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Vianney PERCHET (CREST) – “An adaptive stochastic optimization algorithm for resource allocation”
October 7, 2019, 3:00 pm - 4:15 pm
The Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 7th of October 2019
Place: Room 3001.
Vianney PERCHET (CREST) – “An adaptive stochastic optimization algorithm for resource allocation“
Abstract: In this talk, I will 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 adaptive to the unknown complexity of the problem, expressed in term of the regularity of the returns of the resources, measured by the exponent in the Łojasiewicz 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.
Cristina BUTUCEA, Alexandre TSYBAKOV, Julie JOSSE, Eric MOULINES, Mathieu ROSENBAUM