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113 jmlr-2013-The CAM Software for Nonnegative Blind Source Separation in R-Java

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Author: Niya Wang, Fan Meng, Li Chen, Subha Madhavan, Robert Clarke, Eric P. Hoffman, Jianhua Xuan, Yue Wang

Abstract: We describe a R-Java CAM (convex analysis of mixtures) package that provides comprehensive analytic functions and a graphic user interface (GUI) for blindly separating mixed nonnegative sources. This open-source multiplatform software implements recent and classic algorithms in the literature including Chan et al. (2008), Wang et al. (2010), Chen et al. (2011a) and Chen et al. (2011b). The CAM package offers several attractive features: (1) instead of using proprietary MATLAB, its analytic functions are written in R, which makes the codes more portable and easier to modify; (2) besides producing and plotting results in R, it also provides a Java GUI for automatic progress update and convenient visual monitoring; (3) multi-thread interactions between the R and Java modules are driven and integrated by a Java GUI, assuring that the whole CAM software runs responsively; (4) the package offers a simple mechanism to allow others to plug-in additional R-functions. Keywords: convex analysis of mixtures, blind source separation, afﬁnity propagation clustering, compartment modeling, information-based model selection c 2013 Niya Wang, Fan Meng, Li Chen, Subha Madhavan, Robert Clarke, Eric P. Hoffman, Jianhua Xuan and Yue Wang. WANG , M ENG , C HEN , M ADHAVAN , C LARKE , H OFFMAN , X UAN AND WANG 1. Overview Blind source separation (BSS) has proven to be a powerful and widely-applicable tool for the analysis and interpretation of composite patterns in engineering and science (Hillman and Moore, 2007; Lee and Seung, 1999). BSS is often described by a linear latent variable model X = AS, where X is the observation data matrix, A is the unknown mixing matrix, and S is the unknown source data matrix. The fundamental objective of BSS is to estimate both the unknown but informative mixing proportions and the source signals based only on the observed mixtures (Child, 2006; Cruces-Alvarez et al., 2004; Hyvarinen et al., 2001; Keshava and Mustard, 2002). While many existing BSS algorithms can usefully extract interesting patterns from mixture observations, they often prove inaccurate or even incorrect in the face of real-world BSS problems in which the pre-imposed assumptions may be invalid. There is a family of approaches exploiting the source non-negativity, including the non-negative matrix factorization (NMF) (Gillis, 2012; Lee and Seung, 1999). This motivates the development of alternative BSS techniques involving exploitation of source nonnegative nature (Chan et al., 2008; Chen et al., 2011a,b; Wang et al., 2010). The method works by performing convex analysis of mixtures (CAM) that automatically identiﬁes pure-source signals that reside at the vertices of the multifaceted simplex most tightly enclosing the data scatter, enabling geometrically-principled delineation of distinct source patterns from mixtures, with the number of underlying sources being suggested by the minimum description length criterion. Consider a latent variable model x(i) = As(i), where the observation vector x(i) = [x1 (i), ..., xM (i)]T can be expressed as a non-negative linear combination of the source vectors s(i) = [s1 (i), ..., sJ (i)]T , and A = [a1 , ..., aJ ] is the mixing matrix with a j being the jth column vector. This falls neatly within the deﬁnition of a convex set (Fig. 1) (Chen et al., 2011a): X= J J ∑ j=1 s j (i)a j |a j ∈ A, s j (i) ≥ 0, ∑ j=1 s j (i) = 1, i = 1, ..., N . Assume that the sources have at least one sample point whose signal is exclusively enriched in a particular source (Wang et al., 2010), we have shown that the vertex points of the observation simplex (Fig. 1) correspond