Exploration by Optimisation in Partial Monitoring

We provide a simple and efficient algorithm for adversarial $k$-action $d$-outcome non-degenerate locally observable partial monitoring game for which the $n$-round minimax regret is bounded by $6(d+1) k^{3/2} \sqrt{n \log(k)}$, matching the best known information-theoretic upper bound. The same algorithm also achieves near-optimal regret for full information, bandit and globally observable games.