When DSA Meets SWIPT: A Joint Power Allocation and Time Splitting Scheme Based on Multi-Agent Deep Reinforcement Learning

Multiobjective Optimization of Space–Air–Ground-Integrated Network Slicing Relying on a Pair of Central and Distributed Learning Algorithms

“…APPENDIX A NON-DOMINANCE PROOF OF(42) Firstly, we assume that the four-tuple found by maximal r t 1 (χ * ) can be dominated by other four-tuples in the space of D 1 . By Definition 1 of Pareto optimal solutions in[52], there must be another solution of⟨ o j 1 ,a j i ,r j i ,o ′ j associated with r j d−s ≥ r * d−s , s = 1, 2, 3.In this way, the index χ j s by r j d−s must be higher than the index χ * s by r * d−s , and then the sum of the three agents' indices χ j must be higher than the sum of the three agents' indices χ * .However, we know that χ * is the maximum sum of indices. That is, there exists the contradiction between χ * and χ j , which indicates the assumption is false.…”