to the column vectors of the mixing matrix (Chen et al., 2011b). Via a minimum-error-margin volume maximization, CAM identiﬁes the optimum set of the vertices (Chen et al., 2011b; Wang et al., 2010). Using the samples attached to the vertices, compartment modeling (CM) (Chen et al., 2011a) obtains a parametric solution of A, nonnegative independent component analysis (nICA) (Oja and Plumbley, 2004) estimates A (and s) that maximizes the independency in s, and nonnegative well-grounded component analysis (nWCA) (Wang et al., 2010) ﬁnds the column vectors of A directly from the vertex cluster centers. Figure 1: Schematic and illustrative ﬂowchart of R-Java CAM package. 2900 T HE CAM S OFTWARE IN R-JAVA In this paper we describe a newly developed R-Java CAM package whose analytic functions are written in R, while a graphic user interface (GUI) is implemented in Java, taking full advantages of both programming languages. The core software suite implements CAM functions and includes normalization, clustering, and data visualization. Multi-thread interactions between the R and Java modules are driven and integrated by a Java GUI, which not only provides convenient data or parameter passing and visual progress monitoring but also assures the responsive execution of the entire CAM software. 2. Software Design and Implementation The CAM package mainly consists of R and Java modules. The R module is a collection of main and helper functions, each represented by an R function object and achieving an independent and speciﬁc task (Fig. 1). The R module mainly performs various analytic tasks required by CAM: ﬁgure plotting, update, or error message generation. The Java module is developed to provide a GUI (Fig. 2). We adopt the model-view-controller (MVC) design strategy, and use different Java classes to separately perform information visualization and human-computer interaction. The Java module also serves as the software driver and integrator that use a multi-thread strategy to facilitate the interactions between the R and Java modules, such as importing raw data, passing algorithmic parameters, calling R scripts, and transporting results and messages. Figure 2: Interactive Java GUI supported by a multi-thread design strategy. 2.1 Analytic and Presentation Tasks Implemented in R The R module performs the CAM algorithm and facilitates a suite of subsequent analyses including CM, nICA, and nWCA. These tasks are performed by the three main functions: CAM-CM.R, CAM-nICA.R, and CAM-nWCA.R, which can be activated by the three R scripts: Java-runCAM-CM.R, Java-runCAM-ICA.R, and Java-runCAM-nWCA.R. The R module also performs auxiliary tasks including automatic R library installation, ﬁgure drawing, and result recording; and offers other standard methods such as nonnegative matrix factorization (Lee and Seung, 1999), Fast ICA (Hyvarinen et al., 2001), factor analysis (Child, 2006), principal component analysis, afﬁnity propagation, k-means clustering, and expectation-maximization algorithm for learning standard ﬁnite normal mixture model. 2.2 Graphic User Interface Written in Java Swing The Java GUI module allows users to import data, select algorithms and parameters, and display results. The module encloses two packages: guiView contains classes for handling frames and 2901 WANG , M ENG , C HEN , M ADHAVAN , C LARKE , H OFFMAN , X UAN AND WANG Figure 3: Application of R-Java CAM to deconvolving dynamic medical image sequence. dialogs for managing user inputs; guiModel contains classes for representing result data sets and for interacting with the R script caller. Packaged as one jar ﬁle, the GUI module runs automatically. 