Multi-Objective Generalized Linear Bandits

TL;DR

This paper introduces a novel algorithm for multi-objective generalized linear bandits that leverages contextual information and achieves near-optimal Pareto regret bounds, with promising empirical results.

Contribution

It develops a new algorithm combining online Newton step and UCB for multi-objective GLM bandits with context, achieving optimal Pareto regret bounds.

Findings

Achieves $ ilde O(d oot T)$ Pareto regret bound.

Effectively utilizes contextual information in multi-objective bandits.

Demonstrates strong empirical performance.

Abstract

In this paper, we study the multi-objective bandits (MOB) problem, where a learner repeatedly selects one arm to play and then receives a reward vector consisting of multiple objectives. MOB has found many real-world applications as varied as online recommendation and network routing. On the other hand, these applications typically contain contextual information that can guide the learning process which, however, is ignored by most of existing work. To utilize this information, we associate each arm with a context vector and assume the reward follows the generalized linear model (GLM). We adopt the notion of Pareto regret to evaluate the learner's performance and develop a novel algorithm for minimizing it. The essential idea is to apply a variant of the online Newton step to estimate model parameters, based on which we utilize the upper confidence bound (UCB) policy to construct an approximation of the Pareto front, and then uniformly at random choose one arm from the approximate Pareto front. Theoretical analysis shows that the proposed algorithm achieves an $\tilde O(d\sqrt{T})$ Pareto regret, where $T$ is the time horizon and $d$ is the dimension of contexts, which matches the optimal result for single objective contextual bandits problem. Numerical experiments demonstrate the effectiveness of our method.