Lecture 24 : The Multiplicative Weights Algorithm
نویسندگان
چکیده
In the next two lectures, we will present an alternative algorithm for solving LPs and SDPs. Multiplicative weights is a term for the simple iterative rule underlying these algorithms; it is known by different names in the various fields where it was (re)discovered. The detailed content can be found in a survey by Arora, Hazan and Kale [AHK05]; and our discussion is mainly based on their treatment.
منابع مشابه
MS&E 336 Lecture 11: The multiplicative weights algorithm
This lecture is based on the corresponding paper of Freund and Schapire [2], though with some differences in notation and analysis. We introduce and study the multiplicative weights (MW) algorithm, which is an external regret minimizing (i.e., Hannan consistent) algorithm for playing a game. The same algorithm has been analyzed in various forms, particularly in the study of online learning; see...
متن کاملCS261: A Second Course in Algorithms Lecture #12: Applications of Multiplicative Weights to Games and Linear Programs∗
1 Extensions of the Multiplicative Weights Guarantee Last lecture we introduced the multiplicative weights algorithm for online decision-making. You don't need to remember the algorithm details for this lecture, but you should remember that it's a simple and natural algorithm (just one simple update per action per time step). You should also remember its regret guarantee, which we proved last l...
متن کاملOrie 6334 Spectral Graph Theory Lecture 21
Just like matrix Chernoff bounds were a generalization of scalar Chernoff bounds, the multiplicative weights algorithm can be generalized to matrices. Recall that in the setup for the multiplicative weight update algorithm, we had a sequence of time steps t = 1, . . . , T ; in each time step t, we made a decision i ∈ {1...N} and got a value vt(i) ∈ [0, 1]. After we made a decision in time step ...
متن کاملSolving Flow Problems using Multiplicative Weights
We saw that using the multiplicative weights (MW) algorithm, we find a (1 + ε)-approximate max flow f̂—i.e., a flow of value F that has f̂e ≤ 1 + ε—using O( logm ε2 ) calls to the oracle. In Lecture #14, we saw that using shortest-path routing, you can get ρ = F . Since we can use Dijkstra’s O(m+ n log n) to implement the oracle, this gives an Õ( ε2 ) time algorithm. Relaxed Oracle: For the rest ...
متن کاملMultiplicative Weights
In this lecture, we will study various applications of the theory of Multiplicative Weights (MW). In this section, we briefly review the general version of the MW algorithm that we studied in the previous lecture. The following sections then show how the theory can be applied to approximately solve zero-sum games and linear programs, and how it connects with the theory of boosting and approxima...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016