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__DP.jl
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module __DP
using LinearAlgebra
using ProbUtils
using GridWorld
using InfoUtils
using PlotUtils
using PyPlot
using Distributions
export SolveMazeGoalCond
abstract type TSR <: AbstractArray{Float64,any} end
# const gamma = 0.975
const gamma = 1.0
const nDP = 100
function SolveMazeGoalCond(dims::Tuple, C::Array{Int}, G::Array{Int})
dimX1, dimX2, dimA, dimG, dimH = dims
dimX = dimX1*dimX2
# dimG = dimX
println(dims)
actionProb = 1.0
Pgxi_ai = Array{Float64}(undef, dimG, dimX, dimA, 1, 1)
Pgxiai_xj, Rgxiaixj = InitPxiaig_xj(dims, G, C, actionProb)
Pxiai_xj = Array{Float64}(undef, dimX, dimA, dimX, 1)
Rxiaixj = Array{Float64}(undef, dimX, dimA, dimX, 1)
Vgx = Array{Float64}(undef, dimG, dimX, 1, 1)
Qgxa = Array{Float64}(undef, dimG, 1, dimX, dimA, 1, 1)
for g in 1:dimG#length(G)
Pxiai_xj = Pgxiai_xj[g, :, :, :, :]
Rxiaixj = Rgxiaixj[g, :, :, :, :]
V, Q, Pxi_ai = SolveMaze(dims, C, Pxiai_xj, Rxiaixj)
Pgxi_ai[g, :, :, 1, 1] = Pxi_ai
Vgx[g, :, 1, 1] = V
Qgxa[g, 1, :, :, 1, 1] = Q
end
return Vgx, Qgxa, Pgxi_ai, Pgxiai_xj
end
function SolveMazeGoalCond(dimX1, dimX2, dimA)
dimX = dimX1*dimX2
dimG = dimX
dimH = dimX
dims = (dimX1, dimX2, dimA, dimG, dimH)
C = CreateWalls(dims, "B")
G = GenerateGoalSet(dims, "fullX", C)
actionProb = 1.0
PgxCaC_xN, RgxCaChC_xN = InitPxiaig_xj(dims, G, C, actionProb)
QghC_hN = InitAtBetaInfinityQghC_hN(dims)
Ph_g = zeros(Float64, dimG, 1, 1, dimH, 1, 1, 1)
Ph_g[:, 1, 1, :, 1, 1, 1] = Matrix{Float64}(I, dimG, dimH)
QgxChC_hN = InitAtBetaInfinityQgxChC_hN(dims)
Pxh_g = InitPxh_gAtBetaInfinity(dims)
QxChC_hN = EncoderMarginal(QgxChC_hN, Pxh_g)
IghC_hN = zeros(Float64, (dimG, 1, 1, dimH, 1, 1, dimH))
TotRgxCaChC_xN = RgxCaChC_xN
Vgxh, PxChP_aC = BellmanStateIndependent(dims, PgxCaC_xN, TotRgxCaChC_xN, QghC_hN, Ph_g)
return Vgxh, PxChP_aC
end
function SolveMaze(dims, C, Pxiai_xj, Rxiaixj)
dimX1, dimX2, dimA = dims
dimX = dimX1*dimX2
actionProb = 1.0
Xf = dimX
Xo = 1
Pxi_ai = Normalize(ones(dimX, dimA, 1, 1), (2, ))
Rxiai = Expectation(Rxiaixj, Pxiai_xj, [3])
Qi = zeros(dimX, dimA, 1, 1)
for i in 1:100
Pxiai_xjaj = broadcast(*, Pxiai_xj, permutedims(Pxi_ai, (3, 4, 1, 2)))
Qj = Expectation(Pxiai_xjaj, permutedims(Qi, (3, 4, 1, 2)), [3, 4])
Qi = Rxiai + Qj
if i % 20 == 0
Pxi_ai = zeros(dimX, dimA, 1, 1)
# randn: to prevent bias in Q, caused by the order of the actions
Pxi_ai[findmax(Qi .+ 0.001*randn(dimX, dimA, 1, 1), dims=2)[2]] .= 1.0
end
end
return Expectation(Qi, Pxi_ai, [2]), Qi, Pxi_ai
end
function Horizon10(dims, Pxiai_xj, Pxi_ai, P)
dimX1, dimX2, dimA = dims
dimX = dimX1*dimX2
P = zeros(dimX, dimA, dimX, dimA, dimX, dimA, dimX, dimA, dimX, dimA)
for t = 1:10
end
end
function mainSolveMaze()
dimX1 = 3
dimX2 = 3
dimA = 5
dimX = dimX1*dimX2
dims = (dimX1, dimX2, dimA, -1, -1)
Xf = dimX
Xo = 1
actionProb = 1.0
C = CreateWalls(dims, "B")
Pxiai_xj, Rxiaixj = SetPxj_xiai(dims, actionProb, C, Xf, Xo)
V, Pxi_ai = SolveMaze(dims, C, Pxiai_xj, Rxiaixj)
