Before revision:  To address this, we present off-belief learning (OBL) : at each time step OBL agents assume that all past actions were taken by a given, fixed policy (\pi_0), but  that future actions will be taken by an optimal policy under these same assumptions .
After revision:  To address this, we present off-belief learning (OBL) . At each timestep OBL agents follow a policy \pi_1 that is optimized assuming past actions were taken by a given, fixed policy (\pi_0), but that future actions will be taken by an optimal policy under these same assumptions .