We present two Policy Gradient-based algorithms with general parametrization in the context of infinite-horizon average reward Markov Decision Process (MDP). The first one employs Implicit Gradient Transport for variance reduction, ensuring an expected regret of the order $\tilde{\mathcal{O}}(T^{2/3})$. 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 $\tilde{\mathcal{O}}(T^{3/4})$ regret and achieve the theoretical lower bound. We also show that the average-reward function is approximately $L$-smooth, a result that was previously assumed in earlier works.

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 $\tilde{\mathcal{O}}(1/\sqrt{T})$ 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.

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 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 addresses the challenge of achieving order-optimal sample complexity in reinforcement learning for discounted Markov Decision Processes (MDPs) with general policy parameterization and multi-layer neural network critics. Existing approaches either fail to achieve the optimal rate or assume a linear critic. We introduce 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 $\tilde{\mathcal{O}}(1/\epsilon^2)$, marking a significant improvement over the previous state-of-the-art guarantee of $\tilde{O}(1/\epsilon^3)$. 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.

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 explores the realm of infinite horizon average reward Constrained Markov Decision Processes (CMDPs). To the best of our knowledge, this work is the first to delve into the regret and constraint violation analysis of average reward CMDPs with a general policy parametrization. To address this challenge, we propose a primal dual-based policy gradient algorithm that adeptly manages the constraints while ensuring a low regret guarantee toward achieving a global optimal policy. In particular, our proposed algorithm achieves $\tilde{\mathcal{O}}({T}^{4/5})$ objective regret and $\tilde{\mathcal{O}}({T}^{4/5})$ constraint violation bounds.

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 $\epsilon^{-1}$.

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 $\mathcal{O}(e^{-6})$.

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.

Mean-Field Control (MFC) is a powerful tool to solve Multi-Agent Reinforcement Learning (MARL) problems. Recent studies have shown that MFC can well-approximate MARL when the population size is large and the agents are exchangeable. Unfortunately, the presumption of exchangeability implies that all agents uniformly interact with one another which is not true in many practical scenarios. In this article, we relax the assumption of exchangeability and model the interaction between agents via an arbitrary doubly stochastic matrix. As a result, in our framework, the mean-field ‘seen’ by different agents are different. We prove that, if the reward of each agent is an affine function of the mean-field seen by that agent, then one can approximate such a non-uniform MARL problem via its associated MFC problem within an error of $e=\mathcal{O}(\frac{1}{\sqrt{N}}[\sqrt{|\mathcal{X}|} + \sqrt{|\mathcal{U}|}])$ where $N$ is the population size and $|\mathcal{X}|$, $|\mathcal{U}|$ are the sizes of state and action spaces respectively. Finally, we develop a Natural Policy Gradient (NPG) algorithm that can provide a solution to the non-uniform MARL with an error $\mathcal{O}(\max\{e,\epsilon\})$ and a sample complexity of $\mathcal{O}(\epsilon^{-3})$ for any $\epsilon >0$.

Mean field control (MFC) is an effective way to mitigate the curse of dimensionality of cooperative multi-agent reinforcement learning (MARL) problems. This work considers a collection of $N_{\mathrm{pop}}$ heterogeneous agents that can be segregated into $K$ classes such that the $k$-th class contains $N_k$ homogeneous agents. We aim to prove approximation guarantees of the MARL problem for this heterogeneous system by its corresponding MFC problem. We consider three scenarios where the reward and transition dynamics of all agents are respectively taken to be functions of $(1)$ joint state and action distributions across all classes, $(2)$ individual distributions of each class, and $(3)$ marginal distributions of the entire population. We show that, in these cases, the $K$-class MARL problem can be approximated by MFC with errors given as $e_1=\mathcal{O}(\frac{\sqrt{|\mathcal{X}|}+\sqrt{|\mathcal{U}|}}{N_{\mathrm{pop}}}\sum_{k}\sqrt{N_k})$, $e_2=\mathcal{O}(\left[\sqrt{|\mathcal{X}|}+\sqrt{|\mathcal{U}|}\right]\sum_{k}\frac{1}{\sqrt{N_k}})$ and $e_3=\mathcal{O}\left(\left[\sqrt{|\mathcal{X}|}+\sqrt{|\mathcal{U}|}\right]\left[\frac{A}{N_{\mathrm{pop}}}\sum_{k\in[K]}\sqrt{N_k}+\frac{B}{\sqrt{N_{\mathrm{pop}}}}\right]\right)$, respectively, where $A, B$ are some constants and $|\mathcal{X}|,|\mathcal{U}|$ are the sizes of state and action spaces of each agent. Finally, we design a Natural Policy Gradient (NPG) based algorithm that, in the three cases stated above, can converge to an optimal MARL policy within $\mathcal{O}(e_j)$ error with a sample complexity of $\mathcal{O}(e_j^{-3})$, $j\in\{1,2,3\}$, respectively.

