2,449 research outputs found
Satisficing in multi-armed bandit problems
Satisficing is a relaxation of maximizing and allows for less risky decision
making in the face of uncertainty. We propose two sets of satisficing
objectives for the multi-armed bandit problem, where the objective is to
achieve reward-based decision-making performance above a given threshold. We
show that these new problems are equivalent to various standard multi-armed
bandit problems with maximizing objectives and use the equivalence to find
bounds on performance. The different objectives can result in qualitatively
different behavior; for example, agents explore their options continually in
one case and only a finite number of times in another. For the case of Gaussian
rewards we show an additional equivalence between the two sets of satisficing
objectives that allows algorithms developed for one set to be applied to the
other. We then develop variants of the Upper Credible Limit (UCL) algorithm
that solve the problems with satisficing objectives and show that these
modified UCL algorithms achieve efficient satisficing performance.Comment: To appear in IEEE Transactions on Automatic Contro
Functional Bandits
We introduce the functional bandit problem, where the objective is to find an
arm that optimises a known functional of the unknown arm-reward distributions.
These problems arise in many settings such as maximum entropy methods in
natural language processing, and risk-averse decision-making, but current
best-arm identification techniques fail in these domains. We propose a new
approach, that combines functional estimation and arm elimination, to tackle
this problem. This method achieves provably efficient performance guarantees.
In addition, we illustrate this method on a number of important functionals in
risk management and information theory, and refine our generic theoretical
results in those cases
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
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