Making the most of your day: online learning for optimal allocation of time

TL;DR

This paper investigates online learning strategies for optimal time allocation in sequential task acceptance scenarios, analyzing regret bounds under different knowledge assumptions about rewards and task durations.

Contribution

It introduces a novel framework for online time allocation learning, addressing unknown reward functions and task duration distributions, with theoretical regret analysis.

Findings

Derived regret bounds for known reward functions

Analyzed regret when reward functions are unknown

Identified key differences from standard bandit problems

Abstract

We study online learning for optimal allocation when the resource to be allocated is time. %Examples of possible applications include job scheduling for a computing server, a driver filling a day with rides, a landlord renting an estate, etc. An agent receives task proposals sequentially according to a Poisson process and can either accept or reject a proposed task. If she accepts the proposal, she is busy for the duration of the task and obtains a reward that depends on the task duration. If she rejects it, she remains on hold until a new task proposal arrives. We study the regret incurred by the agent, first when she knows her reward function but does not know the distribution of the task duration, and then when she does not know her reward function, either. This natural setting bears similarities with contextual (one-armed) bandits, but with the crucial difference that the normalized reward associated to a context depends on the whole distribution of contexts.