2.3 Functional Interaction Between R and Java We adopt the open-source program RCaller (http://code.google.com/p/rcaller) to implement the interaction between R and Java modules (Fig. 2), supported by explicitly designed R scripts such as Java-runCAM-CM.R. Speciﬁcally, ﬁve featured Java classes are introduced to interact with R for importing data or parameters, running algorithms, passing on or recording results, displaying ﬁgures, and handing over error messages. The examples of these classes include guiModel.MyRCaller.java, guiModel.MyRCaller.readResults(), and guiView.MyRPlotViewer. 3. Case Studies and Experimental Results The CAM package has been successfully applied to various data types. Using dynamic contrastenhanced magnetic resonance imaging data set of an advanced breast cancer case (Chen, et al., 2011b),“double click” (or command lines under Ubuntu) activated execution of CAM-Java.jar reveals two biologically interpretable vascular compartments with distinct kinetic patterns: fast clearance in the peripheral “rim” and slow clearance in the inner “core”. These outcomes are consistent with previously reported intratumor heterogeneity (Fig. 3). Angiogenesis is essential to tumor development beyond 1-2mm3 . It has been widely observed that active angiogenesis is often observed in advanced breast tumors occurring in the peripheral “rim” with co-occurrence of inner-core hypoxia. This pattern is largely due to the defective endothelial barrier function and outgrowth blood supply. In another application to natural image mixtures, CAM algorithm successfully recovered the source images in a large number of trials (see Users Manual). 4. Summary and Acknowledgements We have developed a R-Java CAM package for blindly separating mixed nonnegative sources. The open-source cross-platform software is easy-to-use and effective, validated in several real-world applications leading to plausible scientiﬁc discoveries. The software is freely downloadable from http://mloss.org/software/view/437/. We intend to maintain and support this package in the future. This work was supported in part by the US National Institutes of Health under Grants CA109872, CA 100970, and NS29525. We thank T.H. Chan, F.Y. Wang, Y. Zhu, and D.J. Miller for technical discussions. 2902 T HE CAM S OFTWARE IN R-JAVA References T.H. Chan, W.K. Ma, C.Y. Chi, and Y. Wang. A convex analysis framework for blind separation of non-negative sources. IEEE Transactions on Signal Processing, 56:5120–5143, 2008. L. Chen, T.H. Chan, P.L. Choyke, and E.M. Hillman et al. Cam-cm: a signal deconvolution tool for in vivo dynamic contrast-enhanced imaging of complex tissues. Bioinformatics, 27:2607–2609, 2011a. L. Chen, P.L. Choyke, T.H. Chan, and C.Y. Chi et al. Tissue-speciﬁc compartmental analysis for dynamic contrast-enhanced mr imaging of complex tumors. IEEE Transactions on Medical Imaging, 30:2044–2058, 2011b. D. Child. The essentials of factor analysis. Continuum International, 2006. S.A. Cruces-Alvarez, Andrzej Cichocki, and Shun ichi Amari. From blind signal extraction to blind instantaneous signal separation: criteria, algorithms, and stability. IEEE Transactions on Neural Networks, 15:859–873, 2004. N. Gillis. Sparse and unique nonnegative matrix factorization through data preprocessing. Journal of Machine Learning Research, 13:3349–3386, 2012. E.M.C. Hillman and A. Moore. All-optical anatomical co-registration for molecular imaging of small animals using dynamic contrast. Nature Photonics, 1:526–530, 2007. A. Hyvarinen, J. Karhunen, and E. Oja. Independent Component Analysis. John Wiley, New York, 2001. N. Keshava and J.F. Mustard. Spectral unmixing. IEEE Signal Processing Magazine, 19:44–57, 2002. D.D. Lee and H.S. Seung. Learning the parts of objects by non-negative matrix factorization. Nature, 401:788–791, 1999. E. Oja and M. Plumbley. Blind separation of positive sources by globally convergent gradient search. Neural Computation, 16:1811–1825, 2004. F.Y. Wang, C.Y. Chi, T.H. Chan, and Y. Wang. Nonnegative least-correlated component analysis for separation of dependent sources by volume maximization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32:857–888, 2010. 2903

