Faster Game Solving via Predictive Blackwell Approachability: Connecting Regret Matching and Mirror Descent

Blackwell approachability is a framework for reasoning about repeated games with vector-valued payoffs. We introduce predictive approachability, where an estimate of the next payoff vector given, and decision maker tries to achieve better performance based on accuracy that estimator. In order derive algorithms we start by showing powerful connection between four well-known algorithms. Follow-the-regularized-leader (FTRL) online mirror descent (OMD) are most prevalent regret minimizers in convex optimization. spite this prevalence, matching (RM) matching+ (RM+) have been preferred practice solving large-scale (as local within counterfactual minimization framework). show RM RM+ result from running FTRL OMD, respectively, select halfspace force at all times underlying game. By applying variants or OMD connection, obtain algorithms, as well RM+. experiments across 18 common zero-sum extensive-form benchmark games, coupled converges vastly faster than fastest prior (CFR+, DCFR, LCFR) but two poker sometimes more orders magnitude.