783 research outputs found
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
Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization
In this paper, we consider the problem of sequentially optimizing a black-box
function based on noisy samples and bandit feedback. We assume that is
smooth in the sense of having a bounded norm in some reproducing kernel Hilbert
space (RKHS), yielding a commonly-considered non-Bayesian form of Gaussian
process bandit optimization. We provide algorithm-independent lower bounds on
the simple regret, measuring the suboptimality of a single point reported after
rounds, and on the cumulative regret, measuring the sum of regrets over the
chosen points. For the isotropic squared-exponential kernel in
dimensions, we find that an average simple regret of requires , and the
average cumulative regret is at least , thus matching existing upper bounds up to the replacement of by
in both cases. For the Mat\'ern- kernel, we give analogous
bounds of the form and
, and discuss the resulting
gaps to the existing upper bounds.Comment: Appearing in COLT 2017. This version corrects a few minor mistakes in
Table I, which summarizes the new and existing regret bound
- …