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ShuvomoyShuvomoy
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‎examples/composite_convex_minimization/three_operator_splitting.jl‎

Lines changed: 60 additions & 60 deletions
Original file line numberDiff line numberDiff line change
@@ -1,60 +1,60 @@
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using PEPit, OrderedCollections
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function wc_three_operator_splitting(mu1, L1, L3, alpha, theta, n; verbose=true)
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problem = PEP()
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f1 = declare_function!(problem, SmoothStronglyConvexFunction, OrderedDict("mu" => mu1, "L" => L1); reuse_gradient=true)
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f2 = declare_function!(problem, ConvexFunction, OrderedDict(); reuse_gradient=false)
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f3 = declare_function!(problem, SmoothConvexFunction, OrderedDict("L" => L3); reuse_gradient=true)
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w0 = set_initial_point!(problem)
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w0p = set_initial_point!(problem)
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set_initial_condition!(problem, (w0 - w0p)^2 <= 1)
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w = w0
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for _ in 1:n
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x, _, _ = proximal_step!(w, f2, alpha)
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gx, _ = oracle!(f3, x)
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y, _, _ = proximal_step!(2 * x - w - alpha * gx, f1, alpha)
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w = w + theta * (y - x)
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end
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wp = w0p
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for _ in 1:n
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xp, _, _ = proximal_step!(wp, f2, alpha)
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gxp, _ = oracle!(f3, xp)
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yp, _, _ = proximal_step!(2 * xp - wp - alpha * gxp, f1, alpha)
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wp = wp + theta * (yp - xp)
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end
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set_performance_metric!(problem, (w - wp)^2)
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pepit_tau = solve!(problem; verbose=verbose)
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theoretical_tau = nothing
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if verbose
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println("*** Example file: worst-case performance of the Three Operator Splitting in distance ***")
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println("\tPEPit guarantee:\t ||w^1_n - w^0_n||^2 <= $(round(pepit_tau, digits=6)) ||w^1_0 - w^0_0||^2")
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end
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return pepit_tau, theoretical_tau
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end
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L3 = 1.0
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alpha = 1 / L3
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pepit_tau, theoretical_tau = wc_three_operator_splitting(0.1, 10.0, L3, alpha, 1.0, 4; verbose=true)
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using PEPit, OrderedCollections
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function wc_three_operator_splitting(mu1, L1, L3, alpha, theta, n; verbose=true)
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problem = PEP()
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f1 = declare_function!(problem, SmoothStronglyConvexFunction, OrderedDict("mu" => mu1, "L" => L1); reuse_gradient=true)
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f2 = declare_function!(problem, ConvexFunction, OrderedDict(); reuse_gradient=false)
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f3 = declare_function!(problem, SmoothConvexFunction, OrderedDict("L" => L3); reuse_gradient=true)
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w0 = set_initial_point!(problem)
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w0p = set_initial_point!(problem)
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set_initial_condition!(problem, (w0 - w0p)^2 <= 1)
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w = w0
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for _ in 1:n
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x, _, _ = proximal_step!(w, f2, alpha)
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gx, _ = oracle!(f3, x)
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y, _, _ = proximal_step!(2 * x - w - alpha * gx, f1, alpha)
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w = w + theta * (y - x)
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end
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wp = w0p
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for _ in 1:n
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xp, _, _ = proximal_step!(wp, f2, alpha)
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gxp, _ = oracle!(f3, xp)
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yp, _, _ = proximal_step!(2 * xp - wp - alpha * gxp, f1, alpha)
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wp = wp + theta * (yp - xp)
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end
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set_performance_metric!(problem, (w - wp)^2)
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pepit_tau = solve!(problem; verbose=verbose)
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theoretical_tau = nothing
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if verbose
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println("*** Example file: worst-case performance of the Three Operator Splitting in distance ***")
