where $\epsilon$ defines the optimality error. This improves the state-of-the-art sample complexity by a $\log(\frac{1}{\epsilon})$ factor. ANPG is a first-order algorithm and unlike some existing literature, does not require the unverifiable assumption that the variance of importance sampling (IS) weights is upper bounded. In the class of Hessian-free and IS-free algorithms, ANPG beats the best-known sample complexity by a factor of $\mathcal{O}(\epsilon^{-\frac{1}{2}})$ and simultaneously matches their state-of-the-art iteration complexity.

Given the necessity of connecting the unconnected, covering blind spots has emerged as a critical task in the next-generation wireless communication network. A direct solution involves obtaining a coverage manifold that visually showcases network coverage performance at each position. Our goal is to devise different methods that minimize the absolute error between the estimated coverage manifold and the actual coverage manifold (referred to as accuracy), while simultaneously maximizing the reduction in computational complexity (measured by computational latency). Simulation is a common method for acquiring coverage manifolds. Although accurate, it is computationally expensive, making it challenging to extend to large-scale networks. In this paper, we expedite traditional simulation methods by introducing a statistical model termed line-of-sight probability-based accelerated simulation. Stochastic geometry is suitable for evaluating the performance of large-scale networks, albeit in a coarse-grained manner. Therefore, we propose a second method wherein a model training approach is applied to the stochastic geometry framework to enhance accuracy and reduce complexity. Additionally, we propose a machine learning-based method that ensures both low complexity and high accuracy, albeit with a significant demand for the size and quality of the dataset. Furthermore, we describe the relationships between these three methods, compare their complexity and accuracy as performance verification, and discuss their application scenarios.

We show that in a cooperative $N$-agent network, one can design locally executable policies for the agents such that the resulting discounted sum of average rewards (value) well approximates the optimal value computed over all (including non-local) policies. Specifically, we prove that, if $|\mathcal{X}|, |\mathcal{U}|$ denote the size of state, and action spaces of individual agents, then for sufficiently small discount factor, the approximation error is given by $\mathcal{O}(e)$ where $e\triangleq \frac{1}{\sqrt{N}}\left[\sqrt{|\mathcal{X}|}+\sqrt{|\mathcal{U}|}\right]$. Moreover, in a special case where the reward and state transition functions are independent of the action distribution of the population, the error improves to $\mathcal{O}(e)$ where $e\triangleq \frac{1}{\sqrt{N}}\sqrt{|\mathcal{X}|}$. Finally, we also devise an algorithm to explicitly construct a local policy. With the help of our approximation results, we further establish that the constructed local policy is within $\mathcal{O}(\max\{e,\epsilon\})$ distance of the optimal policy, and the sample complexity to achieve such a local policy is $\mathcal{O}(\epsilon^{-3})$, for any $\epsilon>0$.

This study explores the vaccine prioritization strategy to reduce the overall burden of the pandemic when the supply is limited. Existing vaccine distribution methods focus on macro-level or simplified micro-level assuming homogeneous behavior within populations without considering mobility patterns. Directly applying these models for micro-level vaccine allocation leads to sub-optimal solutions. To address the issue, we first proposed a Trans-vaccine-SEIR model to incorporate mobility heterogeneity in disease propagation. Then we develop a novel deep reinforcement learning to seek the optimal vaccine allocation strategy for the disease evolution system. The graph neural network is used to effectively capture the structural properties of the mobility network and extract disease features. In our evaluation, the proposed framework reduces 7% - 10% of infections and deaths compared to the baseline strategies. Extensive evaluation shows that the proposed framework is robust to seek the optimal vaccine allocation with diverse mobility patterns. In particular, we find transit usage restriction is significantly more effective than restricting cross-zone mobility for the top 10% age-based and income-based zones under optimal vaccine allocation strategy. These results provide valuable insights for areas with limited vaccines and low logistic efficacy.

Reinforcement Learning (RL) serves as a versatile framework for sequential decision-making, finding applications across diverse domains such as robotics, autonomous driving, recommendation systems, supply chain optimization, biology, mechanics, and finance. The primary objective in these applications is to maximize the average reward. Real-world scenarios often necessitate adherence to specific constraints during the learning process. This monograph focuses on the exploration of various model-based and model-free approaches for Constrained RL within the context of average reward Markov Decision Processes (MDPs). The investigation commences with an examination of model-based strategies, delving into two foundational methods - optimism in the face of uncertainty and posterior sampling. Subsequently, the discussion transitions to parametrized model-free approaches, where the primal-dual policy gradient-based algorithm is explored as a solution for constrained MDPs. The monograph provides regret guarantees and analyzes constraint violation for each of the discussed setups. For the above exploration, we assume the underlying MDP to be ergodic. Further, this monograph extends its discussion to encompass results tailored for weakly communicating MDPs, thereby broadening the scope of its findings and their relevance to a wider range of practical scenarios.