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 This open-source multiplatform software implements recent and classic algorithms in the literature including Chan et al. [sent-12, score-0.094]

2 Keywords: convex analysis of mixtures, blind source separation, afﬁnity propagation clustering, compartment modeling, information-based model selection c 2013 Niya Wang, Fan Meng, Li Chen, Subha Madhavan, Robert Clarke, Eric P. [sent-18, score-0.346]

3 Overview Blind source separation (BSS) has proven to be a powerful and widely-applicable tool for the analysis and interpretation of composite patterns in engineering and science (Hillman and Moore, 2007; Lee and Seung, 1999). [sent-21, score-0.248]

4 BSS is often described by a linear latent variable model X = AS, where X is the observation data matrix, A is the unknown mixing matrix, and S is the unknown source data matrix. [sent-22, score-0.175]

5 The fundamental objective of BSS is to estimate both the unknown but informative mixing proportions and the source signals based only on the observed mixtures (Child, 2006; Cruces-Alvarez et al. [sent-23, score-0.28]

6 While many existing BSS algorithms can usefully extract interesting patterns from mixture observations, they often prove inaccurate or even incorrect in the face of real-world BSS problems in which the pre-imposed assumptions may be invalid. [sent-26, score-0.04]

7 There is a family of approaches exploiting the source non-negativity, including the non-negative matrix factorization (NMF) (Gillis, 2012; Lee and Seung, 1999). [sent-27, score-0.148]

8 This motivates the development of alternative BSS techniques involving exploitation of source nonnegative nature (Chan et al. [sent-28, score-0.239]

9 , xM (i)]T can be expressed as a non-negative linear combination of the source vectors s(i) = [s1 (i), . [sent-36, score-0.114]

10 , aJ ] is the mixing matrix with a j being the jth column vector. [sent-42, score-0.061]

11 Assume that the sources have at least one sample point whose signal is exclusively enriched in a particular source (Wang et al. [sent-49, score-0.212]

12 , 2010), we have shown that the vertex points of the observation simplex (Fig. [sent-50, score-0.036]

13 1) correspond to the column vectors of the mixing matrix (Chen et al. [sent-51, score-0.061]

14 Via a minimum-error-margin volume maximization, CAM identiﬁes the optimum set of the vertices (Chen et al. [sent-53, score-0.035]

15 Using the samples attached to the vertices, compartment modeling (CM) (Chen et al. [sent-56, score-0.07]

16 , 2011a) obtains a parametric solution of A, nonnegative independent component analysis (nICA) (Oja and Plumbley, 2004) estimates A (and s) that maximizes the independency in s, and nonnegative well-grounded component analysis (nWCA) (Wang et al. [sent-57, score-0.25]

17 2900 T HE CAM S OFTWARE IN R-JAVA In this paper we describe a newly developed R-Java CAM package whose analytic functions are written in R, while a graphic user interface (GUI) is implemented in Java, taking full advantages of both programming languages. [sent-60, score-0.308]

18 The core software suite implements CAM functions and includes normalization, clustering, and data visualization. [sent-61, score-0.144]

19 Multi-thread interactions between the R and Java modules are driven and integrated by a Java GUI, which not only provides convenient data or parameter passing and visual progress monitoring but also assures the responsive execution of the entire CAM software. [sent-62, score-0.302]

20 Software Design and Implementation The CAM package mainly consists of R and Java modules. [sent-64, score-0.089]

21 The R module is a collection of main and helper functions, each represented by an R function object and achieving an independent and speciﬁc task (Fig. [sent-65, score-0.242]

22 The R module mainly performs various analytic tasks required by CAM: ﬁgure plotting, update, or error message generation. [sent-67, score-0.349]

23 The Java module is developed to provide a GUI (Fig. [sent-68, score-0.242]

24 We adopt the model-view-controller (MVC) design strategy, and use different Java classes to separately perform information visualization and human-computer interaction. [sent-70, score-0.031]

25 The Java module also serves as the software driver and integrator that use a multi-thread strategy to facilitate the interactions between the R and Java modules, such as importing raw data, passing algorithmic parameters, calling R scripts, and transporting results and messages. [sent-71, score-0.496]

26 1 Analytic and Presentation Tasks Implemented in R The R module performs the CAM algorithm and facilitates a suite of subsequent analyses including CM, nICA, and nWCA. [sent-74, score-0.292]

27 These tasks are performed by the three main functions: CAM-CM. [sent-75, score-0.033]

28 R, which can be activated by the three R scripts: Java-runCAM-CM. [sent-78, score-0.054]

29 The R module also performs auxiliary tasks including automatic R library installation, ﬁgure drawing, and result recording; and offers other standard methods such as nonnegative matrix factorization (Lee and Seung, 1999), Fast ICA (Hyvarinen et al. [sent-82, score-0.466]

30 2 Graphic User Interface Written in Java Swing The Java GUI module allows users to import data, select algorithms and parameters, and display results. [sent-85, score-0.242]