# display(reshape(V[:, 1, 1, 1], dimX1, dimX2)); println()
# display(Pxi_ai); println();
# Pxi_ai = Normalize(ones(dimX, dimA, 1, 1), (2,))
Pxj_aj = permutedims(Pxi_ai, (3, 4, 1, 2))
Px0 = Normalize(ones(dimX, 1, 1, 1), (1,))
# Px0 = zeros(dimX, 1, 1, 1); Px0[1] = 1.0;
Px0_a0x1 = broadcast(*, Pxiai_xj, Pxi_ai)
Px0_x1 = sum(Px0_a0x1, dims=2)
Px0x1 = broadcast(*, Px0, Px0_x1)
Px1 = sum(Px0x1, dims=1)
Px0a0x1 = broadcast(*, Px0_a0x1, Px0)
Px0a0x1a1= broadcast(*, Px0a0x1, Pxj_aj)
Px0a0_x1a1 = broadcast(*, Pxiai_xj, Pxj_aj)
Px1a1 = sum(Px0a0x1a1, dims=[1, 2])
# display(reshape(Px0[:, 1, 1, 1], (dimX1, dimX1))); println()
# display(reshape(Px1[1, 1, :, 1], (dimX1, dimX1))); println()
# display( Px0x1[:, 1, :, 1]); println()
# display(Px0_x1[:, 1, :, 1]); println()
Hx1 = -sum(log2.(Px1 .^ Px1))
Hx0_x1 = -sum(log2.(Px0_x1 .^ Px0x1))
Hx0a0_x1 = -sum(log2.(Pxiai_xj .^ Px0a0x1 ))
Hx1a1 = -sum(log2.( Px1a1 .^ Px1a1))
Hx0a0_x1a1 = -sum(log2.( Px0a0_x1a1 .^ Px0a0x1a1))
println((Hx1, Hx0_x1, Hx0a0_x1))
println("I[x1;x0], I[x1;a0|x0], I[x1, a1; x0, a0])=",(Hx1 - Hx0_x1, Hx0_x1 - Hx0a0_x1, Hx1a1 - Hx0a0_x1a1))
end
function mainSolveMazeGoalCond()
dimX1 = 3
dimX2 = 3
dimA = 5
dimX = dimX1*dimX2
dims = (dimX1, dimX2, dimA, dimX, dimX)
C = CreateWalls(dims, "B")
G = GenerateGoalSet(dims, "fullX", C)
actionProb = 1.0
Pgxi_ai = Array{Float64}(undef, dimX, dimX, dimA, 1, 1)
Pgxiai_xj, Rgxiaixj = InitPxiaig_xj(dims, G, C, actionProb)
Pxiai_xj = Array{Float64}(undef, dimX, dimA, dimX, 1)
Rxiaixj = Array{Float64}(undef, dimX, dimA, dimX, 1)
for g in 1:length(G)
Pxiai_xj = Pgxiai_xj[g, :, :, :, :]
Rxiaixj = Rgxiaixj[g, :, :, :, :]
V, Pxi_ai = SolveMaze(dims, C, Pxiai_xj, Rxiaixj)
Pgxi_ai[g, :, :, 1, 1] = Pxi_ai
# display(reshape(V[:, 1, 1, 1], dimX1, dimX2)); println()
end
# display(Pxi_ai); println();
# Pgxi_ai = Normalize(ones(dimX, dimX, dimA, 1, 1), (3,))
# println(size( Pgxi_ai ))
Pgxj_aj = permutedims(Pgxi_ai, (1, 4, 5, 2, 3))
Px0 = Normalize(ones(1, dimX, 1, 1, 1), (2,))
Pg = Normalize(ones(dimX, 1, 1, 1, 1), (1,))
Pgx0 = broadcast(*, Px0, Pg)
# Px0 = zeros(dimX, 1, 1, 1); Px0[1] = 1.0;
Pgx0_a0x1 = broadcast(*, Pgxiai_xj, Pgxi_ai)
Pgx0a0_x1a1 = broadcast(*, Pgxiai_xj, Pgxj_aj)
Px0_a0x1 = sum(broadcast(*, Pgx0_a0x1, Pg), dims=1)
Px0a0_x1a1 = sum(broadcast(*, Pgx0a0_x1a1, Pg), dims=1)
Px0_x1 = sum(Px0_a0x1, dims=[3])
Px0x1 = broadcast(*, Px0, Px0_x1)
Px1 = sum(Px0x1, dims=4)
Px0a0x1 = broadcast(*, Px0_a0x1, Px0)
Px0a0x1a1= broadcast(*, Px0a0x1, Pgxj_aj)
# Px0a0_x1a1 = broadcast(*, Pxiai_xj, Pgxj_aj)
Px1a1 = sum(Px0a0x1a1, dims=[1, 2])
Hx1 = -sum(log2.(Px1 .^ Px1))
Hx0_x1 = -sum(log2.(Px0_x1 .^ Px0x1))
# println((Hx1, Hx0_x1))
# Hx0a0_x1 = -sum(log2.(Pxiai_xj .^ Px0a0x1 ))
Hx1a1 = -sum(log2.( Px1a1 .^ Px1a1))
println((size(Px0a0_x1a1), size(Px0a0x1a1)))
Hx0a0_x1a1 = -sum(log2.( Px0a0_x1a1 .^ Px0a0x1a1))
#
#
#
# println((Hx1, Hx0_x1, Hx0a0_x1))
println("I[x1;x0], I[x1, a1; x0, a0])=", (Hx1 - Hx0_x1, Hx1a1 - Hx0a0_x1a1))
end
function BellmanIB( dims::Tuple,
Pgxiai_xj::Array{Float64},
R::Array{Float64},
Qgxa_h::Array{Float64},
Pxa_g::Array{Float64}, Px_g::Array{Float64}, beta::Float64, gamma::Float64)
