finite_iteration.md

Finite iteration

By default, dolo looks for solutions, where the time horizon of the optimizing agent is infinite. But it is possible to use it to solve finite horizon problems (only with time-iteration, so far). It requires to do two things:

• Construct a final decision rule to be used for the last period. This can be done with the CustomDR function. ResultingsIt is passed as an initial guess to time_iteration.
• Record the decision rules, obtained in each iteration.

!!! example

```
from dolo import yaml_import, time_iteration, tabulate
from dolo.numeric.decision_rule import CustomDR

model = yaml_import("examples/models/consumption_savings.yaml")

last_dr = CustomDR(
    {"c": "w"},
    model=model
)

T = 10

result = time_iteration(model, 
    dr0=last_dr, 
    maxit=T,
    trace=True # keeps decision rules, from all iterations
)

# example to plot all decision rules
from matplotlib import pyplot as plt
for i,tr in enumerate(result.trace):
    dr = tr['dr']
    tab = tabulate(model, dr, 'w')
    plt.plot(tab['w'], tab['c'], label=f"t={T-i}")
plt.legend(loc='upper left')
plt.show()
```

In the example above, {"c": "w"} stands for a functional identity, i.e. c(y,w) = w. It is a completely different meaning from `c: w` in the calibration section which means that the steady-state value of `c` is initialized to the steady-state value of `w`.

!!!alert

The notation in CustomDR is not yet consistent, with the new timing conventions. In the example above it should be `c[t] = w[t]`. A commission, will be created to examine the creation of an issue, meant to coordinate the implementation of a solution.