BA_class

Implementation of a collection of Blahut-Arimoto type algorithms for information-theoretic bounded rationality for easy access. The class contains one-step rate distortion, two-step parallel and serial cases, as developed in Genewein et al. Bounded Rationality, Abstraction, and Hierarchical Decision-Making: An Information-Theoretic Optimality Principle, an arbitrary depth version of the parallel case, and additionally the option for a bound on the prior adaption.

Simple examples

In order to do a one-step rate distortion iteration, we write

RD = BA.Solver([N,K],beta=[1.0])
RD.iterate(U)

where N and K are the dimensions of the world and action space, respectively, and U is the utility function in form of an NtimesK matrix (numpy array of shape (N,K)). For a two-step iteration with intermediate dimension M we write

ser = BA.Solver([N,M,K],beta=[12.0,10.0],BAtype='ser')            # serial 2-step case
ser.iterate(U)

par = BA.Solver([N,M,K],beta=[12.0,10.0],BAtype='par')            # parallel 2-step case
par.iterate(U)

and for higher depth we just add more intermediate dimension and betas:

par3 = BA.Solver([N,M1,M2,K],beta=[12.0,10.0,5.0],BAtype='par')   # parallel 3-step case
par3.iterate(U)

See also here for a different implementation of some of the cases included here based on pr_func, and here for a modular implementation of Blahut-Arimoto type algorithms for general bounded rational multi-agent architectures based on Gottwald, Braun. Systems of bounded rational agents with information-theoretic constraints.

Overview

Usage

import BA_class as BA                         # import the module
dims = [N,M1,...,Mn,K]                        # dimensions (world,...intermediate...,action)
par = BA.Solver(dims,beta=beta,BAtype='par')  # beta= [beta1,...], len(beta) = number of steps
par = BA.Solver(dims,beta=beta,alpha=alpha,BAtype='par')  # alpha = [alpha1,...] for bounded priors
par.iterate(U)                                # iteration with utility U

Interesting quantities

par.EU            # Expected utility
par.FE            # Free Energy
par.DKL           # Kullback-Leibler divergences between priors and posteriors
par.DKLpr         # Kullback-Leibler divergences between fixed uniform priors and the priors
par.joint         # the joint distribution as a numpy array
par.pagw          # resulting total policy p(a|w) (intermediate variables marginalized out)
par.post          # list of all posteriors
par.prior         # list of all priors (exception: prior[0] is the world state distribution)

Special options

par.iterate(U,max_iterations=10000)           # maximum number of iterations
par.iterate(U,precision=1e-10)                # precision for the stopping condition
par.iterate(U,pw=np.array([]))                # specification of the world state distribution
par.iterate(U,p0=np.array([]))                # fixed prior for the prior restriction

Other methods

BA.show(arr)                                  # plots the array arr (1d: barplot, 2d: pcolor)