dimX1, dimX2, dimA, dimG, dimH = dims
dimX = dimX1*dimX2
Lcurn = zeros(dimG, dimX, dimA, dimH, 1, 1, 1)
Lnext = []
Lxah = []
LnextExpected = []
Pxih_ai = InitProb((1, dimX, dimA, dimH, 1, 1, 1), (3,))
Qxa_hg = JointProb(Qgxa_h, Pxa_g)
# display(Qxa_hg)
# println()
if ~isempty(findall(iszero, Qxa_hg))
println("~isempty(findall(izsero, Qxa_hg))")
exit(1)
end
Qxa_h = Marginal(Qxa_hg, (1,))
Qxah_g = broadcast(/, Qxa_hg, Qxa_h)
Iq = log.(broadcast(/, Qgxa_h, Qxa_h))
for gi = 1:dimG, xi = 1:dimX
if xi == gi
Iq[gi, xi, :, :, 1, 1, 1] .= 0.0
end
end
# println("Iq, $(maximum(Iq)), $(minimum(Iq)), $(mean(Iq))")
r = broadcast(+, (1/beta)*Iq, -(1)*R)
for iter = 1:500
Pxjh_aj = permutedims(Pxih_ai, (1, 5, 6, 4, 2, 3, 7))
Lnext = permutedims(Lcurn, (1, 5, 6, 4, 2, 3, 7))
Pnext = JointProb(Pgxiai_xj, Pxjh_aj)
LnextExpected = Expectation(Pnext, Lnext, [5, 6])
Lcurn = -(r + gamma*LnextExpected)
if mod(iter, 250) == 0
Pxih_ai .= 0.0
Lxah = Expectation(Lcurn, Qxah_g, [1])
# Lxah = Expectation(Lcurn, Px_g, [1])
# Lxah = Expectation(Lcurn, Pxa_g, [1])
Pxih_ai[findmax(Lxah, dims=3)[2]] .= 1.0
end
# println("$(iter), $(maximum(Lcurn)), $(minimum(Lcurn)), $(mean(Lcurn))")
end
# exit(1)
# fi = figure()
# fig = PyPlot.imshow(reshape(Lcurn[1, 1, 1, :], (dimX1, dimX2)), interpolation="none", extent=[1, dimX1, 1, dimX2])
# colorbar(fig, ticks=[minimum(Lcurn[1, 1, 1, :]), maximum(Lcurn[1, 1, 1, :])])
# show()
# close(fi)
return Lcurn, Pxih_ai, LnextExpected, Lxah
end
function BellmanEntropyEncoderStateAction( dims::Tuple,
PgxCaC_xN::Array{Float64},
R::Array{Float64},
QgxChC_hN::Array{Float64},
Pg::Array{Float64})
println("start BellmanStateDependent at $(@__MODULE__), $(@__LINE__)")
dimX1, dimX2, dimA, dimG, dimH = dims
dimX = dimX1*dimX2
Vcurn = zeros(Float64, dimG, dimX, 1, dimH, 1, 1, 1)
PxChP_aC = InitProb((1, dimX, dimA, dimH, 1, 1, 1), (3,))
for iter in 1:nDP
Vnext = permutedims(Vcurn, (1, 5, 3, 7, 2, 6, 4))
Rnext = broadcast(+, R, gamma*Vnext)
Ptrans = JointProb(PgxCaC_xN, QgxChC_hN)
Qgxah = Expectation(Rnext, Ptrans, [5, 7])
Vcurn = Expectation(Qgxah, PxChP_aC, [3]) # Vgxh
if mod(iter, 10) == 0
# println("[$(@__MODULE__), $(@__LINE__)]: iter[$(iter)]")
# Pxh_g = Normalize(exp.(-Vcurn), (1,))
PxChP_aC .= 0.0
Qxah = Expectation(Qgxah, Pxh_g, [1])
PxChP_aC[findmax(Qxah, dims=3)[2]] .= 1.0
end
end
return Vcurn, PxChP_aC, Pxh_g
end
function LogValueIterationGivenEncoder( dims::Tuple,
PgxCaC_xN::Array{Float64},
R::Array{Float64},
Pg::Array{Float64},
Qgxiai_h::Array{Float64},
gamma::Float64, beta::Float64 )
dimX1, dimX2, dimA, dimG, dimH = dims
dimX = dimX1*dimX2
Qgxiai_h, Z = EntropyEncoder(dims, Pxih_ai, PgxCaC_xN, Lxiai, gamma)
Hgsa_h = -sum(Qgxiai_h .* log.(Qgxiai_h), dims=7)
r = Expectation(Hgsa_h + beta*Expectation(PgxCaC_xN, R, [5]), [1])
Lxiai = zeros(1, dimX, dimA, 1, 1, 1, 1 )
Lxiai_prev = Lxiai
# Pxjh_aj = RandomPolicy(dims, true)
for i = 1:100
Pxiai_xjai = sum(JointProb(Pg,JointProb(Qgxiai_h,JointProb(PgxCaC_xN, Pxjh_aj))),dims=[1, 7])
TEST_PROB_UNITY(Pxiai_xjai, "Pxiai_xjai", "LogValueIterationGivenEncoder", [5, 6])