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println("\tPEPit guarantee:\t ||w^1_n - w^0_n||^2 <= $(round(pepit_tau, digits=6)) ||w^1_0 - w^0_0||^2")
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end
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return pepit_tau, theoretical_tau
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end
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L3 = 1.0
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alpha = 1 / L3
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pepit_tau, theoretical_tau = wc_three_operator_splitting(0.1, 10.0, L3, alpha, 1.0, 4; verbose=true)
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‎examples/inexact_proximal_methods/accelerated_inexact_forward_backward.jl‎

Lines changed: 65 additions & 65 deletions
Original file line numberDiff line numberDiff line change
@@ -1,65 +1,65 @@
1-
using PEPit, OrderedCollections
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function wc_accelerated_inexact_forward_backward(L, zeta, n; verbose=true)
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problem = PEP()
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f = declare_function!(problem, SmoothConvexFunction, OrderedDict("L" => L); reuse_gradient=true)
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h = declare_function!(problem, ConvexFunction, OrderedDict(); reuse_gradient=false)
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F = f + h
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xs = stationary_point!(F)
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Fs = value!(F, xs)
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x0 = set_initial_point!(problem)
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set_initial_condition!(problem, (x0 - xs)^2 <= 1)
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gamma = 1 / L
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eta = (1 - zeta^2) * gamma
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A = 0.0
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x = x0
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z = x0
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hx = nothing
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for _ in 1:n
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A_next = A + (eta + sqrt(eta^2 + 4 * eta * A)) / 2
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y = x + (1 - A / A_next) * (z - x)
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gy = gradient!(f, y)
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x, _, hx, _, vx, _, eps_var = inexact_proximal_step!(y - gamma * gy, h, gamma; opt="PD_gapI")
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add_constraint!(h, eps_var <= (zeta * gamma)^2 / 2 * (vx + gy)^2)
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z = z - (A_next - A) * (vx + gy)
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A = A_next
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end
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set_performance_metric!(problem, value!(f, x) + hx - Fs)
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pepit_tau = solve!(problem; verbose=verbose)
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theoretical_tau = 2 * L / (1 - zeta^2) / n^2
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if verbose
54-
println("*** Example file: worst-case performance of an inexact accelerated forward backward method ***")
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println("\tPEPit guarantee:\t F(x_n)-F_* <= $(round(pepit_tau, digits=7)) ||x_0 - x_*||^2")
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println("\tTheoretical guarantee:\t F(x_n)-F_* <= $(round(theoretical_tau, digits=7)) ||x_0 - x_*||^2")
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end
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return pepit_tau, theoretical_tau
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end
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pepit_tau, theoretical_tau = wc_accelerated_inexact_forward_backward(1.3, 0.45, 11; verbose=true)
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using PEPit, OrderedCollections
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function wc_accelerated_inexact_forward_backward(L, zeta, n; verbose=true)
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problem = PEP()
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f = declare_function!(problem, SmoothConvexFunction, OrderedDict("L" => L); reuse_gradient=true)
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h = declare_function!(problem, ConvexFunction, OrderedDict(); reuse_gradient=false)
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F = f + h
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xs = stationary_point!(F)
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Fs = value!(F, xs)
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x0 = set_initial_point!(problem)
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set_initial_condition!(problem, (x0 - xs)^2 <= 1)
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gamma = 1 / L
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eta = (1 - zeta^2) * gamma
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A = 0.0
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x = x0
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z = x0
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hx = nothing
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for _ in 1:n
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A_next = A + (eta + sqrt(eta^2 + 4 * eta * A)) / 2
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y = x + (1 - A / A_next) * (z - x)
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gy = gradient!(f, y)
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x, _, hx, _, vx, _, eps_var = inexact_proximal_step!(y - gamma * gy, h, gamma; opt="PD_gapI")
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add_constraint!(h, eps_var <= (zeta * gamma)^2 / 2 * (vx + gy)^2)
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z = z - (A_next - A) * (vx + gy)
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A = A_next
