使用 Flux.jl 更新函数的参数答案

【问题标题】：Updating parameters of a function with Flux.jl使用 Flux.jl 更新函数的参数
【发布时间】：2019-01-22 21:14:27
【问题描述】：

我在玩flux.jl，但在更新自定义函数的参数时遇到问题。

函数定义如下objective:

    using Distributions
    using Flux.Tracker: gradient, param, Params
    using Flux.Optimise: Descent, ADAM, update!

    D = 2 
    num_samples = 100

    function log_density(params)
        mu, log_sigma = params
        d1 = Normal(0, 1.35)
        d2 = Normal(0, exp(log_sigma))
        d1_density = logpdf(d1, log_sigma)
        d2_density = logpdf(d2, mu)
        return d1_density + d2_density
    end


    function J(log_std)
        H = 0.5 * D * (1.0 + log(2 * pi)) + sum(log_std)
        return H
    end

    function objective(mu, log_std; D=2)
        samples = rand(Normal(), num_samples, D) .* sqrt.(log_std) .+ mu
        log_px = mapslices(log_density, samples; dims=2)
        elbo = J(log_std) + mean(log_px)
        return -elbo
    end

我尝试按如下方式进行一次更新：


    mu = param(reshape([-1, -1], 1, :))
    sigma = param(reshape([5, 5], 1, :))

    grads = gradient(() -> objective(mu, sigma), Params([mu, sigma]))

    opt = Descent(0.001)
    for p in (mu, sigma)
        update!(opt, p, grads[p])
    end

产生错误：

ERROR: Can't differentiate `setindex!`
Stacktrace:
 [1] error(::String) at ./error.jl:33
 [2] setindex!(::TrackedArray{…,Array{Float64,2}}, ::Flux.Tracker.TrackedReal{Float64}, ::CartesianIndex{2}) at /Users/vasya/.julia/packages/Flux/T3PhK/src/tracker/lib/array.jl:63
 [3] macro expansion at ./broadcast.jl:838 [inlined]
 [4] macro expansion at ./simdloop.jl:73 [inlined]
 [5] copyto! at ./broadcast.jl:837 [inlined]
 [6] copyto! at ./broadcast.jl:792 [inlined]
 [7] materialize! at ./broadcast.jl:751 [inlined]
 [8] update!(::Descent, ::TrackedArray{…,Array{Float64,2}}, ::TrackedArray{…,Array{Float64,2}}) at /Users/vasya/.julia/packages/Flux/T3PhK/src/optimise/optimisers.jl:22
 [9] top-level scope at ./REPL[23]:2 [inlined]
 [10] top-level scope at ./none:0

我也尝试将grads[p] 替换为grads[p].data。这不会产生错误，但不会更新参数！

环境详情：
- 朱莉娅版本 1.0.2
- 助焊剂 v0.7.0
- 发行版 v0.16.4

【问题讨论】：

标签： machine-learning optimization julia flux-machine-learning

【解决方案1】：

通过 Slack 的讨论澄清了 update! 函数的正确用法。下面的代码使模块引用显式，并生成更新的参数（for Flux v0.7.0）：

    using Distributions
    using Flux

    D = 2 
    num_samples = 100

    function log_density(params)
        mu, log_sigma = params
        d1 = Normal(0, 1.35)
        d2 = Normal(0, exp(log_sigma))
        d1_density = logpdf(d1, log_sigma)
        d2_density = logpdf(d2, mu)
        return d1_density + d2_density
    end

    function J(log_std)
        H = 0.5 * D * (1.0 + log(2 * pi)) + sum(log_std)
        return H
    end

    function objective(mu, log_std; D=2)
        samples = rand(Normal(), num_samples, D) .* sqrt.(log_std) .+ mu
        log_px = mapslices(log_density, samples; dims=2)
        elbo = J(log_std) + mean(log_px)
        return -elbo
    end

    mu = Flux.Tracker.param(reshape([-1, -1], 1, :))
    sigma = Flux.Tracker.param(reshape([5, 5], 1, :))

    grads = Flux.Tracker.gradient(() -> objective(mu, sigma), Flux.Tracker.Params([mu, sigma]))

    println(mu, sigma)

    opt = Flux.Optimise.Descent(0.01)
    for p in (mu, sigma)
        Flux.Tracker.update!(p, Flux.Optimise.update!(opt, p, Flux.data(grads[p])))
    end

    println(mu, sigma)

打印出来：

    [-1.0 -1.0] (tracked)[5.0 5.0] (tracked)
    [-198.742 -459.423] (tracked)[31.0583 225.657] (tracked)

【讨论】：