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Joint Online Learning and Decision-making via Dual Mirror Descent
Alfonso Lobos Ruiz · Paul Grigas · Zheng Wen

Wed Jul 21 06:25 AM -- 06:30 AM (PDT) @
We consider an online revenue maximization problem over a finite time horizon subject to lower and upper bounds on cost. At each period, an agent receives a context vector sampled i.i.d. from an unknown distribution and needs to make a decision adaptively. The revenue and cost functions depend on the context vector as well as some fixed but possibly unknown parameter vector to be learned. We propose a novel offline benchmark and a new algorithm that mixes an online dual mirror descent scheme with a generic parameter learning process. When the parameter vector is known, we demonstrate an $O(\sqrt{T})$ regret result as well an $O(\sqrt{T})$ bound on the possible constraint violations. When the parameter is not known and must be learned, we demonstrate that the regret and constraint violations are the sums of the previous $O(\sqrt{T})$ terms plus terms that directly depend on the convergence of the learning process.

Author Information

Alfonso Lobos Ruiz (Microsoft)
Paul Grigas (UC Berkeley)
Zheng Wen (DeepMind)

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