  This paper resolves the open question of designing near-optimal algorithms
for learning imperfect-information extensive-form games from bandit feedback.
We present the first line of algorithms that require only
$\widetilde{\mathcal{O}}((XA+YB)/\varepsilon^2)$ episodes of play to find an
$\varepsilon$-approximate Nash equilibrium in two-player zero-sum games, where
$X,Y$ are the number of information sets and $A,B$ are the number of actions
for the two players. This improves upon the best known sample complexity of
$\widetilde{\mathcal{O}}((X^2A+Y^2B)/\varepsilon^2)$ by a factor of
$\widetilde{\mathcal{O}}(\max\{X, Y\})$, and matches the information-theoretic
lower bound up to logarithmic factors. We achieve this sample complexity by two
new algorithms: Balanced Online Mirror Descent, and Balanced Counterfactual
Regret Minimization. Both algorithms rely on novel approaches of integrating
\emph{balanced exploration policies} into their classical counterparts. We also
extend our results to learning Coarse Correlated Equilibria in multi-player
general-sum games.
