Congested Bandits: Optimal Routing via Short-term Resets
This addresses routing optimization for traffic platforms by modeling congestion effects, though it is incremental as it extends existing bandit frameworks to include short-term dependencies.
The authors tackled the problem of routing recommendations in congested traffic by introducing Congested Bandits, where rewards depend on past actions, and developed algorithms achieving policy regret bounds of $ ilde{O}(\sqrt{K \Delta T})$ for multi-armed bandits and $ ilde{O}(\sqrt{dT} + \Delta)$ for contextual bandits.
For traffic routing platforms, the choice of which route to recommend to a user depends on the congestion on these routes -- indeed, an individual's utility depends on the number of people using the recommended route at that instance. Motivated by this, we introduce the problem of Congested Bandits where each arm's reward is allowed to depend on the number of times it was played in the past $Δ$ timesteps. This dependence on past history of actions leads to a dynamical system where an algorithm's present choices also affect its future pay-offs, and requires an algorithm to plan for this. We study the congestion aware formulation in the multi-armed bandit (MAB) setup and in the contextual bandit setup with linear rewards. For the multi-armed setup, we propose a UCB style algorithm and show that its policy regret scales as $\tilde{O}(\sqrt{K ΔT})$. For the linear contextual bandit setup, our algorithm, based on an iterative least squares planner, achieves policy regret $\tilde{O}(\sqrt{dT} + Δ)$. From an experimental standpoint, we corroborate the no-regret properties of our algorithms via a simulation study.