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Buying Data over Time: Approximately Optimal Strategies for Dynamic Data-Driven Decisions

Authors Nicole Immorlica, Ian A. Kash, Brendan Lucier

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Author Details

Nicole Immorlica
  • Microsoft Research, Cambridge, MA, USA
Ian A. Kash
  • Department of Computer Science, University of Illinois at Chicago, IL, USA
Brendan Lucier
  • Microsoft Research, Cambridge, MA, USA


Part of this work was done while Ian Kash was at Microsoft Research. He gratefully acknowledges support from the National Science Foundation via award CCF 1934915.

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Nicole Immorlica, Ian A. Kash, and Brendan Lucier. Buying Data over Time: Approximately Optimal Strategies for Dynamic Data-Driven Decisions. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 77:1-77:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


We consider a model where an agent has a repeated decision to make and wishes to maximize their total payoff. Payoffs are influenced by an action taken by the agent, but also an unknown state of the world that evolves over time. Before choosing an action each round, the agent can purchase noisy samples about the state of the world. The agent has a budget to spend on these samples, and has flexibility in deciding how to spread that budget across rounds. We investigate the problem of choosing a sampling algorithm that optimizes total expected payoff. For example: is it better to buy samples steadily over time, or to buy samples in batches? We solve for the optimal policy, and show that it is a natural instantiation of the latter. Under a more general model that includes per-round fixed costs, we prove that a variation on this batching policy is a 2-approximation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Markov decision processes
  • Online Algorithms
  • Value of Data
  • Markov Processes


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