Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits

Motivated by applications in energy management, this paper presents the Multi-Armed Risk-Aware Bandit (MARAB) algorithm. With the goal of limiting the exploration of risky arms, MARAB takes as arm quality its conditional value at risk. When the user-supplied risk level goes to 0, the arm quality tends toward the essential infimum of the arm distribution density, and MARAB tends toward the MIN multi-armed bandit algorithm, aimed at the arm with maximal minimal value. As a first contribution, this paper presents a theoretical analysis of the MIN algorithm under mild assumptions, establishing its robustness comparatively to UCB. The analysis is supported by extensive experimental validation of MIN and MARAB compared to UCB and state-of-art risk-aware MAB algorithms on artificial and real-world problems.Comment: 16 page

Lifelong Bandit Optimization: No Prior and No Regret

In practical applications, machine learning algorithms are often repeatedly applied to problems with similar structure over and over again. We focus on solving a sequence of bandit optimization tasks and develop LiBO, an algorithm which adapts to the environment by learning from past experience and becoming more sample-efficient in the process. We assume a kernelized structure where the kernel is unknown but shared across all tasks. LiBO sequentially meta-learns a kernel that approximates the true kernel and simultaneously solves the incoming tasks with the latest kernel estimate. Our algorithm can be paired with any kernelized bandit algorithm and guarantees oracle optimal performance, meaning that as more tasks are solved, the regret of LiBO on each task converges to the regret of the bandit algorithm with oracle knowledge of the true kernel. Naturally, if paired with a sublinear bandit algorithm, LiBO yields a sublinear lifelong regret. We also show that direct access to the data from each task is not necessary for attaining sublinear regret. The lifelong problem can thus be solved in a federated manner, while keeping the data of each task private.Comment: 32 pages, 6 figures, preprin