exit(1)
end
end
function LogValueIterationTest( dims::Tuple,
PgxCaC_xN::Array{Float64},
R::Array{Float64},
Pg::Array{Float64},
gamma::Float64, beta::Float64 )
dimX1, dimX2, dimA, dimG, dimH = dims
dimX = dimX1*dimX2
aStr = ActionStrings(dimA)
r = Expectation(PgxCaC_xN, R, [5])
beta = 10.00000010
gamma = 0.97
Lgxiai = zeros(dimG, dimX, dimA, 1, 1, 1, 1 )
# Lgxiai_prev = Lgxiai
# Pxih_ai = Normalize(ones(1, dimX, dimA, dimH, 1, 1, 1), (3,))
hgxMAX = 100.0
hgx = 0.0
vgx = 0.0
Vgx = []
Hgx = []
Q = []
Pxih_ai = []
Pxjh_aj = []
Harr = []
Varr = []
Lgxjaj = []
for beta = 2:0.001:15
# for beta = 2:0.05:15
# Lgxiai = zeros(dimG, dimX, dimA, 1, 1, 1, 1 )
for iSample = 1:1
Pxih_ai = Normalize(ones(1, dimX, dimA, dimH, 1, 1, 1), (3,))
for i = 1:100
Lgxjaj = permutedims(Lgxiai, (1, 5, 6, 4, 2, 3, 7))
Pxjh_aj = permutedims(Pxih_ai, (1, 5, 6, 4, 2, 3, 7))
expArgInner = Expectation(Pxjh_aj, Lgxjaj, [6])
expArg = Expectation(PgxCaC_xN, expArgInner, [5])
Lgxiai = (-log.(sum(exp.(-gamma*expArg), dims=[4])) - beta*r)
if mod(i, 50) == 0
# if false
Pxih_ai = zeros(dimG, dimX, dimA, 1, 1, 1, 1)
Pxih_ai[findmax(Lgxiai, dims=3)[2]] .= 1.0
Pxih_ai = Normalize(Pxih_ai .+ 0.1, (3,))
Vgx = Expectation(Lgxiai, Pxih_ai, [3])
vgx = sum(Vgx)/(dimX*dimG)
Pxih_ai = permutedims(Pxih_ai, (4, 2, 3, 1, 5, 6, 7))
expArgInner = Expectation(Pxjh_aj, Lgxjaj, [6])
expArg = Expectation(PgxCaC_xN, expArgInner, [5])
Q = broadcast(/, exp.(-gamma*expArg), sum(exp.(-gamma*expArg), dims=[4]))
H = -sum(log.(Q.^Q) , dims=[4])
tmp = permutedims(Pxih_ai, (4, 2, 3, 1, 5, 6, 7))
Hgx = Expectation(H, tmp, [4])
hgx = sum(Hgx)/(dimX*dimG)
end
end
# if hgx > hgxMAX
# tmp11 = hgx
# hgx = hgxMAX
# hgxMAX = tmp11
# end
# if mod(i, 10) == 0
if false
Pxih_ai = zeros(dimG, dimX, dimA, 1, 1, 1, 1)
Pxih_ai[findmax(Lgxiai, dims=3)[2]] .= 1.0
Pxih_ai = Normalize(Pxih_ai .+ 0.1, (3,))
Vgx = Expectation(Lgxiai, Pxih_ai, [3])
vgx = sum(Vgx)/(dimX*dimG)
Pxih_ai = permutedims(Pxih_ai, (4, 2, 3, 1, 5, 6, 7))
expArgInner = Expectation(Pxjh_aj, Lgxjaj, [6])
expArg = Expectation(PgxCaC_xN, expArgInner, [5])
Q = broadcast(/, exp.(-gamma*expArg), sum(exp.(-gamma*expArg), dims=[4]))
H = -sum(log.(Q.^Q) , dims=[4])
tmp = permutedims(Pxih_ai, (4, 2, 3, 1, 5, 6, 7))
Hgx = Expectation(H, tmp, [4])
hgx = sum(Hgx)/(dimX*dimG)
end
if false
display(Lgxiai[7, :, :, 1, 1, 1, 1])
println()
Pxih_ai = zeros(dimG, dimX, dimA, 1, 1, 1, 1)
Pxih_ai[findmax(Lgxiai, dims=3)[2]] .= 1.0
Vgx = Expectation(Lgxiai, Pxih_ai, [3])
Pxih_ai = permutedims(Pxih_ai, (4, 2, 3, 1, 5, 6, 7))
for xi = 1:dimX
println(aStr[findall(!iszero, Pxih_ai[1, xi, :, 7, 1, 1, 1])])
end
end
end
if true
display(Lgxiai[7, :, :, 1, 1, 1, 1])
println()
Pxih_ai = zeros(dimG, dimX, dimA, 1, 1, 1, 1)
Pxih_ai[findmin(Lgxiai, dims=3)[2]] .= 1.0
Vgx = Expectation(Lgxiai, Pxih_ai, [3])
Pxih_ai = permutedims(Pxih_ai, (4, 2, 3, 1, 5, 6, 7))
for xi = 1:dimX
println(aStr[findall(!iszero, Pxih_ai[1, xi, :, 7, 1, 1, 1])])
end
end
# H = -sum(log.(Q.^Q) , dims=[4])
# tmp = permutedims(Pxih_ai, (4, 2, 3, 1, 5, 6, 7))
# Hgx = Expectation(H, tmp, [4])
# Vgx = Expectation(Lgxiai, Pxih_ai, [3])
if ~isempty(findall( Vgx .> 0.0))
