Benchmark Models¶

How do you know a numerical solver returned the right answer? One way is to run it on a problem whose answer you already know. The skagent.models.benchmarks registry collects such problems: benchmark dynamic programming models, most of them with an optimal policy known in closed form. Each entry pairs a working DBlock with that policy. A few models, such as the buffer-stock problem, carry no closed form and serve instead for numerical validation against known limiting behavior. The registry has three uses for anyone building or testing solvers with scikit-agent.

Validation. To check a solver, compare its output against the closed-form policy on a set of test states. validate_analytical_solution() does exactly this: it evaluates the analytical policy on a standard grid, checks feasibility together with any model-specific identities, and returns a "PASSED" or "FAILED" status with diagnostics on the consumption range.

Regression testing. The same comparison runs in the test suite, so a regression that breaks an analytical identity surfaces early.

Pedagogy. The closed forms retrace the development of dynamic optimization theory in roughly the order it was discovered. The runnable Benchmark Consumption Models walks through the economics model by model, with equations and plots; this page stays focused on what the registry contains and how to call it.

Roster¶

The models below split into two groups. Seven ship in the BENCHMARK_MODELS registry, each reachable through list_benchmark_models() by the short registry key shown in the table. Those keys, such as D-1 or U-2, are internal identifiers rather than names anyone uses at the whiteboard, so the table leads with each model’s descriptive name. The remaining four models ship as standalone modules.

Registry models (fetch with get_benchmark_model() and the registry key):

Model	Key	Utility	Income	Closed form
Finite-horizon log utility	`D-1`	Log	Wealth only	Remaining-horizon MPC
Infinite-horizon perfect foresight	`D-2`	CRRA	Constant \(y\)	Linear in total wealth
Blanchard mortality	`D-3`	CRRA	Constant \(y\)	Same with \(s\beta\)
Hall random walk	`U-1`	Quadratic	Stochastic[1]	PIH annuity rule
Log utility with permanent shocks (normalized)	`U-2`	Log	Geometric random walk	\(c = (1-\beta)(m + h)\)
Buffer stock	`U-3`	CRRA	Geometric random walk	None (numerical only)
Constrained perfect foresight	`D-4`	CRRA	Constant \(y\), binding constraint	None (VFI reference policy)

Standalone modules (not in BENCHMARK_MODELS):

Module	Problem	Closed form
`fisher`	Fisher two-period	CRRA Euler + budget
`perfect_foresight`	PF with mortality and growth	Linear in total wealth
`perfect_foresight_normalized`	Same, normalized variables	Linear in normalized wealth
`resource_extraction`	Reed (1979) renewable resource	Constant escapement

Using the Registry¶

Look up each entry by its registry key. The typical workflow is to fetch a model, evaluate its analytical policy, and validate a candidate solver against it:

from skagent.models.benchmarks import (
    list_benchmark_models,
    get_benchmark_model,
    get_benchmark_calibration,
    get_analytical_policy,
    has_analytical_policy,
    validate_analytical_solution,
)

list_benchmark_models()
# {'D-1': '...', 'D-2': '...', 'D-3': '...',
#  'U-1': '...', 'U-2': '...', 'U-3': '...', 'D-4': '...'}

block = get_benchmark_model("D-2")
calibration = get_benchmark_calibration("D-2")

# Closed-form entries expose an analytical policy; query before fetching.
if has_analytical_policy("D-2"):
    policy = get_analytical_policy("D-2")

result = validate_analytical_solution("D-2", tolerance=1e-8)
result["validation"]  # 'PASSED'

Models without a closed form report False from has_analytical_policy(), and requesting their analytical policy raises ValueError. The constrained D-4 model instead provides a value-function-iteration reference policy through get_reference_policy(). For the rest, solve numerically with EulerEquationLoss and maliar_training_loop(); see Algorithms Guide.

Benchmark Models¶

Roster¶

Using the Registry¶

See Also¶