Risk-Aversion in Multi-armed Bandits

Amir Sani 1 Alessandro Lazaric 1 Rémi Munos 1
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : Stochastic multi--armed bandits solve the Exploration--Exploitation dilemma and ultimately maximize the expected reward. Nonetheless, in many practical problems, maximizing the expected reward is not the most desirable objective. In this paper, we introduce a novel setting based on the principle of risk--aversion where the objective is to compete against the arm with the best risk--return trade--off. This setting proves to be more difficult than the standard multi-arm bandit setting due in part to an exploration risk which introduces a regret associated to the variability of an algorithm. Using variance as a measure of risk, we define two algorithms, investigate their theoretical guarantees, and report preliminary empirical results.
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Amir Sani, Alessandro Lazaric, Rémi Munos. Risk-Aversion in Multi-armed Bandits. NIPS - Twenty-Sixth Annual Conference on Neural Information Processing Systems, Dec 2012, Lake Tahoe, United States. ⟨hal-00772609⟩

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