break
end
display(reshape(Vgx[7, :, 1, 1, 1, 1, 1] .- 0*maximum(Vgx[7, :, 1, 1, 1, 1, 1]), (dimX1, dimX2)))
println()
display(reshape(Hgx[7, :, 1, 1, 1, 1, 1] .- 0*maximum(Hgx[7, :, 1, 1, 1, 1, 1]), (dimX1, dimX2)))
println()
display((beta, sum(Hgx)/(dimX*dimG), sum(Vgx)/(dimX*dimG)))
println()
push!(Harr, hgx)
push!(Varr, vgx)
end
Varr = Varr
# PyPlot.plot(reverse(Harr), reverse(Varr))
fh = figure(1)
PyPlot.plot(1.44*(Harr[2:end-1]), abs.(Varr[2:end-1]), label=string(L"tempreture, T=1/\beta,", " increases from left to right"))
# PyPlot.ylabel(string(L"Q(s, a)", ", average number of steps to the goal"))
PyPlot.ylabel(string("average number of steps to the goal"))
# PyPlot.xlabel(L"{H}(h\mid g, s, a) = I[h, g\mid s, a] - {H}_{constant\;prior}(h\mid s, a)")
# PyPlot.xlabel(string(L"{H}(h\mid g, s, a)", ", uncertanty (in bits) of ", L"h", " given ", L"g, s, a"))
PyPlot.xlabel(string("uncertanty (in bits) of ", L"h", " given ", L"g, s, a"))
plt.legend()
# plt.title(L"L(s, a)=I[h, g\mid s, a] - \beta Q(s, a)")
plt.title(string(L"g\in G, h\in H", " : original, compressed goals"))
# PyPlot.plot((Varr[2:end-1]), (Harr[2:end-1]))
savefig(string("./plotsDP/", "HvsV.png"), bbox_inches="tight")
close(fh)
# show()
return Lgxiai
end
function LogValueIteration( dims::Tuple,
PgxCaC_xN::Array{Float64},
R::Array{Float64},
Pg::Array{Float64},
gamma::Float64, beta::Float64 )
dimX1, dimX2, dimA, dimG, dimH = dims
dimX = dimX1*dimX2
r = Expectation(PgxCaC_xN, R, [5])
Lxiai = zeros(1, dimX, dimA, 1, 1, 1, 1 )
Lxiai_prev = Lxiai
# Pxih_ai = RandomPolicy(dims)
for i = 1:100
_, Z = EntropyEncoder(dims, Pxih_ai, PgxCaC_xN, Lxiai, gamma)
Lxiai = -Expectation(Pg, log.(Z) + beta*r, [1])
display(Lxiai[1, :, :, 1, 1, 1, 1])
# if i > 1
println(abs(maximum(Lxiai - Lxiai_prev)))
# end
Lxiai_prev = Lxiai
end
return Lxiai
end
function BellmanStateDependent( dims::Tuple,
PgxCaC_xN::Array{Float64},
R::Array{Float64},
QgxChC_hN::Array{Float64}, Pxh_g::Array{Float64})
println("start BellmanStateDependent at $(@__MODULE__), $(@__LINE__)")
dimX1, dimX2, dimA, dimG, dimH = dims
dimX = dimX1*dimX2
Vcurn = zeros(Float64, dimG, dimX, 1, dimH, 1, 1, 1)
PxChP_aC = InitProb((1, dimX, dimA, dimH, 1, 1, 1), (3,))
Qxah = zeros(Float64, 1, dimX, dimA, 1, dimH, 1, 1, 1)
for iter in 1:nDP
Vnext = permutedims(Vcurn, (1, 5, 3, 7, 2, 6, 4))
Rnext = broadcast(+, R, gamma*Vnext)
Ptrans = JointProb(PgxCaC_xN, QgxChC_hN)
Qgxah = Expectation(Rnext, Ptrans, [5, 7])
Vcurn = Expectation(Qgxah, PxChP_aC, [3]) # Vgxh
if mod(iter, 10) == 0
PxChP_aC .= 0.0
Qxah = Expectation(Qgxah, Pxh_g, [1])
if true #last working
PxChP_aC[findmax(Qxah, dims=3)[2]] .= 1.0
else
# maxIds = 0.0
# findmax(A)[2]
end
end
end
return Vcurn, PxChP_aC, Pxh_g, Qxah
end
function BellmanStateIndependent( dims::Tuple,
PgxCaC_xN::Array{Float64},
R::Array{Float64},
QghC_hN::Array{Float64}, Ph_g::Array{Float64})
println("start BellmanStateIndependent at $(@__MODULE__), $(@__LINE__)")
dimX1, dimX2, dimA, dimG, dimH = dims
dimX = dimX1*dimX2
