blog.wouterkoolen.info

Wouter M. Koolen | Adversarial Intelligence

Welcome to my research blog. This page collects assorted insights that I stumbled upon in my daily research and found worth sharing. I plan to post on topics ranging from elegant, curious or useful mathematical identities to interesting techniques in online learning. There is no set schedule; I only post when I have something to say. Subscribe. To learn when that happens. Wouter M. Koolen. The Hedge Algorithm in Continuous Time. We look at the Hedge algorithm in a version of continuous time.

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Wouter M. Koolen | Adversarial Intelligence | blog.wouterkoolen.info Reviews

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Welcome to my research blog. This page collects assorted insights that I stumbled upon in my daily research and found worth sharing. I plan to post on topics ranging from elegant, curious or useful mathematical identities to interesting techniques in online learning. There is no set schedule; I only post when I have something to say. Subscribe. To learn when that happens. Wouter M. Koolen. The Hedge Algorithm in Continuous Time. We look at the Hedge algorithm in a version of continuous time.

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2 enjoy

3 posts

4 unknown games

5 convex duality illustrated

6 differentiability of compositions

7 bimatrix games

8 coupons

9 reviews

10 scam

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Wouter M. Koolen | Adversarial Intelligence | blog.wouterkoolen.info Reviews

https://blog.wouterkoolen.info

Welcome to my research blog. This page collects assorted insights that I stumbled upon in my daily research and found worth sharing. I plan to post on topics ranging from elegant, curious or useful mathematical identities to interesting techniques in online learning. There is no set schedule; I only post when I have something to say. Subscribe. To learn when that happens. Wouter M. Koolen. The Hedge Algorithm in Continuous Time. We look at the Hedge algorithm in a version of continuous time.

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blog.wouterkoolen.info

1

Convex Duality Illustrated

http://www.blog.wouterkoolen.info/convex_duality/convex_duality.html

Wouter M. Koolen. Convex duality is an important tool in machine learning. Here I present an insightful arrangement of the graphs of a convex function, its dual and their derivatives. Convex optimisation, and in particular convex duality, is an important technique that is very useful in machine learning. We investigate one way to visualise what is going on. Let (f : mathbb R to mathbb R ). Be a convex function. The. Is defined by begin{equation*} f *(y) := sup x x y - f(x) end{equation*}. Is not differen...

2

Close to the Perfect Expert, now Without Outcomes

http://www.blog.wouterkoolen.info/noiseless_dtol/noiseless_dtol.html

Close to the Perfect Expert, now Without Outcomes. Wouter M. Koolen. We look at one of the simplest online learning problems: making decisions in the presence of a perfect expert. We derive a non-uniform regret bound. A classic problem in online learning is called. Prediction with expert advice. The idea is that we have a bunch of predictors called. Second, we promise the learner that there is one perfect expert that never incurs any loss. This is known as the. Every round (t ). We consider the following...

3

Bimatrix Games

http://www.blog.wouterkoolen.info/bimatrix/bimatrix.html

Wouter M. Koolen. We show that any two-player zero-sum bimatrix game has a saddle point where both players randomise over the same number of strategies. We consider two-player zero-sum matrix games. Such games have a single round in which the two players independently choose a strategy. If player one chooses (i ). And player two chooses (j ). Then the loss of player one and the gain of player two are given by the entry (A {i,j} ). That completely specifies the game. Fix a matrix ({ boldsymbol{A} ). We fi...

4

Unknown Games

http://www.blog.wouterkoolen.info/unknown_games/ug.html

Wouter M. Koolen. We investigate what happens to simple matrix games and their solutions if we either randomly or strategically choose between two games. In this note we consider two-player zero-sum matrix games. Such games are specified by a payoff matrix. We assume that we have two such games ({ boldsymbol{A} ). And ({ boldsymbol{B} ). To name the rows and columns we may also write ({ boldsymbol{A} ). Probability distribution on rows) and ({ boldsymbol{q} * ). And ({ boldsymbol{q} ). And the expected p...

5

The Hedge Algorithm in Continuous Time

http://www.blog.wouterkoolen.info/continuous_time_Hedge/post.html

The Hedge Algorithm in Continuous Time. Wouter M. Koolen. The Hedge algorithm (see Freund and Schapire (1997). Is one of the fundamental online learning algorithms. Hedge maintains weights on experts, and updates these weights in response to these experts incurring losses. Here we look at a version in smooth time. Instead of handing out the losses instantaneously, we consider what happens if we reveal them gradually. Let’s review the definition of Hedge. Consider (K ). Experts. We denote by (L t k ).

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Welcome to my research blog. This page collects assorted insights that I stumbled upon in my daily research and found worth sharing. I plan to post on topics ranging from elegant, curious or useful mathematical identities to interesting techniques in online learning. There is no set schedule; I only post when I have something to say. Subscribe. To learn when that happens. Wouter M. Koolen. The Hedge Algorithm in Continuous Time. We look at the Hedge algorithm in a version of continuous time.

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