This paper proves an impossibility result for stochastic
network utility maximization for multi-user wireless systems,
including multi-access and broadcast systems. Every time slot an
access point observes the current channel states and opportunistically
selects a vector of transmission rates. Channel state vectors
are assumed to be independent and identically distributed with
an unknown probability distribution. The goal is to learn to make
decisions over time that maximize a concave utility function of
the running time average transmission rate of each user. Recently
it was shown that a stochastic Frank-Wolfe algorithm converges
to utility-optimality with an error of O(log(T)/T ), where T is
the time the algorithm has been running. An existing
O(1/T ) converse is known. The current paper improves the converse
to O(log(T)/T), which matches the known achievability result.
The proof uses a reduction from the opportunistic scheduling
problem to a Bernoulli estimation problem. Along the way, it
refines a result on Bernoulli estimation.
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This content will become publicly available on October 13, 2024
Network utility maximization with unknown utility functions: A distributed, data-driven bilevel optimization approach
Fair resource allocation is one of the most important topics in communication networks. Existing solutions almost exclusively assume each user utility function is known and concave. This paper seeks to answer the following question: how to allocate resources when utility functions are unknown, even to the users? This answer has become increasingly important in the next-generation AI-aware communication networks where the user utilities are complex and their closed-forms are hard to obtain. In this paper, we provide a new solution using a distributed and data-driven bilevel optimization approach, where the lower level is a distributed network utility maximization (NUM) algorithm with concave surrogate utility functions, and the upper level is a data-driven learning algorithm to find the best surrogate utility functions that maximize the sum of true network utility. The proposed algorithm learns from data samples (utility values or gradient values) to autotune the surrogate utility functions to maximize the true network utility, so works for unknown utility functions. For the general network, we establish the nonasymptotic convergence rate of the proposed algorithm with nonconcave utility functions. The simulations validate our theoretical results and demonstrate the great effectiveness of the proposed method in a real-world network.
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- Award ID(s):
- 2326592
- NSF-PAR ID:
- 10505577
- Publisher / Repository:
- International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing
- Date Published:
- Format(s):
- Medium: X
- Location:
- International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing
- Sponsoring Org:
- National Science Foundation
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