Vcurn = zeros(Float64, dimG, dimX, 1, dimH, 1, 1, 1)
PxChP_aC = InitProb((1, dimX, dimA, dimH, 1, 1, 1), (3,))
for iter in 1:nDP
Vnext = permutedims(Vcurn, (1, 5, 3, 7, 2, 6, 4))
Rnext = broadcast(+, R, gamma*Vnext)
Ptrans = JointProb(PgxCaC_xN, QghC_hN)
Qgxah = Expectation(Rnext, Ptrans, [5, 7])
Vcurn = Expectation(Qgxah, PxChP_aC, [3]) # Vgxh
if mod(iter, 10) == 0
println("[$(@__MODULE__), $(@__LINE__)]: iter[$(iter)]")
PxChP_aC .= 0.0
Qxah = Expectation(Qgxah, Ph_g, [1])
PxChP_aC[findmax(Qxah, dims=3)[2]] .= 1.0
end
end
return Vcurn, PxChP_aC
end
function main()
dimX1 = 3
dimX2 = 3
dimX = dimX1*dimX2
dimA = 5
dimG = dimX
dimH = dimX
dims = (dimX1, dimX2, dimA, dimG, dimH)
C = CreateWalls(dims, "B")
G = GenerateGoalSet(dims, "fullX", C)
actionProb = 1/dimA
# actionProb = 1.0
actionProb = 0.8
PgxCaC_xN, RgxCaChC_xN = InitPxiaig_xj(dims, G, C, actionProb)
QghC_hN = InitAtBetaInfinityQghC_hN(dims)
Ph_g = zeros(Float64, dimG, 1, 1, dimH, 1, 1, 1)
Ph_g[:, 1, 1, :, 1, 1, 1] = Matrix{Float64}(I, dimG, dimH)
QgxChC_hN = InitAtBetaInfinityQgxChC_hN(dims)
Pxh_g = InitPxh_gAtBetaInfinity(dims)
Pxh_g = Normalize(Pxh_g .+ 0.01, (1,))
# QxChC_hN = zeros(1, dimX, 1, dimH, 1, 1, dimH)
# for xi in 1:dimX
# QxChC_hN[1, xi, 1, :, 1, 1, :] = ones(dimH, dimH)/dimH
# end
# Pxh_g = zeros(dimG, dimX, 1, dimH, 1, 1, 1)
# for xi in 1:dimX
# Pxh_g[:, xi, 1, :, 1, 1, 1] = ones(dimG, dimH)/dimG
# end
QxChC_hN = EncoderMarginal(QgxChC_hN, Pxh_g)
# println(QxChC_hN[1, 1, 1, 1:3, 1, 1, :])
# exit(1)
# IgxCaChC = zeros(Float64, (dimG, dimX, dimA, 1, 1, 1, dimH))
# IghC_hN = ones(Float64, (dimG, 1, 1, dimH, 1, 1, dimH))
IghC_hN = zeros(Float64, (dimG, 1, 1, dimH, 1, 1, dimH))
beta = 2.0
TotRgxCaChC_xN = broadcast(+, beta*RgxCaChC_xN, IghC_hN)
stateIndependent = false
if stateIndependent
Vgxh, PxChP_aC = BellmanStateIndependent(dims, PgxCaC_xN, TotRgxCaChC_xN, QghC_hN, Ph_g)
Vxh = Expectation(Vgxh, Ph_g, [1])
stepSize = AvrgStepSize(dims, Vxh)
printGridVxh(dims, Vxh, 100, "StateIndpnd", 1.0)
println("\nstepSize=$(stepSize)")
end
Vgxh, PxChP_aC, Pxh_g = BellmanStateDependent(dims, PgxCaC_xN, TotRgxCaChC_xN, QgxChC_hN, Pxh_g)
Vxh = Expectation(Vgxh, Pxh_g, [1])
stepSize = AvrgStepSize(dims, Vxh)
# printGridVxh(dims, Vxh, 100, "StateDpnd", 1.0)
println("\nstepSize=$(stepSize)")
# exit(1)
# QgxChC_hN = Encoder(dims, QxChC_hN, Vgxh, PgxCaC_xN, PxChP_aC, gamma)
# println(QgxChC_hN[1, 1, 1, 1, 1, 1, :])
# exit(1)
# QxChC_hN = EncoderMarginal(QgxChC_hN, Pxh_g)
QgxChC_hN, QxChC_hN = BA(dims, QxChC_hN, Vgxh, PgxCaC_xN, PxChP_aC, Pxh_g, gamma)
# println("QgxChC_hN=\n", QgxChC_hN)
# println("QxChC_hN=\n", QxChC_hN)
MI = UpdateMI(dims, QgxChC_hN, Pxh_g )
# println("MI=")
# display(MI)
for i in 1:50
Vgxh, PxChP_aC, Pxh_g = BellmanStateDependent(dims, PgxCaC_xN, TotRgxCaChC_xN, QgxChC_hN, Pxh_g)
Vxh = Expectation(Vgxh, Pxh_g, [1])
stepSize = AvrgStepSize(dims, Vxh)
# printGridVxh(dims, Vxh, 100, "StateDpnd", 1.0)
println("\nstepSize=$(stepSize)")
QgxChC_hN, QxChC_hN = BA(dims, QxChC_hN, Vgxh, PgxCaC_xN, PxChP_aC, Pxh_g, gamma)
end
end
function mainEntropyEncoder()
dimX1 = 5
dimX2 = 5
