\Phi$ Regret Minimization

Phi-regret minimization is a framework for analyzing online learning algorithms, particularly in game theory, aiming to minimize regret relative to a set of comparator strategies defined by a function Φ. Current research focuses on developing efficient algorithms, such as variants of online mirror descent and $\Phi$-Hedge, to achieve near-optimal regret bounds in complex settings like extensive-form games. This work is significant because it provides theoretical guarantees for convergence to various equilibrium concepts (e.g., Nash, correlated equilibria) and enables efficient learning in large-scale games, with implications for multi-agent systems and AI.