Implicit Q-Learning

Saw from this paper https://arxiv.org/pdf/2505.08078

In this work, we primarily consider the Implicit Q-Learning (IQL) [20] value objectives given its effectiveness on a range of tasks. IQL aims to fit a value function by estimating expectiles τ with respect to actions within the support of the data, and then uses the value function to update the

Q-function. To do so, it aims to minimize the following objectives for learning a parameterized Q-function $Q_{\varphi }$ (with target Q-function Qϕ′ ) and value function Vψ: $L_Q(\varphi )=E(s,a,r,s^{\prime }{)}_{\sim D}[(r+\gamma V_{\theta }(s^{\prime })-Q_{\varphi }(s,a){)}^2]$ $L_V(\psi )=E_{(s,a)\sim D}[L_2^{\tau }(Q_{\varphi }^{\prime }(s,a)-V_{\psi }(s))]$

• where $L_2^{\tau }(x)=|\tau -1(x<0)|x^2$.

Original paper:

• https://arxiv.org/pdf/2110.06169

It learns a Q-function from the offline dataset.

It derives a value function $V(s)$ by “aggregating” the learned Q-function across actions.

It then trains the policy to imitate the best actions in the dataset (using advantage-weighted updates).