CS 364 A : Algorithmic Game Theory Lecture # 17 : No - Regret Dynamics ∗
نویسنده
چکیده
This lecture continues to study the questions introduced last time. Do strategic players reach an equilibrium of a game? How quickly? By what learning processes? Positive results on these questions justify equilibrium analysis, including bounds on the price of anarchy. Last lecture focused on best-response dynamics. These dynamics are most relevant for potential games, which cover many but not all interesting applications. This lecture, we study a second fundamental class of learning dynamics — no-regret dynamics. An attractive feature of these dynamics is their rapid convergence to an approximate equilibrium — a coarse correlated equilibrium (Lecture 13), not generally a Nash equilibrium — in arbitrary games.
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CS 364 A : Algorithmic Game
This lecture continues to study the questions introduced last time. Do strategic players reach an equilibrium of a game? How quickly? By what learning processes? Positive results on these questions justify equilibrium analysis, including bounds on the price of anarchy. Last lecture focused on best-response dynamics. These dynamics are most relevant for potential games, which cover many but not ...
متن کاملCS 364 A : Algorithmic Game Theory Lecture # 16 : Best - Response Dynamics ∗
Affirmative answers to these questions are important because they justify equilibrium analysis. Properties of equilibria, such as a near-optimal objective function value, are not obviously relevant when players fail to find one. More generally, proving that natural learning algorithms converge quickly to an equilibrium lends plausibility to the predictive power of an equilibrium concept. To rea...
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Last lecture we proved that coarse correlated equilibria (CCE) are tractable, in a satisfying sense: there are simple and computationally efficient learning procedures that converge quickly to the set of CCE. Of course, if anything in our equilibrium hierarchy (Figure 1) was going to be tractable, it was going to be CCE, the biggest set. The good researcher is never satisfied and always seeks s...
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1 The Big Picture We now have an impressive list of tractability results — polynomial-time algorithms and quickly converging learning dynamics — for several equilibrium concepts in several classes of games. Such tractability results, especially via reasonably natural learning processes, lend credibility to the predictive power of these equilibrium concepts. See also Figure 1. [Lecture 17] In ge...
متن کاملCS 364 A : Algorithmic Game Theory
Last lecture we proved that coarse correlated equilibria (CCE) are tractable, in a satisfying sense: there are simple and computationally efficient learning procedures that converge quickly to the set of CCE. Of course, if anything in our equilibrium hierarchy (Figure 1) was going to be tractable, it was going to be CCE, the biggest set. The good researcher is never satisfied and always seeks s...
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