31 The module encloses two packages: guiView contains classes for handling frames and 2901 WANG , M ENG , C HEN , M ADHAVAN , C LARKE , H OFFMAN , X UAN AND WANG Figure 3: Application of R-Java CAM to deconvolving dynamic medical image sequence. [sent-86, score-0.37]

32 dialogs for managing user inputs; guiModel contains classes for representing result data sets and for interacting with the R script caller. [sent-87, score-0.061]

33 Packaged as one jar ﬁle, the GUI module runs automatically. [sent-88, score-0.242]

34 com/p/rcaller) to implement the interaction between R and Java modules (Fig. [sent-92, score-0.099]

35 2), supported by explicitly designed R scripts such as Java-runCAM-CM. [sent-93, score-0.089]

36 Speciﬁcally, ﬁve featured Java classes are introduced to interact with R for importing data or parameters, running algorithms, passing on or recording results, displaying ﬁgures, and handing over error messages. [sent-95, score-0.218]

37 Case Studies and Experimental Results The CAM package has been successfully applied to various data types. [sent-103, score-0.089]

38 Using dynamic contrastenhanced magnetic resonance imaging data set of an advanced breast cancer case (Chen, et al. [sent-104, score-0.217]

39 , 2011b),“double click” (or command lines under Ubuntu) activated execution of CAM-Java. [sent-105, score-0.054]

40 jar reveals two biologically interpretable vascular compartments with distinct kinetic patterns: fast clearance in the peripheral “rim” and slow clearance in the inner “core”. [sent-106, score-0.23]

41 It has been widely observed that active angiogenesis is often observed in advanced breast tumors occurring in the peripheral “rim” with co-occurrence of inner-core hypoxia. [sent-110, score-0.168]

42 In another application to natural image mixtures, CAM algorithm successfully recovered the source images in a large number of trials (see Users Manual). [sent-112, score-0.114]

43 Summary and Acknowledgements We have developed a R-Java CAM package for blindly separating mixed nonnegative sources. [sent-114, score-0.268]

44 The open-source cross-platform software is easy-to-use and effective, validated in several real-world applications leading to plausible scientiﬁc discoveries. [sent-115, score-0.064]

45 We intend to maintain and support this package in the future. [sent-118, score-0.089]

46 A convex analysis framework for blind separation of non-negative sources. [sent-136, score-0.256]

47 Cam-cm: a signal deconvolution tool for in vivo dynamic contrast-enhanced imaging of complex tissues. [sent-146, score-0.166]

48 Tissue-speciﬁc compartmental analysis for dynamic contrast-enhanced mr imaging of complex tumors. [sent-156, score-0.129]

49 From blind signal extraction to blind instantaneous signal separation: criteria, algorithms, and stability. [sent-165, score-0.398]

50 Sparse and unique nonnegative matrix factorization through data preprocessing. [sent-169, score-0.159]

51 All-optical anatomical co-registration for molecular imaging of small animals using dynamic contrast. [sent-176, score-0.159]

52 Blind separation of positive sources by globally convergent gradient search. [sent-200, score-0.155]

53 Nonnegative least-correlated component analysis for separation of dependent sources by volume maximization. [sent-210, score-0.155]

