Multi-Objective Generalized Linear Bandits
This addresses the need for contextual multi-objective decision-making in applications like online recommendation, though it is incremental by extending existing bandit methods.
The paper tackles the multi-objective bandits problem by incorporating contextual information via a generalized linear model, achieving an $ ilde O(d\sqrt{T})$ Pareto regret that matches optimal single-objective bounds.
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.