Learning Time Dependent Choice

TL;DR

This paper investigates the learnability of time-dependent choice models, especially discounted utility models, demonstrating significant improvements in learning bounds and exploring active learning scenarios.

Contribution

It introduces a structural criterion for preference models that yields exponential improvements in learning bounds and analyzes the learnability of key intertemporal choice models in various settings.

Findings

Discounted utility models are PAC-learnable with logarithmic VC dimension.

Active learning can outperform PAC learning under certain data access conditions.

Naive algorithms with membership queries outperform complex active learning algorithms.

Abstract

We explore questions dealing with the learnability of models of choice over time. We present a large class of preference models defined by a structural criterion for which we are able to obtain an exponential improvement over previously known learning bounds for more general preference models. This in particular implies that the three most important discounted utility models of intertemporal choice -- exponential, hyperbolic, and quasi-hyperbolic discounting -- are learnable in the PAC setting with VC dimension that grows logarithmically in the number of time periods. We also examine these models in the framework of active learning. We find that the commonly studied stream-based setting is in general difficult to analyze for preference models, but we provide a redeeming situation in which the learner can indeed improve upon the guarantees provided by PAC learning. In contrast to the stream-based setting, we show that if the learner is given full power over the data he learns from -- in the form of learning via membership queries -- even very naive algorithms significantly outperform the guarantees provided by higher level active learning algorithms.