We investigate an infinite-horizon average reward Markov Decision Process (MDP) with delayed, composite, and partially anonymous reward feedback. The delay and compositeness of rewards mean that rewards generated as a result of taking an action at a given state are fragmented into different components, and they are sequentially realized at delayed time instances. The partial anonymity attribute implies that a learner, for each state, only observes the aggregate of past reward components generated as a result of different actions taken at that state, but realized at the observation instance. We propose an algorithm named $\mathrm{DUCRL2}$ to obtain a near-optimal policy for this setting and show that it achieves a regret bound of $\tilde{\mathcal{O}}\left(DS\sqrt{AT} + d (SA)^3\right)$ where $S$ and $A$ are the sizes of the state and action spaces, respectively, $D$ is the diameter of the MDP, $d$ is a parameter upper bounded by the maximum reward delay, and $T$ denotes the time horizon. This demonstrates the optimality of the bound in the order of $T$, and an additive impact of the delay.

Mean-Field Control (MFC) has recently been proven to be a scalable tool to approximately solve large-scale multi-agent reinforcement learning (MARL) problems. However, these studies are typically limited to unconstrained cumulative reward maximization framework. In this paper, we show that one can use the MFC approach to approximate the MARL problem even in the presence of constraints. Specifically, we prove that, an $N$-agent constrained MARL problem, with state, and action spaces of each individual agents being of sizes $|\mathcal{X}|$, and $|\mathcal{U}|$ respectively, can be approximated by an associated constrained MFC problem with an error, $e\triangleq \mathcal{O}\left([\sqrt{|\mathcal{X}|}+\sqrt{|\mathcal{U}|}]/\sqrt{N}\right)$. In a special case where the reward, cost, and state transition functions are independent of the action distribution of the population, we prove that the error can be improved to $e=\mathcal{O}(\sqrt{|\mathcal{X}|}/\sqrt{N})$. Also, we provide a Natural Policy Gradient based algorithm and prove that it can solve the constrained MARL problem within an error of $\mathcal{O}(e)$ with a sample complexity of $\mathcal{O}(e^{-6})$.

The examination of post-disaster recovery (PDR) in a socio-physical system enables us to elucidate the complex relationships between humans and infrastructures. Although existing studies have identified many patterns in the PDR process, they fall short of describing how individual recoveries contribute to the overall recovery of the system. To enhance the understanding of individual return behavior and the recovery of point-of-interests (POIs), we propose an agent-based model (ABM), called PostDisasterSim. We apply the model to analyze the recovery of five counties in Texas following Hurricane Harvey in 2017. Specifically, we construct a three-layer network comprising the human layer, the social infrastructure layer, and the physical infrastructure layer, using mobile phone location data and POI data. Based on prior studies and a household survey, we develop the ABM to simulate how evacuated individuals return to their homes, and social and physical infrastructures recover. By implementing the ABM, we unveil the heterogeneity in recovery dynamics in terms of agent types, housing types, household income levels, and geographical locations. Moreover, simulation results across nine scenarios quantitatively demonstrate the positive effects of social and physical infrastructure improvement plans. This study can assist disaster scientists in uncovering nuanced recovery patterns and policymakers in translating policies like resource allocation into practice.

Mean Field Control (MFC) is a powerful approximation tool to solve large-scale Multi-Agent Reinforcement Learning (MARL) problems. However, the success of MFC relies on the presumption that given the local states and actions of all the agents, the next (local) states of the agents evolve conditionally independent of each other. Here we demonstrate that even in a MARL setting where agents share a common global state in addition to their local states evolving conditionally independently (thus introducing a correlation between the state transition processes of individual agents), the MFC can still be applied as a good approximation tool. The global state is assumed to be non-decomposable i.e., it cannot be expressed as a collection of local states of the agents. We compute the approximation error as $\mathcal{O}(e)$ where $e=\frac{1}{\sqrt{N}}\left[\sqrt{|\mathcal{X}|} +\sqrt{|\mathcal{U}|}\right]$. The size of the agent population is denoted by the term $N$, and $|\mathcal{X}|, |\mathcal{U}|$ respectively indicate the sizes of (local) state and action spaces of individual agents. The approximation error is found to be independent of the size of the shared global state space. We further demonstrate that in a special case if the reward and state transition functions are independent of the action distribution of the population, then the error can be improved to $e=\frac{\sqrt{|\mathcal{X}|}}{\sqrt{N}}$. Finally, we devise a Natural Policy Gradient based algorithm that solves the MFC problem with $\mathcal{O}(\epsilon^{-3})$ sample complexity and obtains a policy that is within $\mathcal{O}(\max\{e,\epsilon\})$ error of the optimal MARL policy for any $\epsilon>0$.

This paper focuses on learning a Constrained Markov Decision Process (CMDP) via general parameterized policies. We propose a Primal-Dual based Regularized Accelerated Natural Policy Gradient (PDR-ANPG) algorithm that uses entropy and quadratic regularizers to reach this goal. For parameterized policy classes with a transferred compatibility approximation error, ε_bias, PDR-ANPG achieves a last-iterate ε optimality gap and ε constraint violation with a sample complexity of 𝒪̃(ε^-2min{ε^-2,ε_bias^-1/3}). If the class is incomplete (ε_bias>0), then the sample complexity reduces to 𝒪̃(ε^-2) for ε<(ε_bias)^1/6. Moreover, for complete policies with ε_bias=0, our algorithm achieves a last-iterate ε optimality gap and ε constraint violation with 𝒪̃(ε^-4) sample complexity. It is a significant improvement over the state-of-the-art last-iterate guarantees of general parameterized CMDPs.