From Predictions to Decisions: The Importance of Joint Predictive Distributions

TL;DR

This paper emphasizes the importance of joint predictive distributions in decision-making tasks, demonstrating their critical role in combinatorial problems, sequential predictions, and multi-armed bandits, and introduces new algorithms and bounds.

Contribution

It highlights the necessity of joint predictions for decision quality and presents an approximate Thompson sampling algorithm with novel regret bounds.

Findings

Joint predictions improve decision performance in various problems.

The proposed algorithm achieves better regret bounds.

Joint distribution focus outperforms marginal prediction approaches.

Abstract

A fundamental challenge for any intelligent system is prediction: given some inputs, can you predict corresponding outcomes? Most work on supervised learning has focused on producing accurate marginal predictions for each input. However, we show that for a broad class of decision problems, accurate joint predictions are required to deliver good performance. In particular, we establish several results pertaining to combinatorial decision problems, sequential predictions, and multi-armed bandits to elucidate the essential role of joint predictive distributions. Our treatment of multi-armed bandits introduces an approximate Thompson sampling algorithm and analytic techniques that lead to a new kind of regret bound.