Jointly Efficient and Optimal Algorithms for Logistic Bandits

TL;DR

This paper introduces new algorithms for Logistic Bandits that are both statistically efficient, achieving near-optimal regret, and computationally efficient, with low per-round complexity, addressing a longstanding trade-off in the field.

Contribution

The authors propose a novel learning procedure that maintains confidence sets efficiently and combines it with planning methods to achieve both statistical and computational efficiency in Logistic Bandits.

Findings

Achieved exponential improvements in regret over previous strategies.

Developed algorithms with near-optimal problem-dependent regret bounds.

First to combine statistical and computational efficiency in Logistic Bandit algorithms.

Abstract

Logistic Bandits have recently undergone careful scrutiny by virtue of their combined theoretical and practical relevance. This research effort delivered statistically efficient algorithms, improving the regret of previous strategies by exponentially large factors. Such algorithms are however strikingly costly as they require $\Omega(t)$ operations at each round. On the other hand, a different line of research focused on computational efficiency ($\mathcal{O}(1)$ per-round cost), but at the cost of letting go of the aforementioned exponential improvements. Obtaining the best of both world is unfortunately not a matter of marrying both approaches. Instead we introduce a new learning procedure for Logistic Bandits. It yields confidence sets which sufficient statistics can be easily maintained online without sacrificing statistical tightness. Combined with efficient planning mechanisms we design fast algorithms which regret performance still match the problem-dependent lower-bound of Abeille et al. (2021). To the best of our knowledge, those are the first Logistic Bandit algorithms that simultaneously enjoy statistical and computational efficiency.