New Algorithm Achieves Optimal Queue Length Regret in Contextual Queueing Bandits
Researchers have developed CQB-η-2, a three-phase algorithm for scheduling heterogeneous jobs under unknown service rates, improving the queue length regret rate from Õ(T^{-1/4}) to Õ(T^{-1/2}). The key insight is that random exploration is only necessary up to a carefully chosen cutoff round, rather than throughout the entire learning horizon. The work also proves a matching minimax lower bound of Ω(T^{-1/2}), establishing that this rate is optimal up to logarithmic factors.
The paper addresses contextual queueing bandits, a framework for learning to schedule heterogeneous jobs when context-dependent service rates are unknown. Prior algorithms under stochastic contexts achieved a queue length regret rate of Õ(T^{-1/4}), measured as the expected difference between the learner's and an oracle's queue lengths at horizon T. The proposed algorithm, CQB-η-2, operates in three phases: pure random exploration to build an initial estimator, η-random exploration combined with an upper confidence bound (UCB) rule to continue learning while maintaining negative drift, and finally pure UCB after a carefully chosen exploration cutoff. The regret analysis decomposes the queue length at the cutoff: before it, negative drift suppresses queue length differences from suboptimal decisions; after it, sufficient exploration samples ensure UCB choices incur small departure-rate gaps. Together these yield the improved Õ(T^{-1/2}) upper bound. A minimax lower bound of Ω(T^{-1/2}) is also established via a coupling argument on two hard, statistically indistinguishable problem instances, confirming the rate is tight up to logarithmic factors.
What's missing
The paper does not discuss empirical or simulation-based validation of CQB-η-2; all results are theoretical. Open questions include how the algorithm performs in non-stochastic or adversarial context settings and how sensitive the cutoff round selection is to problem parameters in practice.
What different sources said
- arXiv cs.LGCenter
Algorithm for Contextual Queueing Bandits with Rate-Optimal Queue Length Regret
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