Game Theory in Machine Learning, part 1 - Costantinos Daskalakis - MLSS 2020, Tübingen

0:00:00 Game Theory in Machine Learning, part 1 - Costantinos Daskalakis - MLSS 2020, Tübingen
0:01:20 Game Theory and Machine Learning
0:02:52 State
0:03:39 Future of A/: learning strategic reasoning
0:04:34 Example 1: Platform Design
0:06:16 Example 2: Recommender Systems
0:07:05 Example 3: Humanoid vs Spider
0:08:37 A dictum
0:11:42 Our focus: min-max optimization
0:13:46 Generative Adversarial Networks (GAN
0:20:50 Training Oscillations: Handwritten Digits
0:21:44 Training Oscillations: even for Gaussian data/bilinear objectives!
0:26:32 Training Oscillations: persistence for variants of Online Gradient Descent
0:27:12 What gives?
0:27:58 Menu
0:34:39 The Min-Max Theorem
0:43:51 Min-Max and No-Regret Learning
0:48:34 [Code Walkthrough]
0:57:19 Training Oscillations
0:59:07 Menu
1:00:22 Gradient Descent w/ Negative Momentum
1:04:04 Negative Momentum: why might it help?
1:07:04 Training Oscillations
1:11:19 Negative Momentum: convergence
1:12:03 Negative Momentum: why might it help?
1:18:54 Negative Momentum: constrained case
1:25:41 Menu
1:27:18 constrained case
1:27:23 Remark 1: Beyond "Last-Iterate"
1:29:39 Remark 3: GAN learning
1:31:48 Thanks!
1:39:16 MLSS 2020 Team

[sebastiang.]

At 24:10 he says that the solution is (3, 4) and (0, 0). Why? If I imagine it as a two-player game, then, as he says, theta should go towards -infinity and w against +infinity. Is the idea that it's the equilibrium point, because it is the only solution for which each player knows that the other can't mess up their solution quality any further? E.g. if w is going towards infinity, then any value of theta that makes the bracket-term go negative would be better than (3, 4), from the eyes of the minimization player. However, the maximization player could simply revert, go towards -infinity now, to turn the whole term positive. So what he calls the solution is the basically the best _stable_ solution?