Congested Bandits: Optimal Routing via Short-term Resets

TL;DR

This paper introduces the Congested Bandits problem, modeling congestion effects in routing as a bandit problem with rewards depending on recent actions, and proposes algorithms with provable regret bounds for both multi-armed and linear contextual settings.

Contribution

It formulates the Congested Bandits problem and develops UCB-style and least squares algorithms with theoretical regret guarantees for congestion-aware routing.

Findings

Regret scales as ( ilde{O}(\u221a{K    T})) in multi-armed case.

Regret scales as ( ilde{O}(  T) + ) in linear contextual case.

Simulation confirms no-regret performance of proposed algorithms.

Abstract

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 $\Delta$ 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 $\tilde{O}(\sqrt{K \Delta T})$. For the linear contextual bandit setup, our algorithm, based on an iterative least squares planner, achieves policy regret $\tilde{O}(\sqrt{dT} + \Delta)$. From an experimental standpoint, we corroborate the no-regret properties of our algorithms via a simulation study.