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end
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set_performance_metric!(problem, value!(f, x) + hx - Fs)
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pepit_tau = solve!(problem; verbose=verbose)
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theoretical_tau = 2 * L / (1 - zeta^2) / n^2
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if verbose
54+
println("*** Example file: worst-case performance of an inexact accelerated forward backward method ***")
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println("\tPEPit guarantee:\t F(x_n)-F_* <= $(round(pepit_tau, digits=7)) ||x_0 - x_*||^2")
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println("\tTheoretical guarantee:\t F(x_n)-F_* <= $(round(theoretical_tau, digits=7)) ||x_0 - x_*||^2")
57+
end
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return pepit_tau, theoretical_tau
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end
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pepit_tau, theoretical_tau = wc_accelerated_inexact_forward_backward(1.3, 0.45, 11; verbose=true)
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‎examples/online_learning/online_gradient_descent.jl‎

Lines changed: 50 additions & 50 deletions
Original file line numberDiff line numberDiff line change
@@ -1,50 +1,50 @@
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using PEPit, OrderedCollections
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function wc_online_gradient_descent(M::Real, D::Real, n::Int; verbose = true)
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problem = PEP()
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gamma = D / (M * sqrt(n))
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fis = [declare_function!(problem, ConvexLipschitzFunction, OrderedDict("M" => M)) for _ in 1:n]
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h = declare_function!(problem, ConvexIndicatorFunction, OrderedDict("D" => D))
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F = sum(fis)
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x_ref = set_initial_point!(problem)
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x_ref, _, _ = proximal_step!(x_ref, h, 1)
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_, F_ref = oracle!(F, x_ref)
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x = set_initial_point!(problem)
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x, _, _ = proximal_step!(x, h, 1)
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f_saved = Vector{Expression}(undef, n)
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for i in 1:n
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g_i, f_i = oracle!(fis[i], x)
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f_saved[i] = f_i
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x, _, _ = proximal_step!(x - gamma * g_i, h, gamma)
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end
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set_performance_metric!(problem, sum(f_saved) - F_ref)
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pepit_tau = solve!(problem; verbose=verbose)
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theoretical_tau = M * D * sqrt(n)
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if verbose != -1
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println("*** Example file: worst-case regret of online gradient descent for fixed step-sizes ***")
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println("\tPEPit guarantee:\t R_n <= $(round(pepit_tau, digits=6))")
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println("\tTheoretical guarantee:\t R_n <= $(round(theoretical_tau, digits=6))")
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end
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return pepit_tau, theoretical_tau
42-
end
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M, D, n = 1.0, 0.5, 2
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pepit_tau, theoretical_tau = wc_online_gradient_descent(M, D, n; verbose=true)
49-
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using PEPit, OrderedCollections
2+
3+
function wc_online_gradient_descent(M::Real, D::Real, n::Int; verbose = true)
4+
5+
problem = PEP()
6+
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gamma = D / (M * sqrt(n))
8+
9+
fis = [declare_function!(problem, ConvexLipschitzFunction, OrderedDict("M" => M)) for _ in 1:n]
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11+
h = declare_function!(problem, ConvexIndicatorFunction, OrderedDict("D" => D))
12+
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F = sum(fis)
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x_ref = set_initial_point!(problem)
16+
x_ref, _, _ = proximal_step!(x_ref, h, 1)
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_, F_ref = oracle!(F, x_ref)
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x = set_initial_point!(problem)
20+
x, _, _ = proximal_step!(x, h, 1)
21+
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f_saved = Vector{Expression}(undef, n)
23+
for i in 1:n
24+
g_i, f_i = oracle!(fis[i], x)
25+
f_saved[i] = f_i
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x, _, _ = proximal_step!(x - gamma * g_i, h, gamma)
27+
end
28+
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set_performance_metric!(problem, sum(f_saved) - F_ref)
30+
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pepit_tau = solve!(problem; verbose=verbose)
32+
33+
theoretical_tau = M * D * sqrt(n)
34+
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if verbose != -1
36+
println("*** Example file: worst-case regret of online gradient descent for fixed step-sizes ***")
37+
println("\tPEPit guarantee:\t R_n <= $(round(pepit_tau, digits=6))")
38+
println("\tTheoretical guarantee:\t R_n <= $(round(theoretical_tau, digits=6))")
39+
end
40+
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return pepit_tau, theoretical_tau
42+
end
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45+
46+
M, D, n = 1.0, 0.5, 2
47+
48+
pepit_tau, theoretical_tau = wc_online_gradient_descent(M, D, n; verbose=true)
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