Approachability Problem

Blackwell approachability is a game-theoretic framework addressing the problem of guiding a decision-maker's average outcome towards a target set, even against an adversarial opponent. Current research focuses on improving the efficiency and convergence rates of algorithms like Blackwell's algorithm and its variants, exploring connections with online learning and regret minimization, and extending the framework to handle time-dependent scenarios and various distance metrics (e.g., ℓ∞-norm). These advancements have implications for diverse applications, including robust forecasting, multi-agent reinforcement learning, and solving optimization problems like saddle-point problems, by providing efficient and parameter-free algorithms.