A Deep Unfolding-Based Scalarization Approach for Power Control in D2D Networks

TL;DR

This paper proposes a scalarization approach to transform the weighted-sum-rate, developing an iterative algorithm that depends on step sizes, a reference, and a direction vector, and optimize these parameters by presenting the iterative algorithm as a finite sequence of steps, enabling it to be trained as a deep neural network.

Abstract

Optimizing network utility in device-to-device networks is typically formulated as a non-convex optimization problem. This paper addresses the scenario where the optimization variables are from a bounded but continuous set, allowing each device to perform power control. The power at each link is optimized to maximize a desired network utility. Specifically, we consider the weighted-sum-rate. The state of the art benchmark for this problem is fractional programming with quadratic transform, known as FPLinQ. We propose a scalarization approach to transform the weighted-sum-rate, developing an iterative algorithm that depends on step sizes, a reference, and a direction vector. By employing the deep unfolding approach, we optimize these parameters by presenting the iterative algorithm as a finite sequence of steps, enabling it to be trained as a deep neural network. Numerical experiments demonstrate that the unfolded algorithm performs comparably to the benchmark in most cases while exhibiting lower complexity. Furthermore, the unfolded algorithm shows strong generalizability in terms of varying the number of users, the signal-to-noise ratio and arbitrary weights. The weighted-sum-rate maximizer can be integrated into a low-complexity fairness scheduler, updating priority weights via virtual queues and Lyapunov Drift Plus Penalty. This is demonstrated through experiments using proportional and max-min fairness.

Figures (9)

• Figure 1: Example of a D2D network with $K = 4$ Links.
• Figure 2: Vector optimization: a) definition of a $\mathcal{K}$-optimal point with $\mathcal{K}=\mathbb{R}_+^2$ and b) an example of moving a weighted cone along $\mathbf{a}+\mathbf{r}$.
• Figure 3: Example for Pascoletti and Serafini scalarization, with $\bf a,r$ based on the Utopian point, for weighted cone $\mathcal{K}_{\bf w}$. Here for $K=2$.
• Figure 4: Impact of normalization and enforcing constraints on $\lambda$, by testing the algorithm on the same network, with different step-sizes: a) The primal-dual algorithm, without normalization and projection of $\lambda$. b) primal-dual algorithm with discussed normalization and projection. It can be observed that in a) a slight change in step-size already leads to oscillation, while in b) this is not the case.
• Figure 5: Training history for LUVA with $N=10$ for $n_\text{train} = \lbrace 50, 100, 500\rbrace$ of the (fixed) testing dataset, with $500$ samples, for $K = 10$. The observed jumps come from going one layer to another, thus we see this staircase behaviour.