We analyze a Cognitive Radio-based Internet-of-Things (CR-IoT) network employing Microwave Power Transfer (MPT) method for energy-harvesting, targeted for smart city applications. In our model, multiple IoT sensors, operated by an IoT operator, coexist with a Primary Network Provider (PNP), where the IoT sensors opportunistically exploit the spectrum holes in the PNP’s licensed band. We develop an Imbedded Markov Chain based approach to analyze this system. During PNP’s inactivity periods, the Accesss Points (APs) under the IoT operator have to judiciously use PNP’s licensed band for data collection from the IoT sensors and charging them via the MPT method. Our analysis finds the balance between these activities while maintaining the Quality-of-Service and preventing energy deficit in the IoT sensors. We characterize PNP’s activity using any distribution, rather than exponential distribution used in literature, making our framework more accurate. We also consider the possibility of interruptions in the IoT operator’s activity due to PNP’s transmission, which has been overlooked in the literature. Extensive simulations demonstrate the accuracy of our analysis. Our analysis can identify the values of system parameters that makes the system sustainable. We have also shown how to extend our model to accommodate multiple PNPs in the same CR-IoT network.

In this paper, we consider an opportunistic cognitive radio (CR) network comprising of a primary base station (PBS) and a secondary base station (SBS), both associated with multiple users. SBS obtains the right to use the licensed spectrum of PBS by paying a remuneration. Moreover, both PBS and SBS provide service to their corresponding users in exchange of an economic price. PBS, being a profit maximizer, optimally balances between the revenue directly coming from its own users and the monetary reward provided by SBS. On the other hand, SBS must maintain a positive gain to support its infrastructure. Thus, a two-person non-cooperative bargaining game is formulated where both PBS and SBS concur at the values of two parameters, i.e., the activity factor of PBS and the payment made by SBS for opportunistically accessing the licensed spectrum. PBS has knowledge of detection and false-alarm probabilities of the spectrum sensing by SBS and hence can infer how the interference created by missed detection can degrade its achievable capacity. In this framework, we utilize Nash solution to determine a mutually beneficial outcome of the bargaining process. The solution leads to a mathematical relation dictating the viability of the network in the long-run. This result holds for arbitrary continuous user demand functions. For linear user demand, we obtain closed-form expression of the bargaining solution that enables us to analyze the influence of different key system parameters on the economic outcomes.

Encouraging new service providers to participate in the competition is one of the key ways to enhance users' utility in cellular networks. However, entry-deterrence strategy employed by the incumbents turns out to be a major obstacle in achieving this goal. Fortunately, we have recently demonstrated that the government, in its capacity as the sole provider of bandwidth, can resist such predatory behaviour by choosing suitable quadratic pricings for spectrum leasing. However, this result was premised on the presumption that both entrant and incumbent deploy base stations with same density. Moreover, their operational costs were also taken to be same. Evidently, such assumptions do not align with the reality. In this article, we investigate predation blocking strategies in real cellular networks where the above presumptions might not hold true. This generalization reveals several insightful results. For example, it shows that the government cannot block predation if the entrant's base station density is below a certain threshold. Alongside, we have also examined how these predation blocking strategies influence the spectrum revenue earned by the government. Numerical results suggest that blocking of predation is likely to degrade the government's revenue for a large number of network scenario. Finally, we study how the network economics evolves with time if the predation blocking strategies are applied repeatedly. Interestingly, we observe that after a sufficiently large number of repetitions, the incumbent eventually loses an incentive to exhibit the predatory behavior.