Firms perform online experiments with multi-armed bandits to personalize what consumers are shown while balancing exploration and exploitation. However, third-parties can infer consumers' underlying segments from observing which banners, ads, or recommendations consumers receive. To control this inference, we propose a privacy risk budget that firms can set ex ante to bound such third party belief updating using differential privacy. To spend this privacy risk budget, we propose two strategies: a constant privacy risk strategy and a dynamic privacy risk strategy that spend privacy risk differently across visitor. We study how privacy risk budgets affect experimentation performance in two applications--website design and a recommendation system--under these strategies. For both strategies, we analytically find privacy risk budgets that optimally balance exploration and exploitation. We then extend the idea of an experiment-level privacy risk budget to a firm-wide privacy risk budget. We apply this firm-wide privacy risk budget in an empirical setting with 78 experiments. We find that the dynamic strategy is particularly valuable in longer and more complex experiments, and that optimizing the allocation of a firm-wide privacy risk budget across experiments substantially improves learning performance.
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