Non-orthogonal multiple access (NOMA) is a key technology to enable massive machine type communications (mMTC) in 5G networks and beyond. In this paper, NOMA is applied to improve the random access efficiency in high-density spatially-distributed multi-cell wireless IoT networks, where IoT devices contend for accessing the shared wireless channel using an adaptive p-persistent slotted Aloha protocol. To enable a capacity-optimal network, a novel formulation of random channel access with NOMA is proposed, in which the transmission probability of each IoT device is tuned to maximize the geometric mean of users' expected capacity. It is shown that the network optimization objective is high dimensional and mathematically intractable, yet it admits favourable mathematical properties that enable the design of efficient learning-based algorithmic solutions. To this end, two algorithms, i.e., a centralized model-based algorithm and a scalable distributed model-free algorithm, are proposed to optimally tune the transmission probabilities of IoT devices to attain the maximum capacity. The convergence of the proposed algorithms to the optimal solution is further established based on convex optimization and game-theoretic analysis. Extensive simulations demonstrate the merits of the novel formulation and the efficacy of the proposed algorithms.

The canonical solution methodology for finite constrained Markov decision processes (CMDPs), where the objective is to maximize the expected infinite-horizon discounted rewards subject to the expected infinite-horizon discounted costs constraints, is based on convex linear programming. In this brief, we first prove that the optimization objective in the dual linear program of a finite CMDP is a piece-wise linear convex function (PWLC) with respect to the Lagrange penalty multipliers. Next, we propose a novel two-level Gradient-Aware Search (GAS) algorithm which exploits the PWLC structure to find the optimal state-value function and Lagrange penalty multipliers of a finite CMDP. The proposed algorithm is applied in two stochastic control problems with constraints: robot navigation in a grid world and solar-powered unmanned aerial vehicle (UAV)-based wireless network management. We empirically compare the convergence performance of the proposed GAS algorithm with binary search (BS), Lagrangian primal-dual optimization (PDO), and Linear Programming (LP). Compared with benchmark algorithms, it is shown that the proposed GAS algorithm converges to the optimal solution faster, does not require hyper-parameter tuning, and is not sensitive to initialization of the Lagrange penalty multiplier.