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In this paper, a rather general online problem called dynamic resourceallocation with capacity constraints (DRACC) is introduced and studied in therealm of posted price mechanisms. This problem subsumes several applications ofstateful pricing, including but not limited to posted prices for online jobscheduling and matching over a dynamic bipartite graph. As the existing onlinelearning techniques do not yield vanishing-regret mechanisms for this problem,we develop a novel online learning framework defined over deterministic Markovdecision processes with dynamic state transition and reward functions. We thenprove that if the Markov decision process is guaranteed to admit an oracle thatcan simulate any given policy from any initial state with bounded loss -- acondition that is satisfied in the DRACC problem -- then the online learningproblem can be solved with vanishing regret. Our proof technique is based on areduction to online learning with switching cost, in which an online decisionmaker incurs an extra cost every time she switches from one arm to another. Weformally demonstrate this connection and further show how DRACC can be used inour proposed applications of stateful pricing.

Stateful Posted Pricing with Vanishing Regret via Dynamic Deterministic Markov Decision Processes