Log In Sign Up

Improved Optimistic Algorithms for Logistic Bandits

by   Louis Faury, et al.

The generalized linear bandit framework has attracted a lot of attention in recent years by extending the well-understood linear setting and allowing to model richer reward structures. It notably covers the logistic model, widely used when rewards are binary. For logistic bandits, the frequentist regret guarantees of existing algorithms are Õ(κ√(T)), where κ is a problem-dependent constant. Unfortunately, κ can be arbitrarily large as it scales exponentially with the size of the decision set. This may lead to significantly loose regret bounds and poor empirical performance. In this work, we study the logistic bandit with a focus on the prohibitive dependencies introduced by κ. We propose a new optimistic algorithm based on a finer examination of the non-linearities of the reward function. We show that it enjoys a Õ(√(T)) regret with no dependency in κ, but for a second order term. Our analysis is based on a new tail-inequality for self-normalized martingales, of independent interest.


page 1

page 2

page 3

page 4


An Experimental Design Approach for Regret Minimization in Logistic Bandits

In this work we consider the problem of regret minimization for logistic...

Improved Optimistic Algorithm For The Multinomial Logit Contextual Bandit

We consider a dynamic assortment selection problem where the goal is to ...

UCB-based Algorithms for Multinomial Logistic Regression Bandits

Out of the rich family of generalized linear bandits, perhaps the most w...

Improved Confidence Bounds for the Linear Logistic Model and Applications to Linear Bandits

We propose improved fixed-design confidence bounds for the linear logist...

Bandit Learning with General Function Classes: Heteroscedastic Noise and Variance-dependent Regret Bounds

We consider learning a stochastic bandit model, where the reward functio...

Dual Instrumental Method for Confounded Kernelized Bandits

The contextual bandit problem is a theoretically justified framework wit...

Jointly Efficient and Optimal Algorithms for Logistic Bandits

Logistic Bandits have recently undergone careful scrutiny by virtue of t...