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Dynamic Games and Applications
Erschienen in: Dynamic Games and Applications 1/2016

01.03.2016

A General Internal Regret-Free Strategy

verfasst von: Ehud Lehrer, Eilon Solan

Erschienen in: Dynamic Games and Applications | Ausgabe 1/2016

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Abstract

We study sequential decision problems where the decision maker does not observe the states of nature, but rather receives a noisy signal, whose distribution depends on the current state and on the action that she plays. We do not assume that the decision maker considers the worst-case scenario, but rather has a response correspondence, which maps distributions over signals to subjective best responses. We extend the concept of internal regret-free strategy to this setup and provide an algorithm that generates such a strategy.
Vorheriger Artikel Strong and Weak Rarity Value: Resource Games with Complex Price–Scarcity Relationships
Nächster Artikel Hopf Bifurcations in Delayed Rock–Paper–Scissors Replicator Dynamics

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Fußnoten
1
For a finite set \(Z\), the set of probability distributions over \(Z\) is denoted by \(\Delta (Z)\).
 
2
Unless indicated otherwise, we use the supremum norm: for every two vectors \(x,x' \in {\mathbb {R}}^d\), the distance between \(x\) and \(x'\) is \(d(x,x') = \max \{ |x_i-x'_i|, 1 \le i \le d\}\), and for every subset \(D \subseteq {\mathbb {R}}^d\), the distance between \(x\) and \(D\) is \(d(x,D) := \inf _{x' \in D} d(x,x')\). Likewise, the distance between two subsets \(Y_1\) and \(Y_2\) of \(Y\) is given by \(d(Y_1,Y_2) := \max _{y_1 \in Y_1} \min _{y_2 \in Y_2}d(y_1,y_2)\).
 
3
We say that event \(B\) holds on event \(A\) if \({\mathbb {P}}(A \cap B) = {\mathbb {P}}(A)\). Thus, a certain inequality holds on event \(A\) if the probability of all points in \(A\) that do not satisfy it is 0.
 
4
For convenience, in the examples we allow payoffs to be greater than \(1\).
 
5
The compactness of \(Y(\mu )\) and the concavity of the entropy function ensure that \(y^\mathrm{ENT}_{\mu }\) is well defined.
 
6
Because the range of \(\sigma \) is finite, we can omit the dependency of \(T'\) on \(x\).
 
7
[19] refer to Blackwell’s invited address to the Institute of Mathematical Statistics, Seattle, August 1956, entitled “Controlled random walks”.
 
8
In most applications of Blackwell’s theory in game theory, the payoffs are uniquely determined by the actions of the players. In our proof, as in Blackwell’s original paper, the payoffs are random variables.
 
9
For any two vectors \(a,b\in {\mathbb {R}}^d\), we denote by \(a \cdot b\) the coordinate-wise product: \((a\cdot b)_k:=a_kb_k\) for every \(k\). Similarly, \(\frac{a}{b} \) denotes the coordinate-wise quotient of \(a\) and \(b\): \((\frac{a}{b})_k := \frac{a_k}{b_k}\) for every \(k\).
 
Literatur
1.
Aumann RJ, Maschler M (1995) Repeated games with incomplete information. MIT Press, CambridgeMATH
2.
Bartók G, Foster D, Pál D, Rakhlin A, Szepesvári C (2013) Partial monitoring-classification, regret bounds, and algorithms, preprint
3.
4.
5.
Cesa-Bianchi N, Lugosi G (2006) Prediction, learning, and games. Cambridge University Press, CambridgeCrossRefMATH
6.
7.
Foster DP (1999) A proof of calibration via Blackwell’s approachability theorem. Games Econ Behav 29:73–78CrossRefMATH
8.
9.
10.
11.
12.
Hannan J (1957) Approximation to Bayes risk in repeated play. Contrib Theory Games 3:97–139MATH
13.
14.
15.
Hazan E, Kakade SM (2012) (weak) Calibration is computationally hard. In: Conference on learning theory (COLT) 2012
16.
Lehrer E (2002) Approachability in infinitely dimensional spaces. Int J Game Theory 31:255–270MathSciNetMATH
17.
Lehrer E (2012) Partially specified probabilities: decisions and games. Am Econ J Microecon 4:70–100CrossRef
18.
Lehrer E, Solan E (2007) Learning to play partially specified equilibrium. Mimeo
19.
Luce DR, Raiffa H (1958) Games and decisions. Wiley, NYMATH
20.
21.
Mannor S, Shimkin N (2003) On-line learning with imperfect monitoring. In: Proceedings of the 16th annual conference on learning theory. Springer, Berlin, pp 552–567
22.
Perchet V (2009) Calibration and internal no-regret with random signals. In: ALT2009, pp 68–82
23.
Perchet V (2011) Internal regret with partial monitoring calibration-based optimal algorithms. J Mach Learn Res 12:1893–1921MathSciNetMATH
24.
25.
Piccolboni A, Schindelhauer C (2001) Discrete prediction games with arbitrary feedback and loss. In: COLT 2001, annual conference on computational learning theory #14, lecture notes in computer science, 2111, pp 208–223
26.
Rockafeller RT, Wets RJB (2009) Variational analysis. Springer, Berlin
27.
28.
Stoltz G, Lugosi G (2005) Internal regret in on-line portfolio selection. Mach Learn 59:125–159CrossRefMATH
Metadaten
Titel
A General Internal Regret-Free Strategy
verfasst von
Ehud Lehrer
Eilon Solan
Publikationsdatum
01.03.2016
Verlag
Springer US
Erschienen in
Dynamic Games and Applications / Ausgabe 1/2016
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-015-0143-5

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