Present-Biased Optimization

TL;DR

This paper extends existing models of present-biased agents to analyze their behavior in various optimization tasks, providing bounds on their cost ratios and a comprehensive understanding of their decision-making patterns.

Contribution

It introduces a generalized framework for present-biased optimization, analyzing different scenarios and establishing bounds on cost ratios for various problem types.

Findings

Cost ratios vary significantly depending on problem constraints.

Extended analysis covers all combinations of cost underestimation/overestimation.

Provides upper bounds on cost ratios for multiple scenarios.

Abstract

This paper explores the behavior of present-biased agents, that is, agents who erroneously anticipate the costs of future actions compared to their real costs. Specifically, the paper extends the original framework proposed by Akerlof (1991) for studying various aspects of human behavior related to time-inconsistent planning, including procrastination, and abandonment, as well as the elegant graph-theoretic model encapsulating this framework recently proposed by Kleinberg and Oren (2014). The benefit of this extension is twofold. First, it enables to perform fine grained analysis of the behavior of present-biased agents depending on the optimisation task they have to perform. In particular, we study covering tasks vs. hitting tasks, and show that the ratio between the cost of the solutions computed by present-biased agents and the cost of the optimal solutions may differ significantly depending on the problem constraints. Second, our extension enables to study not only underestimation of future costs, coupled with minimization problems, but also all combinations of minimization/maximization, and underestimation/overestimation. We study the four scenarios, and we establish upper bounds on the cost ratio for three of them (the cost ratio for the original scenario was known to be unbounded), providing a complete global picture of the behavior of present-biased agents, as far as optimisation tasks are concerned.