Browsing by Subject "Dynamic risk-aversion"

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Open Access
Risk-averse allocation indices for multiarmed bandit problem
(IEEE, 2021-01-25) Malekipirbazari, Milad; Çavuş, Özlem
In classical multiarmed bandit problem, the aim is to find a policy maximizing the expected total reward, implicitly assuming that the decision-maker is risk-neutral. On the other hand, the decision-makers are risk-averse in some real-life applications. In this article, we design a new setting based on the concept of dynamic risk measures where the aim is to find a policy with the best risk-adjusted total discounted outcome. We provide a theoretical analysis of multiarmed bandit problem with respect to this novel setting and propose a priority-index heuristic which gives risk-averse allocation indices having a structure similar to Gittins index. Although an optimal policy is shown not always to have index-based form, empirical results express the excellence of this heuristic and show that with risk-averse allocation indices we can achieve optimal or near-optimal interpretable policies.
Open Access
Risk-averse multi-armed bandit problem
(2021-08) Malekipirbazari, Milad
In classical multi-armed bandit problem, the aim is to ﬁnd a policy maximizing the expected total reward, implicitly assuming that the decision maker is risk-neutral. On the other hand, the decision makers are risk-averse in some real life applications. In this study, we design a new setting for the classical multi-armed bandit problem (MAB) based on the concept of dynamic risk measures, where the aim is to ﬁnd a policy with the best risk adjusted total discounted outcome. We provide theoretical analysis of MAB with respect to this novel setting, and propose two diﬀerent priority-index heuristics giving risk-averse allocation indices with structures similar to Gittins index. The ﬁrst proposed heuristic is based on Lagrangian duality and the indices are expressed as the Lagrangian multiplier corresponding to the activation constraint. In the second part, we present a theoretical analysis based on Whittle’s retirement problem and propose a gener-alized version of restart-in-state formulation of the Gittins index to compute the proposed risk-averse allocation indices. Finally, as a practical application of the proposed methods, we focus on optimal design of clinical trials and we apply our risk-averse MAB approach to perform risk-averse treatment allocation based on a Bayesian Bernoulli model. We evaluate the performance of our approach against other allocation rules, including ﬁxed randomization.