A Problem-Adaptive Algorithm for Resource Allocation
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We consider a sequential stochastic resource allocation problem under the gradient feedback, where the reward of each resource is concave. We construct a generic algorithm that is adaptive to the complexity of the problem, which is measured using the exponent in Łojasiewicz inequality. Our algorithm interpolates between the non-strongly concave and the strongly-concave rates without depending on the strong-concavity parameter and recover the fast rate of classical multi-armed bandit (corresponding roughly to linear reward functions).
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