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Abstract: This paper introduces the rllib as an original C++ template-based library oriented toward value function estimation. Generic programming is promoted here as a way of having a good ﬁt between the mathematics of reinforcement learning and their implementation in a library. The main concepts of rllib are presented, as well as a short example. Keywords: reinforcement learning, C++, generic programming 1. C++ Genericity for Fitting the Mathematics of Reinforcement Learning Reinforcement learning (RL) is a ﬁeld of machine learning that beneﬁts from a rigorous mathematical formalism, as shown for example by Bertsekas (1995). Although this formalism is well accepted in the ﬁeld, its translation into efﬁcient computer science tools has surprisingly not led to any standard yet, as mentioned by Kovacs and Egginton (2011). The claim of this paper is that genericity enables a natural expression of the mathematics of RL. The rllib (2011) library implements this idea in the C++ language, where genericity relies on templates. Templates automate the re-writing of some generic code involving user types, offering a strong type checking at compile time that improves the code safety. Using the rllib templates requires that the user-deﬁned types ﬁt some documented concepts. For example, some class C deﬁning an agent should be designed so that C::state type is the type used for the states, C::action type is the type used for the actions, and the method C::action type policy(const C::state type& s) const is implemented, in order to compute the action to be performed in a given state. This concept deﬁnition speciﬁes what is required for an agent mathematically. Note that C does not need to inherit from any kind of abstract rl::Agent class to be used by the rllib tools. It can be directly provided as a type argument to any rllib template requiring an argument ﬁtting the concept of an agent, so that the re-written code actually compiles. 2. A Short Example Let us consider the following toy-example. The state space contains values from 0 to 9, and actions consist in increasing or decreasing the value. When the value gets out of bounds, a reward is returned ∗. Also at UMI 2958 Georgia Tech / CNRS, 2-3, rue Marconi, 57070 Metz, France. c 2013 Herv´ Frezza-Buet and Matthieu Geist. e F REZZA -B UET AND G EIST (-1 for bound 0, 1 for bound 9). Otherwise, a null reward is returned. Let us deﬁne this problem and run Sarsa. First, a simulator class ﬁtting the concept Simulator described in the documentation is needed. c l a s s Sim { / / Our s i m u l a t o r c l a s s . No i n h e r i t a n c e r e q u i r e d . private : i n t c u r r e n t ; double r ; public : typedef int phase type ; typedef int observation type ; t y p e d e f enum { up , down} a c t i o n t y p e ; t y p e d e f d o u b l e r e w a r d t y p e ; Sim ( v o i d ) : c u r r e n t ( 0 ) , r ( 0 ) {} v o i d s e t P h a s e ( c o n s t p h a s e t y p e &s; ) { c u r r e n t = s %10;} c o n s t o b s e r v a t i o n t y p e& s e n s e ( v o i d ) c o n s t { r e t u r n c u r r e n t ; } reward type reward ( void ) const { return r ;} v o i d t i m e S t e p ( c o n s t a c t i o n t y p e &a; ) { i f ( a == up ) c u r r e n t ++; e l s e c u r r e n t −−; i f ( c u r r e n t < 0 ) r =−1; e l s e i f ( c u r r e n t > 9 ) r = 1 ; e l s e r = 0 ; i f ( r ! = 0 ) throw r l : : e x c e p t i o n : : T e r m i n a l ( ” Out o f r a n g e ” ) ; } }; Following the concept requirements, the class Sim naturally implements a sensor method sense that provides an observation from the current phase of the controlled dynamical system, and a method timeStep that computes a transition consecutive to some action. Note the use of exceptions for terminal states. For the sake of simplicity in further code, the following is added. typedef typedef typedef typedef typedef Sim : : p h a s e t y p e Sim : : a c t i o n t y p e r l : : I t e r a t o r t y p e d e f r l : : a g e n t : : o n l i n e : : E p s i l o n G r e e d y Critic ; ArgmaxCritic ; TestAgent ; LearnAgent ; The rllib expresses that Sarsa provides a critic, offering a Q-function. As actions are discrete, the best action (i.e., argmaxa∈A Q(s, a)) can be found by considering all the actions sequentially. This is what ArgmaxCritic offers thanks to the action enumerator Aenum, in order to deﬁne greedy and ε-greedy agents. The main function then only consists in running episodes with the appropriate agents. i n t main ( i n t a r g c , char ∗ a r g v [ ] ) { Sim simulator ; Transition transition ; ArgmaxCritic c r i t i c ; LearnAgent learner ( critic ); TestAgent tester ( critic ); A a; S s; int episode , length , s t e p =0; // // // // // // // T h i s i s what t h e