Question about Chance-constrained Active Inference example

[Flawless1202]

When I learn the Chance-constrained Active Inference example, I try to enlarge the wind as this:

wind(t::Int64) = -5.0*(60 <= t < 100) # Time-dependent wind profile

And I set the hyper parameters as follows:

lo = 5.0 # Chance region lower bound
hi = 10.0 # Chance region upper bound

Then the result is

In which the Elevation is not satisfy the constraint $[5.0, 10.0]$. What is the reason behind this result? How to make the result satisfy the constraint?

[Flawless1202]

I think the result may be the definition of transition model in regulator_model, i.e. x[k] ~ x_k_last + u[k], missing the influence of wind, so I modify the model as follows:

@model function regulator_model(T, m_u, v_u, x_t, wind_t, lo, hi, epsilon, atol)
    
    # Loop over horizon
    x_k_last = x_t
    for k = 1:T
        u[k] ~ NormalMeanVariance(m_u[k], v_u[k]) # Control prior
        x[k] ~ x_k_last + u[k] + wind_t # Transition model
        x[k] ~ ChanceConstraint(lo, hi, epsilon, atol) where { # Simultaneous constraint on state
            dependencies = RequireMessageFunctionalDependencies(out = NormalWeightedMeanPrecision(0.0, 0.01))} # Predefine inbound message to break circular dependency
        x_k_last = x[k]
    end
 
end

At the same time, I modify the compute function in initializeAgent:

    function compute(x_t::Float64, wind_t::Float64)
        model_t = regulator_model(;T=T, lo=lo, hi=hi, epsilon=epsilon, atol=atol)
        data_t = (m_u = m_u, v_u = v_u, x_t = x_t, wind_t = wind_t)

        result = infer(
            model = model_t,
            data = data_t,
            iterations = n_its)

        pol = mode.(result.posteriors[:u][1])
        
        return pol

What's more, I modify the control prior precision to 0.1:

lambda = 0.1 # Control prior precision

Now I think I have got a better result:

[ThijsvdLaar]

Thanks for your question. The wind illustrates a misalignment between the generative process (GP, the environment) and the generative model (GM, the agent beliefs). This example simulates an event (a gust of wind) that is unexpected by the agent, and therefore the agent may not be able to correct for it.

When the agent models the event explicitly, then GP and GM will align again (the event is expected), and corrections may be more effective. (Although I suspect your timing is off by one). Note that, even if the GP and GM align, there is per definition a non-zero probability that the chance constraint is violated.

[Flawless1202]

Thanks a lot!