dimX = dimX1*dimX2
dimA = 5
dimG = dimX
dimH = dimX
dims = (dimX1, dimX2, dimA, dimG, dimH)
C = CreateWalls(dims, "B")
G = GenerateGoalSet(dims, "fullX", C)
actionProb = 1/dimA
actionProb = 1.0
beta = 1.0
PgxCaC_xN, RgxCaChC_xN = InitPxiaig_xj(dims, G, C, actionProb)
QghC_hN = InitAtBetaInfinityQghC_hN(dims)
Ph_g = zeros(Float64, dimG, 1, 1, dimH, 1, 1, 1)
Ph_g[:, 1, 1, :, 1, 1, 1] = Matrix{Float64}(I, dimG, dimH)
QgxChC_hN = InitAtBetaInfinityQgxChC_hN(dims)
Pxh_g = InitPxh_gAtBetaInfinity(dims)
Pg = Normalize(ones(dimG, 1, 1, 1, 1, 1, 1), (1,))
IghC_hN = zeros(Float64, (dimG, 1, 1, dimH, 1, 1, dimH))
# beta = 2.0
# TotRgxCaChC_xN = broadcast(+, beta*RgxCaChC_xN, IghC_hN)
TotRgxCaChC_xN = beta*RgxCaChC_xN
Vgxh, PxChP_aC, Pxh_g, Qxah = BellmanStateDependent(dims, PgxCaC_xN, TotRgxCaChC_xN, QgxChC_hN, Pxh_g)
Vxh = Expectation(Vgxh, Pxh_g, [1])
Qgxa = permutedims(Qxah, (4, 2, 3, 1, 5, 6, 7))
Pgxi_ai = permutedims(PxChP_aC, (4, 2, 3, 1, 5, 6, 7))
Vgx = Expectation(Qgxa, Pgxi_ai, [3])
Qxa = Expectation(Qgxa, Pg, [1])
for hi = 1:dimX
display( reshape( Vxh[1, :, 1, hi, 1, 1, 1], (dimX1, dimX2) ) )
println("\nVgx:")
display( reshape( Vgx[hi, :, 1, 1, 1, 1, 1], (dimX1, dimX2) ) )
println()
end
println("\nVx:")
Vx = Expectation(Vgx, Pg, [1])
# Vx = sum(Vgx, dims=1)
display( reshape( Vx[1, :, 1, 1, 1, 1, 1], (dimX1, dimX2) ) )
println()
display(Vgx)
println()
display(sum(Vgx, dims=1))
plotGridFxiai(dims, Qxa, 897, "SSS", beta)
exit(1)
# Lxiai = LogValueIteration(dims, PgxCaC_xN, RgxCaChC_xN, Pg, gamma, beta)
# plotGridFxiai(dims, Lxiai, 777, "Lxiai", beta)
# LogValueIterationGivenEncoder(dims, PgxCaC_xN, R, Pg, Qgxiai_h, gamma, beta)
end
function mainLogValueIterationTest()
dimX1 = 3
dimX2 = 3
dimX = dimX1*dimX2
dimA = 5
dimG = dimX
dimH = dimX
dims = (dimX1, dimX2, dimA, dimG, dimH)
actionProb = 1/dimA
rctionProb = 1.0
actionProb = 0.75
beta = 1.0
gamma = 0.975
gamma = 1.0
C = CreateWalls(dims, "B")
G = GenerateGoalSet(dims, "fullX", C)
PgxCaC_xN, RgxCaChC_xN = InitPxiaig_xj(dims, G, C, actionProb)
Pg = Normalize(ones(dimG, 1, 1, 1, 1, 1, 1), (1,))
Lgxiai = LogValueIterationTest( dims, PgxCaC_xN, RgxCaChC_xN, Pg, gamma,beta)
end
function mainIB()
dimX1 = 3
dimX2 = 3
dimX = dimX1*dimX2
dimA = 5
dimG = dimX
dimH = dimX
dims = (dimX1, dimX2, dimA, dimG, dimH)
C = CreateWalls(dims, "B")
G = GenerateGoalSet(dims, "fullX", C)
actionProb = 1/dimA
actionProb = 1.0
# actionProb = 0.8
PgxCaC_xN, RgxCaChC_xN = InitPxiaig_xj(dims, G, C, actionProb)
QghC_hN = InitAtBetaInfinityQghC_hN(dims)
Ph_g = zeros(Float64, dimG, 1, 1, dimH, 1, 1, 1)
Ph_g[:, 1, 1, :, 1, 1, 1] = Matrix{Float64}(I, dimG, dimH)
IghC_hN = zeros(Float64, (dimG, 1, 1, dimH, 1, 1, dimH))
beta = 1.0
TotRgxCaChC_xN = broadcast(+, beta*RgxCaChC_xN, IghC_hN)
Vgxh, PxChP_aC = BellmanStateIndependent(dims, PgxCaC_xN, TotRgxCaChC_xN, QghC_hN, Ph_g)
Vxh = Expectation(Vgxh, Ph_g, [1])
stepSize = AvrgStepSize(dims, Vxh)
printGridVxh(dims, Vxh, 100, "StateIndpnd", 1.0)
println("\nstepSize=$(stepSize)")
PxC_g = Normalize(ones(dimG, dimX, 1, 1, 1, 1, 1), (1,))