a g e n t c o n t r o l s . T h i s i s some s , a , r , s ’ , a ’ d a t a . T h i s c o m p u t e s Q and argmax a Q( s , a ) . SARSA u s e s t h i s a g e n t t o l e a r n t h e p o l i c y . This behaves according to the c r i t i c . Some a c t i o n . Some s t a t e . f o r ( e p i s o d e = 0 ; e p i s o d e < 1 0 0 0 0 ; ++ e p i s o d e ) { / / L e a r n i n g p h a s e s i m u l a t o r . setPhase ( rand ()%10); r l : : episode : : sa : : r u n a n d l e a r n ( simulator , l e a r n e r , t r a n s i t i o n , 0 , length ) ; } try { / / T e s t phase simulator . setPhase (0); while ( true ) { s = simulator . sense ( ) ; a = t e s t e r . policy ( s ) ; s t e p ++; s i m u l a t o r . t i m e S t e p ( a ) ; } } c a t c h ( r l : : e x c e p t i o n : : T e r m i n a l e ) { s t d : : c o u t << s t e p << ” s t e p s . ” << s t d : : e n d l ; } return 0 ; / / t h e message p r i n t e d i s ‘ ‘10 s t e p s . ’ ’ } 3. Features of the Library Using the library requires to deﬁne the features that are speciﬁc to the problem (the simulator and the Q-function architecture in our example) from scratch, but with the help of concepts. Then, the speciﬁc features can be handled by generic code provided by the library to implement RL techniques with value function estimation. 627 F REZZA -B UET AND G EIST Currently, Q-learing, Sarsa, KTD-Q, LSTD, and policy iteration are available, as well as a multi-layer perceptron architecture. Moreover, some benchmark problems (i.e., simulators) are also provided: the mountain car, the cliff walking, the inverted pendulum and the Boyan chain. Extending the library with new algorithms is allowed, since it consists in deﬁning new templates. This is a bit more technical than only using the existing algorithms, but the structure of existing concepts helps, since it reﬂects the mathematics of RL. For example, concepts like Feature, for linear approaches mainly (i.e., Q(s, a) = θT ϕ(s, a)) and Architecture (i.e., Q(s, a) = fθ (s, a) for more general approximation) orient the design toward functional approaches of RL. The algorithms implemented so far rely on the GNU Scientiﬁc Library (see GSL, 2011) for linear algebra computation, so the GPL licence of GSL propagates to the rllib. 4. Conclusion The rllib relies only on the C++ standard and the availability of the GSL on the system. It offers state-action function approximation tools for applying RL to real problems, as well as a design that ﬁts the mathematics. The latter allows for extensions, but is also compliant with pedagogical purpose. The design of the rllib aims at allowing the user to build (using C++ programming) its own experiment, using several algorithms, several agents, on-line or batch learning, and so on. Actually, the difﬁcult part of RL is the algorithms themselves, not the script-like part of the experiment where things are put together (see the main function in our example). With a framework, in the sense of Kovacs and Egginton (2011), the experiment is not directly accessible to the user programs, since it is handled by some libraries in order to offer graphical interface or analyzing tools. The user code is then called by the framework when required. We advocate that allowing the user to call the rllib functionality at his/her convenience provides an open and extensible access to RL for students, researchers and engineers. Last, the rllib ﬁts the requirements expressed by Kovacs and Egginton (2011, Section 4.3): support of good scientiﬁc research, formulation compliant with the domain, allowing for any kind of agents and any kind of approximators, interoperability of components (the Q function of the example can be used for different algorithms and agents), maximization of run-time speed (use of C++ and templates that inline massively the code), open source, etc. Extensions of rllib can be considered, for example for handling POMDPs, and contributions of users are expected. The use of templates is unfortunately unfamiliar to many programmers, but the effort is worth it, since it brings the code at the level of the mathematical formalism, increasing readability (by a rational use of typedefs) and reducing bugs. Even if the approach is dramatically different from existing frameworks, wrappings with frameworks can be considered in further development. References Dimitri P. Bertsekas. Dynamic Programming and Optimal Control. Athena Scientiﬁc, 3rd (20052007) edition, 1995. GSL, 2011. http://http://www.gnu.org/software/gsl. Tim Kovacs and Robert Egginton. On the analysis and design of software for reinforcement learning, with a survey of existing systems. Machine Learning, 84:7–49, 2011. rllib, 2011. http://ims.metz.supelec.fr/spip.php?article122. 628

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