This paper investigates the Restless Multi-Armed Bandit (RMAB) framework under individual penalty constraints to address resource allocation challenges in dynamic wireless networked environments. Unlike conventional RMAB models, our model allows each user (arm) to have distinct and stringent performance constraints, such as energy limits, activation limits, or age of information minimums, enabling the capture of diverse objectives including fairness and efficiency. To find the optimal resource allocation policy, we propose a new Penalty-Optimal Whittle (POW) index policy. The POW index of an user only depends on the user's transition kernel and penalty constraints, and remains invariable to system-wide features such as the number of users present and the amount of resource available. This makes it computationally tractable to calculate the POW indices offline without any need for online adaptation. Moreover, we theoretically prove that the POW index policy is asymptotically optimal while satisfying all individual penalty constraints. We also introduce a deep reinforcement learning algorithm to efficiently learn the POW index on the fly. Simulation results across various applications and system configurations further demonstrate that the POW index policy not only has near-optimal performance but also significantly outperforms other existing policies.
Figures & tables
Figure 1. Average reward and average constraint violation for throughput maximization with activation constraints.
Figure 2. Comparison of learning policies for throughput maximization with activation constraints.
Figure 3. Average reward and average constraint violation for remote sensing.
Figure 4. Comparison of learning policies for remote sensing.
Figure 5. Average reward and average constraint violation for throughput maximization with service regularity.
Figure 6. Comparison of learning policies for throughput maximization with service regularity.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
TP w/ Activation Constraint
(N,C)
θ0
θ1
δ
(4,1)
[.3,.5,.7,.9]
4×[.02]
[.35,.35,.05,.05]
(6,1)
[.3,.4,…,.9]
6×[.02]
[.2,.2,.1,.1,.05,.05]
Remote Sensing
(N,C)
p
B
(4,1)
[.2,.4,.6,.8]
[.9,.9,.1,.1]
Appendix
Table 1. Parameter settings for all three simulation scenarios.