This paper considers the fundamental convergence time for opportunistic scheduling over time-varying channels. The channel state probabilities are unknown and algorithms must perform some type of estimation and learning while they make decisions to optimize network utility. Existing schemes can achieve a utility within ε of optimality, for any desired ε > 0, with convergence and adaptation times of O(1/ε^2). This paper shows that if the utility function is concave and smooth, then O(log(1/ε)/ε) convergence time is possible via an existing stochastic variation on the Frank-Wolfe algorithm, called the RUN algorithm. Next, a converse result is proven to show it is impossible for any algorithm to have convergence time better than O(1/ε), provided the algorithm has no a- priori knowledge of channel state probabilities. Hence, RUN is within a logarithmic factor of convergence time optimality. However, RUN has a vanishing stepsize and hence has an infinite adaptation time. Using stochastic Frank-Wolfe with a fixed step- size yields improved O(1/ε^2) adaptation time, but convergence time increases to O(1/ε^2), similar to existing drift-plus-penalty based algorithms. This raises important open questions regarding optimal adaptation.
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Optimal Convergence and Adaptation for Utility Optimal Opportunistic Scheduling
This paper considers the fundamental convergence time for opportunistic scheduling over time-varying channels. The channel state probabilities are unknown and algorithms must perform some type of estimation and learning while they make decisions to optimize network utility. Existing schemes can achieve a utility within ε of optimality, for any desired ε > 0, with convergence and adaptation times of O(1/ε^2). This paper shows that if the utility function is concave and smooth, then O(log(1/ε)/ε) convergence time is possible via an existing stochastic variation on the Frank-Wolfe algorithm, called the RUN algorithm. Next, a converse result is proven to show it is impossible for any algorithm to have convergence time better than O(1/ε), provided the algorithm has no a- priori knowledge of channel state probabilities. Hence, RUN is within a logarithmic factor of convergence time optimality. However, RUN has a vanishing stepsize and hence has an infinite adaptation time. Using stochastic Frank-Wolfe with a fixed step- size yields improved O(1/ε^2) adaptation time, but convergence time increases to O(1/ε^2), similar to existing drift-plus-penalty based algorithms. This raises important open questions regarding optimal adaptation.
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- Award ID(s):
- 1718477
- NSF-PAR ID:
- 10074986
- Date Published:
- Journal Name:
- Proc. Allerton Conference on Communication, Control, and Computing
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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