Correlated Gaussian multi-objective multi-armed bandit across arms algorithm

Stochastic multi-objective multi-Armed bandit problem, (MOMAB), is a stochastic multi-Armed problem where each arm generates a vector of rewards instead of a single scalar reward. The goal of (MOMAB) is to minimize the regret of playing suboptimal arms while playing fairly the Pareto optimal arms. In this paper, we consider Gaussian correlation across arms in (MOMAB), meaning that the generated reward vector of an arm gives us information not only about that arm itself but also on all the available arms. We call this framework the correlated-MOMAB problem. We extended Gittins index policy to correlated (MOMAB) because Gittins index has been used before to model the correlation between arms. We empirically compared Gittins index policy with multi-objective upper confidence bound policy on a test suite of correlated-MOMAB problems. We conclude that the performance of these policies depend on the number of arms and objectives.</p

Annealing linear scalarized based multi-objective multi-armed bandit algorithm

A stochastic multi-objective multi-armed bandit problem is a particular type of multi-objective (MO) optimization problems where the goal is to find and play fairly the optimal arms. To solve the multi-objective optimization problem, we propose annealing linear scalarized algorithm that transforms the MO optimization problem into a single one by using a linear scalarization function, and finds and plays fairly the optimal arms by using a decaying parameter ϵt. We compare empirically linear scalarized-UCB1 algorithm with the annealing linear scalarized algorithm on a test suit of multi-objective multi-armed bandit problems with independent Bernoulli distributions using different approaches to define weight sets. We used the standard approach, the adaptive approach and the genetic approach. We conclude that the performance of the annealing scalarized and the scalarized UCB1 algorithms depend on the used weight approach