An adaptive stochastic optimization algorithm for resource allocation

Xavier Fontaine; Shie Mannor; Vianney Perchet

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arXiv · 1902.04376

An adaptive stochastic optimization algorithm for resource allocation

Xavier Fontaine·Shie Mannor·Vianney Perchet

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Abstract

We consider the classical problem of sequential resource allocation where a decision maker must repeatedly divide a budget between several resources, each with diminishing returns. This can be recast as a specific stochastic optimization problem where the objective is to maximize the cumulative reward, or equivalently to minimize the regret. We construct an algorithm that is {\em adaptive} to the complexity of the problem, expressed in term of the regularity of the returns of the resources, measured by the exponent in the {\L}ojasiewicz inequality (or by their universal concavity parameter). Our parameter-independent algorithm recovers the optimal rates for strongly-concave functions and the classical fast rates of multi-armed bandit (for linear reward functions). Moreover, the algorithm improves existing results on stochastic optimization in this regret minimization setting for intermediate cases.

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BibTeX RIS

Xavier Fontaine, Shie Mannor, Vianney Perchet. 2019-02-12. An adaptive stochastic optimization algorithm for resource allocation. https://arxiv.org/abs/1902.04376

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