PgxC_aC = permutedims(PxChP_aC, [4, 2, 3, 1, 5, 6, 7])
Px_ag = broadcast(*, PgxC_aC, PxC_g)
# for xi = 1:dimX
# display(Px_ag[:, xi, :, 1, 1, 1, 1])
# println()
# end
Pxg_h, Px_h, Pxh_a, Pxh_g = IB(dims, Px_ag, 100.0)
display(PxC_g[:, :, 1, 1, 1, 1, 1]')
println()
display(Px_h[1, :, 1, :, 1, 1, 1])
A1 = permutedims(PxC_g[:, :, 1, 1, 1, 1, 1], (2, 1))
A2 = Px_h[1, :, 1, :, 1, 1, 1]
plotPxi_xj(dims, A1, 333, "Px_g", 1.0)
plotPxi_xj(dims, A2, 333, "Px_h", 1.0)
plotGridPx_ag(dims, Px_ag, 444, "Px_ag", 1.0)
Px_ah = broadcast(*, Pxh_a, Px_h)
A3 = permutedims(Px_ah, (4, 2, 3, 1, 5, 6, 7))
plotGridPx_ag(dims, A3, 444, "Px_ah", 1.0)
# Pgxi_xj = sum(broadcast(*, PgxCaC_xN, PxChP_aC), dims=3)
# for hi in dimH
# println("hi=$(hi)")
# display((Pgxi_xj[1, :, 1, hi, :, 1, 1]))
# println()
# display((Pgxi_xj[1, :, 1, hi, :, 1, 1]^8))
# println()
# display((Pgxi_xj[1, :, 1, hi, :, 1, 1]^9))
# println()
# display((Pgxi_xj[1, :, 1, hi, :, 1, 1]^10))
# println()
# end
exit(1)
end
function mainEstimatePxa_g()
dimX1 = 3
dimX2 = 3
dimX = dimX1*dimX2
dimA = 5
dimG = dimX
dimH = dimX
dims = (dimX1, dimX2, dimA, dimG, dimH)
C = CreateWalls(dims, "B")
G = GenerateGoalSet(dims, "fullX", C)
actionProb = 1.0
Pgxiai_xj, Rgxiaixj = InitPxiaig_xj(dims, G, C, actionProb)
Ph_g = zeros(Float64, dimG, 1, 1, dimH, 1, 1, 1)
Ph_g[:, 1, 1, :, 1, 1, 1] = Matrix{Float64}(I, dimG, dimH)
QgxChC_hN = InitAtBetaInfinityQgxChC_hN(dims)
Pxh_g = InitPxh_gAtBetaInfinity(dims)
IghC_hN = zeros(Float64, (dimG, 1, 1, dimH, 1, 1, dimH))
beta = 1.0
R = broadcast(+, beta*Rgxiaixj, IghC_hN)
Vgxh, PxChP_aC, Pxh_g = BellmanStateDependent(dims, Pgxiai_xj, R, QgxChC_hN, Pxh_g)
Vxh = Expectation(Vgxh, Ph_g, [1])
stepSize = AvrgStepSize(dims, Vxh)
printGridVxh(dims, Vxh, 100, "StateIndpnd", 1.0)
Pgxi_ai = permutedims(PxChP_aC, (4, 2, 3, 1, 5, 6, 7))
Pgsa = EstimatePxa_g(dims, Pgxiai_xj, Pgxi_ai)
Pxa_g = broadcast(/, Pgsa, sum(Pgsa, dims=1))
Psg = Marginal(Pgsa, (3,))
Ps_g = broadcast(/, Psg, sum(Psg, dims=2))
# println(sum(Pxa_g, dims=1))
# exit(1)
aStr = ActionStrings(dimA)
# println(size(Ps_g))
# println(size(Pxa_g))
#
# display(Pgsa)
# exit(1)
for xi = 1:dimX
println("P(g | xi=$(xi)):")
display(reshape(Ps_g[:, xi, 1, 1, 1, 1, 1], (dimX1, dimX2)))
println()
end
for xi = 1:dimX, ai = 1:dimA
println("xi=$(xi), $(aStr[ai])")
display(reshape(Pxa_g[:, xi, ai, 1, 1, 1, 1], (dimX1, dimX2)))
println()
end
end
function mainBellmanIB()
dimX1 = 3
dimX2 = 3
dimX = dimX1*dimX2
dimA = 5
dimG = dimX
dimH = dimX
dims = (dimX1, dimX2, dimA, dimG, dimH)
C = CreateWalls(dims, "B")
G = GenerateGoalSet(dims, "fullX", C)
actionProb = 0.8
Pgxiai_xj, Rgxiaixj = InitPxiaig_xj(dims, G, C, actionProb)
Ph_g = zeros(Float64, dimG, 1, 1, dimH, 1, 1, 1)
Ph_g[:, 1, 1, :, 1, 1, 1] = Matrix{Float64}(I, dimG, dimH)
QgxChC_hN = InitAtBetaInfinityQgxChC_hN(dims)
Pxh_g = InitPxh_gAtBetaInfinity(dims)
IghC_hN = zeros(Float64, (dimG, 1, 1, dimH, 1, 1, dimH))
beta = 1.0
R = broadcast(+, beta*Rgxiaixj, IghC_hN)
Vgxh, PxChP_aC, Pxh_g = BellmanStateDependent(dims, Pgxiai_xj, R, QgxChC_hN, Pxh_g)
printBellmanSolution = false
if printBellmanSolution