Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgment
- Notation
- Part I Introductory Material
- Part II Game Solving and Regret Minimization
- 4 Regret Minimization and the Minimax Theorem
- 5 Blackwell Approachability and Regret Matching
- 6 Self-Play via Regret Minimization
- 7 Optimism and Fast Convergence of Self-Play
- 8 Extensive-Form Games
- 9 Stackelberg Equilibrium and Security Games
- 10 Fixed-Point Theorems and Equilibrium Existence
- Part III Fair Allocation and Market Equilibrium
- Part IV Auctions and Internet Advertising Markets
- Appendix A Optimization Background
- Appendix B Probability Background
- References
- Index
4 - Regret Minimization and the Minimax Theorem
from Part II - Game Solving and Regret Minimization
Published online by Cambridge University Press: 20 August 2026
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgment
- Notation
- Part I Introductory Material
- Part II Game Solving and Regret Minimization
- 4 Regret Minimization and the Minimax Theorem
- 5 Blackwell Approachability and Regret Matching
- 6 Self-Play via Regret Minimization
- 7 Optimism and Fast Convergence of Self-Play
- 8 Extensive-Form Games
- 9 Stackelberg Equilibrium and Security Games
- 10 Fixed-Point Theorems and Equilibrium Existence
- Part III Fair Allocation and Market Equilibrium
- Part IV Auctions and Internet Advertising Markets
- Appendix A Optimization Background
- Appendix B Probability Background
- References
- Index
Summary
This chapter introduces no-regret learning, and introduces several of the most popular algorithms, including online mirror descent and the multiplicative weights update algorithm. We also prove von Neumann’s minimax theorem via no-regret learning.
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- Games, Markets, and Online Learning , pp. 35 - 48Publisher: Cambridge University PressPrint publication year: 2026
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