Evaluating the Bayesian capabilities of LLM
Like humans, to be effective, LLMs’ user interactions require constant updating of probabilistic estimates of the user’s preferences based on each new interaction with them. Here we ask: Do LLMs function as if they have probabilistic estimates that are updated as expected from optimal Bayesian inference? To the extent that the behavior of LLMs deviates from the optimal Bayesian strategy, how can we minimize these deviations?
To test this, we used a simplified flight recommendation task, in which LLMs interact with a simulated user as an assistant for five rounds. In each round, three flight options were presented to both the user and the assistant. Each flight was defined by departure time, duration, number of stops and cost. Each simulated user was characterized by a set of preferences: for each feature, they could have a strong or weak preference for high or low values ​​of the feature (for example, they might prefer longer or shorter flights), or they could have no preference with respect to this feature.
We compared the behavior of LLM with a model bayesian assistantwhich follows the optimal Bayesian strategy. This model maintains a probability distribution that represents an estimate of the user’s preferences and usages. Bayes’ rule Update this distribution as new information about user preferences becomes available. Unlike many real-life scenarios, where the Bayesian strategy is difficult to specify and implement computationally, in this controlled setting it is easy to implement and allows us to accurately estimate the extent to which the LLM deviates from it.
The goal of the assistant was to recommend a flight that matches the user’s preferences. At the end of each round, the user indicated to the assistant whether he or she had chosen correctly, and provided him or her with the correct answer.
