generating, by a computing system comprising one or more computing devices, a recall loss function indicating an error metric for the search engine based on a tuning vector and a set of approximate nearest neighbor (ANN) search results that is based on a multi-level set of quantizations of a set of vector embeddings for a set of data objects;

generating, by the computing system, a tradeoff objective function indicating a tradeoff between the error metric and a search cost for the search engine, wherein the tradeoff objective function is based on the recall loss function, a search cost constraint, the tuning vector, and a Lagrange multiplier;

determining, by the computing system, a value for the Lagrange multiplier based on a value for the tradeoff between the error metric and the search cost for the search engine;

determining, by the computing system, values for components of the tuning vector based on the value for the Lagrange multiplier and the tradeoff objective function;

configuring, by the computing system, the search engine based on the values for the components of the tuning vector; and

processing, by the computing system, one or more search queries using the configured search engine in an online mode.