# Context Most IRL estimators frame reward recovery as a min-max problem: choose a reward function and a policy, then alternate between improving each. IQ-Learn collapses this adversarial game into a single concave optimization over a soft Q-function. The Q-function determines both the policy (through the softmax mapping) and a Bellman-implied reward (through the inverse Bellman operator), so there is no discriminator to train and no inner loop to stabilize. ## Source Ideas The construction comes from {ref}`Garg et al. (2021) `. The key observation is that in a max-entropy policy framework the optimal policy is always the softmax of Q, so it suffices to optimize over Q alone. The chi-squared divergence objective adds a quadratic penalty on the temporal difference term, which bounds the objective and prevents Q from drifting to numerical overflow. The simple (TV-distance) objective is also implemented but has no upper bound on a free tabular Q table and should not be used there. ## Where IQ-Learn Fits IQ-Learn sits with AIRL, f-IRL, GLADIUS, and MCE-IRL in the IRL family. Like the others it does not impose a structural Bellman fixed point as a hard constraint. Unlike AIRL and f-IRL it avoids adversarial training; unlike MCE-IRL and GLADIUS it does not start from a parameterized reward function but from a parameterized Q directly. The {ref}`Garg et al. (2021) ` paper shows that IQ-Learn generalizes behavioral cloning: setting the divergence penalty weight to zero recovers a pure log-likelihood maximizer over the Q-induced logit choice probabilities. This connection makes IQ-Learn a natural bridge between BC and Bellman-aware IRL, and the alpha hyperparameter controls where on that path the estimator sits. ## Package Position IQ-Learn is the right tool when you want an imitation policy without adversarial training and a Q-based reward diagnostic alongside it. It is not the right tool when structural counterfactual validity is required; the current evidence shows that reward, value, and Q recovery do not pass their checks on any tested cell. For structural use, see NFXP, CCP, or UFXP.