From Predictions to Decisions: The Importance of Joint Predictive Distributions
This addresses a fundamental challenge in machine learning for decision-making systems, though it appears incremental in extending existing methods to joint predictions.
The paper tackles the problem of prediction in intelligent systems, showing that accurate joint predictive distributions are essential for good performance in combinatorial decision problems, sequential predictions, and multi-armed bandits, with results including a new approximate Thompson sampling algorithm and regret bound.
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.