Automatic Link Selection in Multi-Channel Multiple Access with Link Failures

TL;DR

This paper introduces adaptive algorithms for optimal link selection in multi-channel access systems with unknown failure probabilities, achieving fast convergence and practical implementation, validated through simulations.

Contribution

It proposes two new adaptive algorithms with different convergence rates for link selection under bandit feedback, balancing computational complexity and performance.

Findings

Fast convergence algorithms with $ ilde{O}(1/\sqrt{T})$ and $\tilde{O}(1/\sqrt[3]{T})$ rates.

Efficient implementation for single-channel scenarios.

Simulation results showing rapid adaptation and performance trade-offs.

Abstract

This paper focuses on the problem of automatic link selection in multi-channel multiple access control using bandit feedback. In particular, a controller assigns multiple users to multiple channels in a time-slotted system, where in each time slot, at most one user can be assigned to a given channel, and at most one channel can be assigned to a given user. Given that user $i$ is assigned to channel $j$, the transmission fails with a fixed unknown probability $1-q_{i,j}$. The assignments are made dynamically using success/failure feedback. The goal is to maximize the time-average utility, where we consider an arbitrary (possibly nonsmooth) concave, entrywise nondecreasing utility function. The first proposed algorithm has fast $\mathcal{O}(\sqrt{\log(T)/T})$ convergence. However, this algorithm requires solving a convex optimization problem within each iteration, which can be computationally expensive. The second algorithm has slower $\mathcal{O}(\sqrt[3]{\log(T)/T})$ convergence, while avoiding the costly inner optimization. Both of these algorithms are adaptive. In particular, the convergence guarantee holds for any interval of $T$ consecutive slots during which the success probabilities do not change. We further study several special cases. In the single-channel setting, we obtain both fast $\mathcal{O}(\sqrt{\log(T)/T})$ convergence and efficient implementation via a simpler adaptive mechanism. We also consider a UCB-based non-adaptive algorithm with max-weight-type decisions. Simulations highlight intriguing performance trade-offs and demonstrate rapid adaptation of the proposed adaptive schemes.