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Exponentially Weighted Algorithm for Online Network Resource Allocation with Long-Term Constraints

Ahmed Sid-Ali, Ioannis Lambadaris, Yiqiang Q. Zhao, Gennady Shaikhet, Amirhossein Asgharnia

TL;DR

This work tackles online resource reservation across a network of servers with possible inter-server transfers under a long-term constraint on combined violation and transfer costs. It introduces a randomized exponentially weighted algorithm that operates on the discrete reservation space, incorporating a history-based penalty to enforce time-averaged constraints and achieving sublinear regret with vanishing constraint violations. The approach is theoretically analyzed to yield explicit regret and constraint-violation bounds and is empirically compared against a tailored reinforcement learning baseline, where the proposed method generally outperforms RL in dynamic-demand scenarios. The results demonstrate the practical viability of history-aware, constraint-aware online optimization for network resource management, with potential for broader application in similar discrete-action, long-horizon constrained problems.

Abstract

This paper studies an online optimal resource reservation problem in communication networks with job transfers where the goal is to minimize the reservation cost while maintaining the blocking cost under a certain budget limit. To tackle this problem, we propose a novel algorithm based on a randomized exponentially weighted method that encompasses long-term constraints. We then analyze the performance of our algorithm by establishing an upper bound for the associated regret and the cumulative constraint violations. Finally, we present numerical experiments where we compare the performance of our algorithm with those of reinforcement learning where we show that our algorithm surpasses it.

Exponentially Weighted Algorithm for Online Network Resource Allocation with Long-Term Constraints

TL;DR

This work tackles online resource reservation across a network of servers with possible inter-server transfers under a long-term constraint on combined violation and transfer costs. It introduces a randomized exponentially weighted algorithm that operates on the discrete reservation space, incorporating a history-based penalty to enforce time-averaged constraints and achieving sublinear regret with vanishing constraint violations. The approach is theoretically analyzed to yield explicit regret and constraint-violation bounds and is empirically compared against a tailored reinforcement learning baseline, where the proposed method generally outperforms RL in dynamic-demand scenarios. The results demonstrate the practical viability of history-aware, constraint-aware online optimization for network resource management, with potential for broader application in similar discrete-action, long-horizon constrained problems.

Abstract

This paper studies an online optimal resource reservation problem in communication networks with job transfers where the goal is to minimize the reservation cost while maintaining the blocking cost under a certain budget limit. To tackle this problem, we propose a novel algorithm based on a randomized exponentially weighted method that encompasses long-term constraints. We then analyze the performance of our algorithm by establishing an upper bound for the associated regret and the cumulative constraint violations. Finally, we present numerical experiments where we compare the performance of our algorithm with those of reinforcement learning where we show that our algorithm surpasses it.
Paper Structure (13 sections, 2 theorems, 32 equations, 5 figures, 1 table, 2 algorithms)

This paper contains 13 sections, 2 theorems, 32 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Online resource reservation in communication networks
  3. Online randomized reservations
  4. Exponentially weighted algorithm with long-time constraints
  5. Performance analysis
  6. Regret bound
  7. Violation constraint bound
  8. Numerical experiments and comparison with reinforcement learning
  9. Reinforcement learning algorithm
  10. Piecewise-Fixed Requests
  11. Randomly generated requests
  12. Conclusion
  13. Appendix

Key Result

Theorem 5.1

For any $0<\delta<1$, the regret related to Algorithm sad-algo satisfies, with a probability at least $1-\delta$, where $\kappa=\frac{\eta}{8} (1+2 \lambda)^2\Theta^2$. In particular, if $\eta=\frac{1}{\sqrt{T}}$, then $R_T=\mathcal{O}(\sqrt{T})$ (sublinear in $T$).

Figures (5)

  • Figure 1: (a) The network model for three nodes at time $t$. (b) The reservation, job requests, and cost calculation timeline.
  • Figure 2: (a) The input request to each node. (b) The average regret of both methods. (b) The Euclidean distance between two consecutive probability distributions produced by Algorithm \ref{['sad-algo']}. (c) Reservation cost ($C(A^t)$) for each time slot $t$. (d) The blocking cost ($C_0(A^t,B^t)$)
  • Figure 3: (a) The input request to node 1. The rest inputs are analogous. (b) The average regret of both methods. (b) The Euclidean distance between two consecutive probability distributions produced by Algorithm \ref{['sad-algo']}. (c) Reservation cost ($C(A^t)$) for each time slot $t$. (d) The blocking cost ($C_0(A^t,B^t)$)
  • Figure 4: (a) The regret of both methods. (b) The Euclidean distance between two consecutive probability distributions produced by Algorithm \ref{['sad-algo']}, (c) the corresponding reservation const ($E[C(A^t,B^t)]$), and (d) the blocking cost ($E[C_0(A^t,B^t)]$)
  • Figure 5: (a) The regret of both methods. (b) The Euclidean distance between two consecutive probability distributions produced by Algorithm \ref{['sad-algo']}, (c) the corresponding reservation const ($E[C(A^t,B^t)]$), and (d) the blocking cost ($E[C_0(A^t,B^t)]$)

Theorems & Definitions (3)

  • Remark 1
  • Theorem 5.1
  • Theorem 5.2