When Are We Near Nash? Certifying Solutions in General-Sum Games

Key points

• We ask what a solver can know about its own iterates from the regret accumulators and the terminal-distribution accumulators its updates already maintain.1
• In two-player games the NashGap of a weighted average strategy equals, at the maximizing player, the weighted external regret plus a signed value correction.1
• Run a portfolio of training-free regret-matching solvers, output the iterate with the smallest certificate, and verify that iterate once.1
• On the benchmark's biased Leduc family a pool of sixteen training-free solvers, seven original and nine recent variants, solves $89%$ of the $64$ instances at threshold $10^{-5}$ this way, matching the trajectory-minimum union of the solvers.1

Sources (1)

• [1]When Are We Near Nash? Certifying Solutions in General-Sum Games
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 21, 06:53 AM

  Heuristic solvers for general-sum extensive-form games produce a stream of iterates, and practice reports the NashGap of the returned profile.

  We ask what a solver can know about its own iterates from the regret accumulators and the terminal-distribution accumulators its updates already maintain.

Extractive summary: sentences quoted from the sources.